Direct measurement of galactic cosmic ray fluxes with the orbital detector AMS-02

U S B

F S M F N

D R F, XV C

PhD Thesis

Direct measurement of galactic cosmicray fluxes with the orbital detector

AMS-02

D C

Advisor:

Chiar.mo Prof.

A C

PhD Coordinator:Chiar.mo Prof.

G V

Bologna, Italy, March 10, 2003

Introduction

The Alpha Magnetic Spectrometer (AMS) experiment is a high energy particledetector developed to measure cosmic ray fluxes outside the Earth atmosphere.The first version of the detector, called AMS-01, successfully flew aboard of theshuttle Discovery on June 2–12, 1998 (NASA STS-91 mission), collecting overone hundred million events. The next version of the detector, called AMS-02, willbe installed on the International Space Station (ISS) Alpha at the end of 2005,where it will operate for at least three years.

Cosmic rays (CR) are charged (and neutral) particles coming from the outerspace that span a very wide energy range (from few MeV up to 1020 eV), and arebelieved to be accelerated by supernova explosions in our Galaxy for energy be-low 1015 eV per nucleon. For higher energies their acceleration sites may be othergalactic objects (like pulsars), whereas for the highest energies an extragalacticorigin seems to be necessary to explain the uniform distribution of the CR incom-ing direction. Their global spectrum is described in chapter 1, where the modelof charged particle acceleration by supersonic shock waves is sketched. In addi-tion, this chapter describes the particles diffusion inside the Galaxy and inside theeliosphere, where they may finally reach the Earth.

The cosmic rays composition is very rich: in addition to protons, that consti-tute about 90% of the total number of particles, He nuclei (about 10%), electrons(about 1%), positrons and all other stable and instable nuclei are present, withthe exception of the isotopes with a very short life time. Chapter 2 shows thatthe relative abundances with respect to solar system and galactic averages may beexplained by the different volatility of the elements, being favored the accelera-tion of less volatile elements. In addition, this chapter reviews the CR electronand positron Physics, emphasizing the local nature of the direct measurementsin contrast with proton measurements, that are more representative of a galacticaverage.

The main motivation to support the AMS experiment is the search of primary

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antimatter in cosmic rays. The experimental tests carried on with accelerators af-firm that every time we create new fermions we must create the same amount ofanti-fermions (more precisely, each reaction must conserve separately the bary-onic and leptonic numbers), as reviewed in chapter 3. On the other hand, astro-nomic measurements show that we live in a homogeneus domain composed en-tirely of matter, at least up to the galaxy clusters scale, immersed in a thermal bathof photons (the cosmic microwave background). These photons are consideredthe relics of the matter-antimatter annihilation epoch, where the radiation decou-pled from the matter. An important question is whether the cosmic baryogenesiswas matter-antimatter symmetric, or some form of symmetry breaking happened,violating the laws of the “standard model”.

In addition to large homogeneus antimatter domains, that could have beencreated as fluctuations over a globally symmetric scenario in the same way as ourmatter domain, primordial antimatter could have survived in the form of globularclusters of antistars, that may even be present in our Galaxy. If the homogeneusdomains are not too distant from the Milky Way, or if antistars exist in the Galaxy,we could detect antinuclei in the solar system (the probability to create them dur-ing CR collision with the interstellar medium is negligible). The most probableantinucleus is antihelium, but also anticarbon, antinitrogen or antioxygen couldbe produced by antistars: their detection would be considered the proof that anti-matter domains do exist indeed.

Antiprotons and positrons are commonly created during the cosmic ray inter-actions with the interstellar medium, hence they are not good candidates for thesearch of primordial antimatter. Howewer, their purely secondary spectrum can beaccurately predicted, and experimental data can be checked to see if exotic sourcesexist. For example, proton-antiproton and electron-positron pairs can be createdby the annihilation of the dark matter candidates, like supersymmetric particles.

The dark matter is not directly visible but has important gravitational effects:the energy density of the universe is due for 70% to the vacuum constant and for30% to the matter, while the radiation gives a negligible contribution. On the otherhand, the baryonic fraction of the matter component in the universe can not behigher than few percent, in order to be consistent with the primordial nucleosyn-thesis model. Hence, the majority of the matter component is due to non baryonic(i.e. not strongly interacting) dark (i.e. not charged) particles. Collider data ex-clude candidates with mass lower than roughly hundred GeV/c2, hence their an-nihilations may produce a “bump” in the spectrum of antiprotons and positrons athigh energies, where no data are presently available. The AMS-02 detector would

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be able to make a precise measurement up to 1–2 TeV, thus having the potentialto discover the first signatures of new particles.

Chapter 4 illustrates the working principles of AMS and describes the AMS-01 and AMS-02 detectors, built by an international Collaboration where the Italiancontribution is very important: the time of flight (TOF) system is completely de-veloped and built in the INFN laboratories in Bologna, that is also partecipatingin the proximity focusing ring imaging Cerenkov (RICH) detector; the tracker ismainly developed by the INFN Perugia group; the electromagnetic calorimeter(ECAL) is mainly developed by the Pisa and Siena INFN groups; the Roma 1INFN people partecipate in the development of the transition radiation detector(TRD) electronics.

I have been working on AMS in the Bologna group since 1996, when I startedfollowing the development and construction of the AMS-01 TOF system. Duringthe last three years I worked on the AMS-02 TOF and RICH systems, and on theanalysis of AMS-01 data. In particular, I collaborated with the mechanical engi-neers for the design and positioning of the light guides and for the choice of theshape of the scintillator counters of TOF, following the constraints imposed by thehigh magnetic field in the photomultipliers zone, by the geometrical acceptanceand the weight budget, as described in chapter 5.

In parallel, I worked on the conical mirror of the RICH subdetector, startingwith samples of different types and finally studying the reflectivity of the mandrelthat is used to build the mirror. In addition I partecipated to the calibration ofthe multi-pixel phototubes used by the RICH, and worked on the problem of themagnetic shielding of these photomultipliers, as described in chapter 6.

Recently (October 2002) I organized the ion beam test at CERN SPS for theTOF group. The test was requested by the RICH Collaboration, and the RICHprototype was the main experiment. Howewer, “parasitic” detectors could be ac-comodated in the same area, allowing for a combined test of a tracker prototypeand a couple of TOF counters. Preliminar results of this ion beam test are pre-sented in chapter 7.

Presently I organize the work of the development of the S-crate electronics,that contains the front-end boards of TOF and ACC (the anticoincidence system),the high voltage power supplies, and the slow control boards.

Bologna, March 2003 Diego Casadei

v

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vi

Contents

Introduction iii

1 Cosmic rays below 1 TeV 11.1 High energy particles from space . . . . . . . . . . . . . . . . . . 11.2 Cosmic ray acceleration . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Shock waves . . . . . . . . . . . . . . . . . . . . . . . . 91.2.2 Particle acceleration by shock waves . . . . . . . . . . . . 12

1.3 Interstellar propagation . . . . . . . . . . . . . . . . . . . . . . . 151.4 Propagation inside the eliosphere . . . . . . . . . . . . . . . . . . 17

1.4.1 Solar modulation . . . . . . . . . . . . . . . . . . . . . . 181.4.2 Geomagnetic cutoff . . . . . . . . . . . . . . . . . . . . . 19

2 Cosmic ray composition 232.1 Cosmic ray ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.1.1 CR source composition . . . . . . . . . . . . . . . . . . . 242.1.2 Propagation models . . . . . . . . . . . . . . . . . . . . . 262.1.3 Measurements of CR ions spectra . . . . . . . . . . . . . 28

2.2 Cosmic ray electrons . . . . . . . . . . . . . . . . . . . . . . . . 312.2.1 Energy losses . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Cosmic antimatter 373.1 Antimatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.1 CPT theorem . . . . . . . . . . . . . . . . . . . . . . . . 383.1.2 Anti-systems . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 Cosmic antimatter . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.1 Can total annihilation be avoided? . . . . . . . . . . . . . 413.2.2 Antimatter domains . . . . . . . . . . . . . . . . . . . . . 42

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CONTENTS

3.3 Can we detect cosmic antimatter? . . . . . . . . . . . . . . . . . 443.3.1 Indirect ways . . . . . . . . . . . . . . . . . . . . . . . . 443.3.2 Direct detection . . . . . . . . . . . . . . . . . . . . . . . 49

3.4 Antimatter cosmic rays . . . . . . . . . . . . . . . . . . . . . . . 503.4.1 Positrons and antiprotons . . . . . . . . . . . . . . . . . . 503.4.2 Antihelium and antinuclei . . . . . . . . . . . . . . . . . 51

4 The AMS experiment 554.1 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . 55

4.1.1 Rigidity measurement . . . . . . . . . . . . . . . . . . . 564.1.2 Charge measurement . . . . . . . . . . . . . . . . . . . . 574.1.3 Velocity measurement . . . . . . . . . . . . . . . . . . . 58

4.2 The AMS-01 detector . . . . . . . . . . . . . . . . . . . . . . . . 594.2.1 The magnet . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.2 The tracking system . . . . . . . . . . . . . . . . . . . . 624.2.3 The time of flight system . . . . . . . . . . . . . . . . . . 644.2.4 The anticoincidence system . . . . . . . . . . . . . . . . 674.2.5 The threshold Cerenkov counter . . . . . . . . . . . . . . 694.2.6 The AMS-01 trigger . . . . . . . . . . . . . . . . . . . . 71

4.3 Results of the STS-91 mission . . . . . . . . . . . . . . . . . . . 734.3.1 Primary CR spectra . . . . . . . . . . . . . . . . . . . . . 744.3.2 Secondary spectra . . . . . . . . . . . . . . . . . . . . . 79

4.4 The AMS-02 detector . . . . . . . . . . . . . . . . . . . . . . . . 854.4.1 The magnet . . . . . . . . . . . . . . . . . . . . . . . . . 864.4.2 The tracking system . . . . . . . . . . . . . . . . . . . . 884.4.3 The time of flight system . . . . . . . . . . . . . . . . . . 884.4.4 The anticoincidence system . . . . . . . . . . . . . . . . 894.4.5 The RICH detector . . . . . . . . . . . . . . . . . . . . . 904.4.6 The trasition radiation detector . . . . . . . . . . . . . . . 914.4.7 The electromagnetic calorimeter . . . . . . . . . . . . . . 92

5 The AMS-02 TOF system 955.1 The time of flight system of AMS-02 . . . . . . . . . . . . . . . . 965.2 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.3 Mechanical design . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.3.1 The TOF planes . . . . . . . . . . . . . . . . . . . . . . . 1035.3.2 The TOF counters . . . . . . . . . . . . . . . . . . . . . 103

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5.4 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.4.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . 1075.4.2 Slow control . . . . . . . . . . . . . . . . . . . . . . . . 1085.4.3 Powering . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.5 The beam test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.5.1 Selection cuts . . . . . . . . . . . . . . . . . . . . . . . . 1105.5.2 Charge peaks . . . . . . . . . . . . . . . . . . . . . . . . 1185.5.3 Time resolution . . . . . . . . . . . . . . . . . . . . . . . 124

6 The AMS-02 RICH subdetector 1296.1 The Cerenkov emission . . . . . . . . . . . . . . . . . . . . . . . 129

6.1.1 Particle energy loss in the radiator . . . . . . . . . . . . . 1306.1.2 Cerenkov radiation . . . . . . . . . . . . . . . . . . . . . 133

6.2 The RICH design . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.2.1 Large acceptance proximity focusing RICH detector . . . 1356.2.2 Radiator . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.2.3 Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.2.4 Photomultipliers and light guides . . . . . . . . . . . . . 1426.2.5 Magnetic shielding . . . . . . . . . . . . . . . . . . . . . 144

6.3 The beam test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1496.3.1 The RICH prototype . . . . . . . . . . . . . . . . . . . . 1496.3.2 The radiators . . . . . . . . . . . . . . . . . . . . . . . . 149

7 Ion beam test at CERN SPS 1537.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 154

7.1.1 RICH prototype . . . . . . . . . . . . . . . . . . . . . . . 1547.1.2 Tracker prototype . . . . . . . . . . . . . . . . . . . . . . 1577.1.3 TOF counters . . . . . . . . . . . . . . . . . . . . . . . . 158

7.2 Preliminary results . . . . . . . . . . . . . . . . . . . . . . . . . 158

A Abbreviations 163

B TOF PMT positioning and field 165

Bibliography 178

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x

Chapter 1

Cosmic rays below 1 TeV

1.1 High energy particles from space

At the beginning of the XX century, it was discovered that a lot of energetic par-ticles come to the Earth from all directions. Such cosmic rays (CR) are consistingmainly of protons (about 90%), but Helium nuclei (∼ 10%), electrons (∼ 1%) andall isotopes are present, spanning a very wide energy range (from few MeV up tofew 1020 eV) (for a review see for example [1], [2], [3]). In addition to chargedparticles, also a detectable flux of energetic photons and neutrinos is present.

Figure 1.1 shows the differential flux of all primary cosmic ray charged par-ticles, from about hundred MeV to the highest measured energies (few 1020 eV).With the exception of solar particles, whose energies are usually below 10 GeV(but they can overcome this limit during violent solar flares), the CR particles inthis broad energy range have origin outside the solar system. Below few hundredMeV a different component emerges that is mainly composed of hydrogen and he-lium, called “anomalous cosmic rays”, but we will not describe it further becauseit is below the range of the AMS experiment (for a review see for example [4]).

A visual inspection of figure 1.1 makes it clear that the CR spectrum is fastlydecreasing with increasing energy following a power law with very few structures.The first evident deviation from a power law is at the low energy corner: here thespectrum flattens and the flux reaches the maximum (some thousand particles persquare meter per steradian per second). The flux of particles with lower energiesis dumped by the solar wind, and the maximum oscillates following the 11 yearsolar half-cycles: the energy spectrum of galactic cosmic rays is influenced bythe solar activity. This process is known as the solar modulation, and will be

1

C 1 TV

Knee

Ankle

2nd knee

2(1 particle per m per second)

(1 particle per m per year)2

(1 particle per km per year)2

Flu

x (

)

m

sr s

GeV

2−1

eVEnergy ( )

Flux of Cosmic Rays

Figure 1.1: All particle cosmic ray spectrum, adapted from [2] and [3].

described below (§1.4).

Starting from about 10 GeV to about 4 PeV (= 4 × 1015 eV) the spectrumhas a smooth shape, as is better seen in figure 1.2, that shows the differential fluxof the most important CR nuclei through a compilation of several measurementsdone before 1998 [5]. For kinetic energy E higher than few GeV per nucleon, the

2

1.1 — High energy particles from space

Dif

fere

ntia

l flu

x (m

2 sr

s M

eV/n

ucle

on)−

1

/

H

He

C

Fe

105 10610410310210 107

10−5

10−6

10−7

10−8

10−9

10−4

10−3

10−2

0.1

10

1

Kinetic energy ( MeV nucleon )

Figure 1.2: Compilation of several experimental measurements of the differentialcosmic ray flux of hydrogen, helium, carbon, and iron nuclei [5].

energy spectra are well described by a power law:

Φi(E < E0) =

∫ E0

0N(E) dE =

∫ E0

0kiE−γi dE , (1.1)

where Φi(E < E0) is the integral flux of CR particles of species i (usually ex-

3

C 1 TV

0.1

0.2

0.5

1

2

5

10

E2.

7d

N/d

E (

cm−2

sr−1

s−1 G

eV1.

7)

E (eV/nucleus)1012 1014 1016 1018 10 20

Figure 1.3: All cosmic ray particles energy spectrum [5], multiplied by E2.7 inorder to better show the spectral index changes.

pressed in particles m−2 sr−1 s−1), γi is the spectral index of the power law, andki is the normalization constant.

The spectral indices are around 2.7 for all nuclei below the spectrum “knee”(roughly at 4 PeV), when the spectrum abruptly steepens (the spectral index be-comes equal to 3; see figure 1.3). Above the knee, the experimental techniquesused insofar are not able to measure the elemental composition of the cosmicrays: at most the analysis of atmospheric showers can give us the logarithm of theatomic mass of the incoming particles [6].

Recently it was pointed out (see for example Horandel [3] and referencestherein) that the spectrum shows a slight change in the spectral index startingfrom about 400 PeV (the “second knee”): the spectrum smoothly increases theslope up to few 1018 eV (the “ankle”), when it flattens again, reaching a spectralindex of about 2.5 (figure 1.3).

At the highest energies ever detected (few 1020 eV) the measured flux is lim-ited by the very low statistics of such rare events: only a total of few tens of eventswere discovered by the various esperiments in the last 30 years. Such particleshave a curvature radius larger than the Galaxy disk thickness, hence they follow

4

1.1 — High energy particles from space

pratically a straight line between the acceleration site and the Earth. At present,the measured ultra-high energy cosmic rays (UHECR) incoming direction distri-bution is nearly uniform (with the exception of an ambiguous possible clusteringalong the line of sight of the Galaxy center [7] [8]), indicating an extragalacticorigin.

The various changes in the spectral index of the CR spectrum reflect the differ-ent origin and the propagation history of cosmic rays with different energy: belowthe knee their curvature radius is smaller than the galactic disk thickness, hencetheir sources must belong to our Galaxy, where CR propagate by diffusion (§1.3).

The curvature radius of a particle with charge ze in a uniform magnetic fieldis:

r =p

zeB≈ 10 E(15)

ze B(−6)pc , (1.2)

where E(15) is the particle energy in PeV and B(−6) is the field intensity in µG.Above the knee, the curvature radius become greater than the disk thickness, andCR may escape into the galactic halo, where the density is very low and the mag-netic field is weaker than the disk one. Only a fraction of the particles that arediffusing through the halo can re-enter the disk, going into a zone with strongermagnetic field. This “leakage” of CR induces an increase of the spectral indexbecause the escape probability is greater for higher energy particles.

The power required to mantain the observed CR energy density wCR ≈ 1 eVcm−3 [1] can be provided by supernova explosions, whose rate in our Galaxyis about (30 y)−1, if a mechanism with typical efficiency of order 10% is found.The preferred theory is diffusive acceleration applied to the strong shock wavesoriginated by supernova explosions (§1.2).

This mechanism is based on the repeated crossing of the shock front by theambient particles of charge ze, that on the average gain energy on each encounterwith the supersonic wave (the so called “first order Fermi mechanism”), and itis effective up to energies of z × 1015 eV (§1.2.2). Hence different species willshow different cut-off limits, when their spectra must change slope [3]. This maybe the cause of the shape of the all-particle spectrum between the knee and thesecond knee. Actually, the results from KASKADE [6] show that the knee canbe explained as the effect of this cut-off energy for protons and helium, the mostabundant species in cosmic rays.

On the other hand, the propagation itself could be responsible for the sec-ond knee [6], due to the charge dependence of the “escape time” τesc from theGalaxy. Extrapolation of τesc from the GeV range to higher energies gives at 3

5

C 1 TV

PeV cτesc ∼ 300 pc for protons, comparable with the disk thickness. Hence oneshould expect increasing anisotropies with larger energies, and a cut-off energyagain proportional to the particle charge. The origin of the structure between theknee and the second knee in the CR spectrum is still debated, and other possibleexplanations have been suggested [6].

During supernova explosion, the expanding shock wave is able to acceleratecharged particles up to the knee range, hence the existence of measurable CRfluxes at higher energies requires a new kind of engine in our Galaxy. The spec-trum above the knee is smoothly connected to the flux below the cut-off energies,and the most natural way to obtain this effect is to imagine that the second acceler-ation process acts on the particles accelerated by supernovae. This reaccelerationmechanism can take place in the vicinity of pulsars [9], where the rapidly rotat-ing magnetic field is a powerful astrophysical dynamo, that is able to acceleratecharged particles up to ultra high energies.

At the ankle even the most heavy elements have energies beyond the super-novae (and may be also the pulsar) acceleration limit, hence a new component isrequired to explain the observed flux [3]. In addition, above the ankle the cos-mic ray energy is so big that their trajectory is not bended very much even by thedisk interstellar magnetic field, and can be considered a straight line. Because ofthe quite uniform distribution of the incident directions over the whole sky, it isprobable that such particles were originated outside our Galaxy.

In the following, we will focus on charged cosmic rays in the energy rangeabove few hundred MeV and below few TeV, that are the target of the AMS ex-periment (chapter 4). Such particles are originated by galactic sources and theirspectra give us informations about the sources, the interstellar medium, the galac-tic magnetic field, and the eliosphere. Thus, the study of the cosmic ray flux ofprotons, electrons, helium and all other nuclei, when combined with informationsabout their reaction cross sections, energy loss and interactions with magneticfields, is a fundamental probe for the knowledge of our Galaxy.

1.2 Cosmic ray acceleration

While both hydrogen and helium can be of primordial origin, the latter and allheavier cosmic ray nuclei up to iron are produced in stellar cores and are injectedin the Galaxy by stellar winds and supernova explosions. Supernovae are alsoresponsible for the formation of heavier nuclei up to the most massive elements,

6

1.2 — Cosmic ray acceleration

and are thought to be the main engine for the cosmic ray acceleration below theknee.

Following Schlickeiser [10], we can generally say that energetic charged par-ticles can get accelerated both by momentum diffusion due to cyclotron and/ortransit-time damping of the electric fields of the ambient electromagnetic fluctu-ations, and by momentum convection due to compression of the CR scatteringcenters.

This can be seen in the diffusion approximation to CR dynamics, based onthe observation that energetic particles have usually a nearly isotropic pitch angledistribution relative to the ambient plasma. One can thus interpret this isotropyas the result of the scattering of CR by the low-frequency magneto-hydrodynamicturbolence, for example by Alfven waves and fast magnetosonic waves, both withvelocity much less than the light speed (hence with magnetic component muchgreater than the electric one: |δB| = (c/V)|δE| is the relation between the twokinds of fluctuation).

Due to the existence of such e.m. fluctuations, that act as scattering centers forenergetic charged particles, it is possible to describe the evolution of the isotropicpart of the distribution function of the particles of species a in the phase-spaceMa(x, p, t) (averaged over all momentum directions) with a diffusion-convectionequation for non-relativistic bulk speeds of the background medium [10], in themixed comoving coordinate system, where position is referred to the observerreference system while momentum is measured in the rest frame of the streamingplasma:

∂Ma

∂t− S a(x, p, t) =

∂

∂z

[κzz∂Ma

∂z− V Ma

]

+1p2

∂

∂p

(p2A2

∂Ma

∂p+

p3

3∂V∂z

Ma − p2 pMa

)− Ma

Tc(z, p)

(1.3)

where the ambient magnetic field defines the z direction, κi j is the spatial diffusiontensor, U � c is the non-relativistic bulk speed of the plasma and

V ≡ U +1

4p2

∂(p2vA1)∂p

(1.4)

is the effective cosmic ray bulk speed; A1 is the rate of adiabatic deceleration,and A2 is the momentum diffusion coefficient. S a(x, p, t) is the injection function(including sources and sinks) and Tc(z, p) is the momentum loss time, that dependson the interactions made by the particle with the surrounding medium.

7

C 1 TV

The transport equation (1.3) contains spatial diffusion along the field linesand spatial convection (first and second term inside square brackets, respectively),momentum diffusion and convection (first and second term inside parentheses,respectively), continuous momentum losses (last term inside parentheses), and“catastrophic” momentum losses (last term) due to point-like interactions. Mostof existing models of CR propagation and acceleration make use of this equation(usually with simplifications).

The total number density of CR particles of type a at position x is

Na(x, t) = 4π∫ ∞

0Ma(x, p, t)p2 dp , (1.5)

while the corresponding total injection rate is

Qa(x, t) = 4π∫ ∞

0S a(x, p, t)p2 dp . (1.6)

Integrating equation (1.3) over momentum from 0 to∞ after having multipliedit for 4πp2 dp gives1:

∂Na

∂t− Qa(x, t) =

∂

∂z

[κzz∂Na

∂z− VNa

]− Na

Tc(1.7)

where the momentum-averaged spatial diffusion coefficient and catastrophic losstime are

κzz ≡4π

∫ ∞0κzzMa p2 dp

Na(1.8a)

Tc(z) ≡ Na

4π∫ ∞

0 dp p2Ma/Tc(z, p)(1.8b)

respectively.By integrating equation (1.7) over the confinement volume V for the cosmic

rays, using the Gauss’ theorem to convert a volume integral into a surface integral,we get:

∂Na

∂t= Qa(t) + Ga − Na

Tc, (1.9)

1This integration over the momentum variations (terms in equation (1.3) inside parentheses) isobviously evaluated to zero, because the population is unchanged.

8


where

Na(t) =

∫

VNa(x, t) d3x , (1.10a)

Qa(t) =

∫

VQa(x, t) d3x , (1.10b)

Ga(t) =

∫

Sdσ ·

[κzz∂Na

∂z− VNa

]. (1.10c)

HereGa is the number of CR particles escaping from the surfaceS of the confiningregion.

The balance equation (1.9) says that the number of cosmic ray particles inthe confinement region can only change due to new particles being injected bythe sources with rate Qa; particles destroied by spallation, annihilation or naturaldecay (the Na/Tc term); particles escaping the region through its boundary withrate Ga.

1.2.1 Shock wavesBoth momentum diffusion and momentum convection, the possible causes of par-ticle acceleration [10], occur near cosmic shock waves. These are direct conse-quences of violent dynamical phenomena in the universe, as high-velocity stellarwinds and supernova expanding shells impinging on the surrounding medium.

In such cases a discontinuity is formed as the separation between the regiondominated by the expanding medium and the surrounding plasma. The mass fluxthrough this discontinuity is

G ≡ ρux (1.11)

where ρ is the plasma density and ux is its velocity component normal to the dis-continuity surface (uy is the trasversal component). With stationary discontinuitiesG = 0, while G , 0 with shocks.

If we mark with index “1” the upstream values and with index “2” the down-stream values, and use the notation

[A] ≡ A1 − A2 (1.12)

for the variation of any physical quantity A after crossing the shock front, wecan write the fundamental system of equations of discontinuities in magnetic fluid

9

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dynamics [10] in the following form:

[P] + G2[V] + [B2y]/8π = 0 (1.13a)

G [uy] = Bx [By]/4π (1.13b)Bx [uy] = G [VBy] (1.13c)

G [w + G2V2/2 + u2y/2 + VB2

Y/4π] = Bx [uyBy]/4π (1.13d)

where P is the gas pressure, V = 1/ρ is the specific volume of the fluid, Bx and By

are the normal and trasversal components of the magnetic field respectively, and

w = e + P/ρ (1.14)

is the enthalpy per unit fluid mass, where e is its internal energy. In ideal gasses

w =γ

γ − 1PV , (1.15)

where γ is the ratio of specific heats.We will consider charged particles acceleration by a fast, but non-relativistic,

super-Alfvenic parallel shock front [10], where the upstream Alfven waves have aKolmogorov spectrum I(k) ∝ Θ(k−k0)k−q and the spectral index is q = 2. Θ(k−k0)is the step function and k0 is the minimum wavenumber.

Parallel shock waves. A parallel shock wave is one whose normal is parallel tothe magnetic field B. In this case equations (1.13a)–(1.13d) reduce to

[P + G2V] = [P + Gux] = 0 (1.16a)

[w + G2V2/2] = [w + u2x/2] = 0 (1.16b)

that can be conbined into a single equation:

w1 − w2 +12

(V1 + V2)(P2 − P1) = 0 . (1.17)

Using equation (1.15) and the ideal gas law PV ∝ T we get the temperatureratio between the particles that have crossed the shock front and those that havenot:

T2

T1=

(γ + 1)P1 + (γ − 1)P2

(γ − 1)P1 + (γ + 1)P2

P2

P1= r

P2

P1, (1.18)

10


where the compression ratio has been introduced:

r ≡ ρ2

ρ1=

GV1

GV2=

(γ + 1)P1 + (γ − 1)P2

(γ − 1)P1 + (γ + 1)P2. (1.19)

From the last equation (1.19) it follows:

P2

P1=

r(γ + 1) − (γ − 1)γ + 1 − r(γ − 1)

. (1.20)

Introducing the Alfvenic Mach number of the flow

MA,1 ≡ ux,1

VA,1(1.21)

in terms of the upstream normal gas velocity component ux,1 and the gas Alfvenvelocity

VA ≡ B√4π(mp + me)ne

= 2.18 × 1011( B1 G

) ( ne

1 cm−3

)−1/2, (1.22)

and the sound Mach number of the flow

Ms,1 ≡ ux,1

vs,1=

G2V1

γP1=

1 − (P2/P1)γ[(V2/V1) − 1]

, (1.23)

one gets the compression ratio expressed as

r =(γ + 1)M2

s,1

(γ − 1)M2s,1 + 2

=(γ + 1)M2

A,1

(γ − 1)M2A,1 + 2β

, (1.24)

where

β =

(MA,1

Ms,1

)2

=

(vs,1

VA,1

)2

= 4πγP1

B2x. (1.25)

For strong shocks MA,1 � 1 and the compression ratio approaches the limit

r(MA,1 � 1)→ γ + 1γ − 1

. (1.26)

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1.2.2 Particle acceleration by shock wavesThe steady-state upstream transport equation for relativistic charged particles, inthe case of a fast parallel shock with Alfvenic waves with a power spectrum q = 2,can be written in the following way [10]:

∂

∂x

(κ1∂F1

∂x

)+ V1

∂F1

∂x= −Q1(x, p) (x > 0) , (1.27)

where the index “1” is used to mark upstream quantities, F(x, p, t) is the isotropicpart of the gyrophase-averaged particle phase space density, κ(x) is the spatial dif-fusion coefficient (it is idependent of momentum for relativistic particles), Q(x, p)represents sources and sinks, and V1 = u1 + Hc1VA,1 is the CR bulk speed. Hc ∈[−1,+1] is the normalized cross helicity state:

Hc =(δBf)2 − (δBb)2

(δBf)2 + (δBb)2 (1.28)

(“f” represents forward particles, moving in the same direction as the fluid, “b” isfor backward particles, with opposite direction).

On the other hand, the steady-state downstream transport equation is:

∂

∂x

(κ2∂F2

∂x

)+ V2

∂F2

∂x+ϑ

p2

∂

∂p

V2

A,1p4

rκ2

∂F2

∂p

= −Q2(x, p) (x < 0) , (1.29)

where the downstream CR bulk velocity V2 = u2 + Hc2,kVA,2, Hc2,k is the down-stream cross helicity at constant wavenumber k, ϑ is a parameter that depends onthe spectral index q = 2, the magnetic helicity state of the upstream waves, andthe ration between reflected and transmitted coefficiens [10]. The term with squarebrackets represents momentum diffusion, and contains the compression ratio r.

To solve equations (1.27) and (1.29) we impose the following boundary andcontinuity conditions [10]:

1. far upstream (x →∞) we require no accelerated particles: F1(+∞, p) = 0;

2. no damping of Alfven waves: these act as infinite source of energy. In orderto avoid that particles may reach any energy, we impose a finite size L forthe downstream region: F2(−L, p) = 0;

3. Q1 = Q2 = 0: particle injection at the position of the shock only, with rateq0(p);

12


4. the phase space density must be continue at the shock front: F1(0, p) =

F2(0, p). The same must be true for the current density:[κ1∂F1

∂x+ V1F1

]

(x→0+)−

[κ2∂F2

∂x+ V2F2

]

(x→0−)

+V1 − V2

3p2

∂

∂p(p3F1) + q0 = 0 .

(1.30)

Upstream solution. Multiplying (1.27) with κ1(x) and introducing the new vari-able

µ1(x) =

∫ x

0

dx′

κ1(x′), (1.31)

the solution in the upstream region is

F1(x > 0, p) = F0(p) exp(−V1µ1) . (1.32)

Downstream solution. Multiplying (1.29) with κ2(x) and introducing the newvariable

µ(x) =

∫ x

0

dx′

κ2(x′), (1.33)

the downstream equation (1.29) can be written in the form:

∂2F2

∂µ2 + V2∂F2

∂p+

Ap2

∂

∂p

(p4∂F2

∂p

)= 0 (1.34)

with A ≡ ϑV2A,1/r.

It can be shown [10] that the solution of this equation can be written in thefollowing form:

F2(µ, p) =

∫ ∞

0q0(p) G(µ, p, t) dt , (1.35)

where the Green’s function has the following complicated expression:

G(µ, p, t) =2e−V2µ/2

tV2

∞∑

m=1

( pt

)ωm[∂D∂ω

]−1

ω=ωm

sin[S (ωm)

2

(1 +

µ

η

)], (1.36)

where ω is the Fourier conjugated variable of t, η ≡ −µ(−L), S (ω) is a complexfunction that depends on the compression ratio, the parameters η, ϑ and Hc2,k, theupstream Alfvenic Mach number, and the downstream bulk velocity. The complexfunction D(ω) depends on S (ω) and the values ωm are the zeroes of D(ω).

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C 1 TV

Zero momentum diffusion. The very complicated analytical solution (1.36)admits a quite simple representation for the case of zero momentum diffusion,when calculated at the position of the shock fornt (µ = 0) with injection q0(p) =

δ(p − p0):

F2(0, p) =3(p/p0)−s

p0V2(R − 1)(1.37)

where R = V1/V2 is the scattering center compression ratio and s is the only non-vanishing zero of D(ω):

s = −ω = 3R + (e2N − 1)−1

R − 1. (1.38)

The “Peclet number” N = ηV2/2 measures the importance of the acceleration bythe downstream Alfven wave field. In case of strong acceleration

s(N � 1)→ 3RR − 1

, (1.39)

while in the opposite case

s(N � 1)→ 32N(R − 1)

. (1.40)

With large Peclet numbers, the spectral index of the power law of the accel-erated particles depends only upon the scattering center compression ratio R =

V1/V2. The differential intensity of CR particles is:

dΦ

dE∝ p2F2(0, p) ∝ p−Γ , (1.41)

withΓ = s − 2 =

R + 2R − 1

. (1.42)

If the scattering center compression ratio R equals the gas compression ratior, as in the infinite Mach number limit, the spectral index Γ is Γgas ≥ 2, since1 < r ≤ 4 for adiabatic shocks with γ = 5/3.

Finite momentum diffusion. For finite momentum diffusion, the solutions aremathematically much more complex: equation (1.36) shows that they can be writ-ten as infinite sums of power laws whose spectral indices follow from a trascen-dental eigenvalue equation [10]. Each individual power law component is weighted

14

1.3 — Interstellar propagation

by coefficients that depend on the actual downstream position. In addition, theyand the eigenvalues ωm depend on the scattering center compression ratio, theshock wave Peclet number and the level of momentum diffusion.

Usually the general solution (1.36) is simplified imposing additional con-straints, and computed with numerical methods. Hence it can be used in complexsimulations, where specific models for the source of the shock wave are assumed,and specific functional forms may be used for the injection spectrum q0(p) andthe diffusion coefficients κi(x).

Maximum particle energy. An important assumption for the previous treat-ment to be correct [10] is that the cosmic ray gyroradius RL is less than the maxi-mum wavelength λmax of the plasma waves: RL/λmax ≤ 1.

As upper bound for λmax one can use the characteristic size L of the system, inorder to get a limit on the maximum achievable particle rigidity2:

R ≡ pcze≤ BL , (1.43)

where p is the relativistic momentum, c is the speed of light, ze is the particlecharge, and B is the ambient magnetic field. A useful way to write the same thingis: (

B1µG

) (L

1 pc

)≥ E/z

1015 eV. (1.44)

Supernova shock waves have L ∼ 1 pc and B ∼ (10–100) µG, hence they cannotaccelerate cosmic rays to rigidities much above ∼ 1015 V. This is the energy rangewhere the spectrum knee shows itself: the spectral index change can be caused bythe cut-off of the protons, that are the most abundant CR fraction. Other elementsreach higher and higher cut-off energies, and the second knee could correspond tothe maximum energy achievable by Fe nuclei [3].

1.3 Interstellar propagationUp to the knee range of the cosmic rays spectrum, the supernovae can be the sitesof the CR acceleration and the resulting spectrum can be well represented by apower law in momentum. Then accelerated particles start to diffuse through the

2R has the dimensions of an energy divided by a charge, i.e. of an electric potential: when p ismeasured in GeV/c, R is measured in giga-Volt (GV).

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C 1 TV

Galaxy, where they travel on the average for several million years before reachingthe Earth.

Due to their different interaction cross sections, the elements have a slightlydifferent propagation history, and the measured abundances on the Earth can beused to infer their characteristic diffusion time (about 20 My) and the matter depth(5–10 g cm−2) traversed during propagation.

Before reaching the detector, the cosmic rays must diffuse inside the elio-sphere, where they loose energy due to the interactions with the magnetic fieldtransported by the solar wind, and finally they interact with the geomagnetic field(§1.4), that is like a “filter” that forbids very low energy particles to reach theEarth atmosphere (but at the same time all “soft” secondary particles are trappedinside the magnetosphere).

The simplest galactic propagation model is the leaky box one: the galactic diskis assumed to be a cylinder with radius of order 10 kpc and height of about 1 kpc,and cosmic rays are assumed to travel freely inside the disk, where a magneticfield of (3–6) µG exists. When CR reach the cylinder boundary they bounce elas-tically, but there is a finite probability (increasing with the particle momentum)that they cross the boundary and escape from the Galaxy. This model is analyt-ically solvable and suggests that the CR spectrum remains a power law, with ahigher spectral index than at the source, but it is far too simplistic to be able toexplain the spectra of different elements.

As further steps, one can introduce a bigger cylinder fully containing the diskbut with weaker magnetic field, as a model for the galactic halo. One may thenconsider a diffusion process within a medium with two different densities (fordisk and halo), then add other informations about the spiral arms, the galacticbulge, the magnetic field configurations, and so on. The problem will becomevery complicate and in general only numerical methods can be used to sketch thesolution, for different configurations in the parameters space.

The diffusion steady state equation for element j can be written [11]:

∇·(K j∇N j − VcN j) − ∂

∂E

[∇·Vc

3Ek

(2m + Ek

m + Ek

)N j

]+

∂

∂E(b jN j) − 1

2∂2

∂E2 (d jN j) + Γ jN j =

q j +∑

mk>m j

Γk jNk

(1.45)

The first terms represent diffusion (K j is the diffusion coefficient) and convection

16

1.4 — Propagation inside the eliosphere

(Vc is the convection velocity). The divergence of Vc is connected to the energyloss due to adiabatic expansion of cosmic rays. The next term represent the ion-ization and Coulomb energy losses, plus the first term of the reacceleration, allincluded in b j [12]:

b j(E) =

⟨dEdt

⟩

ion+

⟨dEdt

⟩

Coul+

⟨dEdt

⟩

adiab+

⟨dEdt

⟩

reac. (1.46)

The next is the second order term in reacceleration (d j is the energy diffusioncoefficient), and the inelastic collision term with the ISM. On the right side, q j

is the source term, while the last sum is over the spallation reactions producingnuclei of kind j. This equation may be used to determine the source compositionstarting from the measured abundances at Earth (chapter 2).

1.4 Propagation inside the eliosphereMeasuring cosmic rays from the Earth obviously means considering a sample ofparticles diffusing inside the eliosphere and reaching at least the distance 1 AUfrom the Sun (1 AU = 1.496 × 108 km). Hence the measured spectrum is not thesame as the average galactic spectrum, neither it is the same as the local interstellarspectrum (LIS, i.e. the spectrum outside the eliosphere but not too distant from theSun).

Cosmic rays entering the eliosphere (that has a boundary at a distance of order100 AU from the Sun) must diffuse inside a zone where a continuous outflowof highly conductive plasma exists. This “solar wind” is composed mostly byhydrogen and helium isotopes, but electrons, positrons and the isotopes of severallight elements are also present [1].

The solar wind particle kinetic energy is usually below few GeV per nucleon,in solar quiet periods, but during solar flares it can reach 100 GeV per nucleon.The magnetic field lines are “frozen” inside this plasma, that is expanding. Dueto the rotation of the Sun around its axis these lines tend to assume a spiral shape,but the magnetic field configuration inside the eliosphere is complicated by thepolarity reversal of the solar field every 11 years. Hence the energy spectrumof the measured particles is affected by the solar activity and shows periodicalbehavior (solar modulation), at least below few GeV per nucleon.

At low energy it is necessary also to take into consideration the Earth magneticfield, that is not a perfect dipole (figure 1.4). The typical energy of the geomag-netic field is lower than the eliomagnetic field at 1 AU, and can be neglected down

17

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Shock front or bow shockso

lar

win

d

Van Allen radiation belt

magnetopause

Figure 1.4: A sketch of the structure of the Earth magnetosphere.

to few Earth radii. Using a detailed model of the Earth magnetic field it is possibleto trace incident particles (and to “back-trace” the measured particles [13, 14]), tostudy the geomagnetic effect.

1.4.1 Solar modulationThe simplest model of solar modulation [15] uses a spherical approximation ofthe eliosphere and has as free parameters the solar wind velocity V(r, t) and theradial diffusion coefficient k(r, Ek, t). Charged particles with kinetic energy Ek

propagate by diffusion and convection and adiabatically exchange energy with theexpanding solar wind. Their differential density U(r, Ek, t) at distance r from theSun and time t can be found by solving the equation:

∂U∂t

= ∇k · ∇U − ∇· (UV) +13∇·V ∂

∂Ek(α(Ek)EkU) , (1.47)

where the left side term is the temporal variation of the cosmic ray density, that hasa small periodic fluctuation following the 11 years half solar cycle, and in the righthand side the three terms describe: 1) the particle diffusion inside the magneticfield generated by the Sun, 2) convection, and 3) the adiabatic deceleration.

18


The diffusion coefficient in this model has the form k = λv/3, where v is theparticle velocity and λ = λ(r,R, t) is the mean free path in the magnetic field,that depends on the time t, the radial distance r and the particle rigidity R. In thespherical approximation one can write [15]:

k = βR k1(r, t) , (1.48)

where β = v/c and k1(r, t) is the diagonal component of the diffusion tensor.The last term of equation (1.47) contains the term

α(Ek) =Ek + 2E0

Ek + E0(1.49)

where E0 = Mc2 is the total particle energy at rest.Gleeson and Axford [15] showed that the solution of equation (1.47) corre-

sponding to the stationary case with constant k and V , can be expressed in thefollowing form:

J(r, E, t) =E2 − E2

0

(Φ(t) + E)2 − E20

J(∞, E + Φ(t)) , (1.50)

where E = Ek + E0 is the total particle energy. Hence the particle flux J(r, E, t)inside the eliosphere at time t and distance r from the Sun can be related to thestationary interstellar flux J(∞, E + Φ(t)) through an expression that depends onthe energy Φ(t) lost by the particle reaching this radial distance from infinity.

Neglecting any charge sign asymmetry one can write

Φ(t) = |z|eφ(t) , (1.51)

where the solar modulation parameter φ =∫ rb

rdrV/(3k1) is usually directly in-

ferred by the experimental data. This can be done basicaly in two ways [16]: byrelating the total cosmic ray flux on the top of the atmosphere (extrapolated byneutron counting facilities) to the solar activity (for example the number of sunspots), or by unfolding a reference spectrum (usually the proton one) using therelation (1.50).

1.4.2 Geomagnetic cutoff

The Earth “magnetosphere” has a long tail, produced by the interaction of the solarwind with the geomagnetic field (see figure 1.4). Between Sun and Earth, at about

19

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Figure 1.5: Isocountours of the geomagnetic field in a low orbit altitude (400 kmabove sea level).

15 Earth radii from our planet, the solar wind produces a shock front beacuse it issupersonic with respect to the Earth atmosphere. This “bow shock” [17] is a shieldagainst the energetic particles coming from the Sun, that can penetrate only nearthe polar caps. On the opposite side from Sun, along the tail of the magnetosphere,the geomagnetic field joins the solar field forming a complicate structure in whichthere are accessible and forbidden zones for charged particles.

Low energy cosmic rays are affected by this structure, and their flux on theEarth depends on the geomagnetic coordinates (figure 1.5). In particular, thereis a zone, called “South Atlantic Anomaly” (SAA) where the lower Van Allenbelt, usually beyond 600 km above sea level, reaches about 250 km a.s.l. andis crossed by space-crafts flying at “low orbit” altitudes. The SAA is above theAtlantic Ocean, near the Brazil coast3, and is filled by low energy (down to 10MeV) protons, electrons and few light nuclei.

3See http://www.oulu.fi/˜spaceweb/textbook/radbelts.html for example.

20

http://www.oulu.fi/~spaceweb/textbook/radbelts.html


geomagnetic cp|min Ek |min

latit. θ (◦) (GeV) (GeV)0 14.9 14.0

40 5.1 4.360 0.93 0.48

Table 1.1: Geomagnetic cut-off for radially incident protons [1].

The geomagnetic field acts as a filter for low energy particles, that can pene-trate only regions that depend on their charge, momentum and incident direction.For example, the table 1.1 shows the minimum momentum or energy for radiallyincident protons at three different geomagnetic latitudes. On the other hand, softsecondaries produced in the atmosphere will likely be trapped, if they have energybelow the cut-off.

For protons with momentum direction at angle ω with respect to the normal tothe geomagnetic meridian plane, one has [18]:

cp|min = 59.4[RT

Rcos2 θ

1 +√

1 − cosω cos3 θ

]2

(GeV) , (1.52)

where RT = 6.378 × 103 km is the Earth radius and R is the orbital radius.

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22

Chapter 2

Cosmic ray composition

Cosmic rays consist of protons, α particles (He nuclei), electrons and positrons,and nuclei of all the isotopes. Even though their positive charge is high, during thepropagation through the low-density interstellar medium (ISM) the high energynuclei are not able to capture electrons, hence they are usually fully ionized whendetected above the Earth atmosphere.

At low energy (about 10 MeV per nucleon) there is a population of partiallyionized nuclei that are called “anomalous cosmic rays” (ACR). They are thoughtto be neutral atoms ionized by the solar wind that are accelerated by shocks in thesolar system (for example on the eliopause) [4]. We will not consider ACR herebecause their energy is below the threshold of AMS.

The relative abundances of the different elements are related to the composi-tion at the source and the propagation history of cosmic rays. The isotopic spectraof few elements are expecially important because they are of pure secondary ori-gin (like B, for example) or radioactive (like 10Be and 26Al), thus allowing for anestimation of the matter thickness traversed by CR and of the propagation timebetween sources and detection.

Electrons (and positrons) have very rapid energy losses through electromag-netic processes, while heavy particles mainly degrade their energy by ionizing theinterstellar medium. Hence e− and e+ diffuse in smaller volumes than ions andtheir measured spectra are mostly determined by the last recent and near super-novae. Positrons are thought to be produced during the CR propagation in theISM. For this reason they are also very useful for the fine tuning of the parametersof propagation models.

Protons and antiprotons, and electrons and positrons, are also important fortwo reasons. First, particle and antiparticle are pratically equivalent for propa-

23

C

gation models, because they differ only by the sign of the electric charge. Thisdifference can be used to study the charge-dependent effects of the solar modula-tion. Second, the antiparticle spectra may show distinctive features that could beinterpreted as signatures of the annihilation of the exotic particles that consitutethe dark matter in our Galaxy (as in the rest of the universe).

2.1 Cosmic ray ions

The primordial nucleosynthesis produced the protons and the bulk of the heliumnuclei, but only a negligible part of heavier elements (7Li is the only detectablefraction) [19]. The rest of the baryonic matter was (and is being) produced bystellar nucleosynthesis (up to Fe) and SN explosions.

2.1.1 CR source composition

Although supernova (SN) shocks are generally believed to be the engines of thecosmic rays acceleration, at least below the spectrum knee, the sources of theparticles that are accelerated are still debatable [20]. The most efficient site forparticle acceleration is the low-density hot ISM, where the energy that the parti-cles gained interacting with the shock front is not efficiently dissipated. Howewer,the accelerated particles may come from the cooler and partially ionized phase ofthe medium, or they could be pre-accelerated by stellar coronae in a manner de-pending on the first ionization potential (FIP) (see [20] and references therein).Recently, a different scenario emerged that is based on the interstellar grain ac-celeration by SN shock waves, where the different volatility of the elements is theimportant quantity, determining the relative abundances in the cosmic rays [21].

Figure 2.1 shows the results from the model of Ellison et al. [21] about thesource abundances of the different elements, obtained requiring that after the prop-agation from the source to the Earth the relative abundances best fit the experimen-tal results (as of 1997). The elements are divided into refractory, semivolatile,volatile, and highly volatile groups, based on decreasing condensation tempera-ture. The refractories are essentially completely locked in grains in the ISM, whilethe highly volatile are gaseous.

Meyer et al. [22] showed that the galactic CR composition data are orderedin terms of the following behaviors: the abundances strongly increase with themass number A for volatile elements (hydrogen is an exception); the refractory

24

2.1 — Cosmic ray ions

Figure 2.1: Galactic CR source aboundances versus atomic mass number, ob-tained with the model by Ellison et al. [21].

elements are all enhanced with respect to the volatile elements, without any massdependence. Hence the acceleration process is more efficient for those elementslocked in grains.

Diffusive acceleration naturally leads to acceleration efficiencies that increaseas the particle rigidity, i.e. as the A/Q ratio. Dust grains have great mass andsmall charge, produced by ionization caused by collisions with plasma electronsor other grains, and by photoelectric effect caused by UV photons [21]. The resultis a very high A/Q ratio, i.e. a very high acceleration efficiency. However grainssuffer energy losses and can escape from the region more easily than protons andnuclei, hence they cannot be accelerated above ∼ 100 keV per nucleon.

Gain erosion by sputtering produces free ions with low effective charge Q∗ .3e (usually they are not fully ionized), and the elements with high ionization po-tential have high probability to escape as neutral particles from the accelerationsite. The ions have high probability to be scattered back to the shock by the

25

C

magnetic irregularities of the ambient plasma, becoming the “seeds” of the usualdiffusive acceleration process. But they have on the average higher energy of theambient volatile elements, hence they can be accelerated to high energy (withE/A|max ∼ 1014Q/A eV) more easily [21].

This scenario predicts that all the gaseous elements accelerated out of the ISMor circumstellar matter reach the abundances that lie between the dotted and dash-dotted lines in figure 2.1. Motivated by the observed 22Ne excess, in addition tothe average interstellar medium a source of heavy elements (as a12C-, 16O- and22Ne-enriched Wolf-Rayet stellar wind) seems to be necessary [21]. This explainswhy they are above the predicted level in figure 2.1. No significant amount of SNejecta material is accelerated by the shock wave: supernovae are the engines ofthe CR acceleration, but they act upon a medium that is composed by their paststellar wind elements, the surrounding material and the additional component ofheavy elements. Thus, the similarities between the solar abundances (FIP biased)and the CR source composition (volatility biased) seems to be purely coincidental[21].

Recently it was pointed out that the various models of CR acceleration, whennormalized to the observed Fe spectrum, unpredict the Be data by a large factor,suggesting a scenario where CR metals are accelerated out of SN ejecta in superbubbles [20]. In this case, a given supernova acts upon the material ejected bynearby and recent supernovae, whose explosions were “triggered” by other explo-sions, producing a “depleted” dominion rich of heavy elements.

Due to the fact that supernova progenitors form mostly in O-B associations andhave short lifetimes, the great majority of the core-collapse supernovae explodein hot, low-density superbubbles that are hundreds of parsecs large and can lastfor tens of megayears. C and O nuclei accelerated by these successive SN shocksinteract with ambient H and He, producing the bulk of the beryllium in the Galaxy.

2.1.2 Propagation models

The relative abundances of the different species in cosmic rays give important in-formations on the propagation details and on the source composition. For examplethe instable nuclei can be used to infer the propagation time of CR in the Galaxy,while pure secondary nuclei constrain the matter thickness (usually in g cm−2)traversed during propagation.

The simplest model is the “leaky box”, where the CR are freely propagating ina given volume and have finite probability to escape its boundaries. In stationary

26


conditions, the sources produce particles that may be lost due to inelastic interac-tions or to escape, and the number density variation due to these processes can bewritten in a very simple form: N/τi + N/τe, where τi is the mean interaction timeand τe is the mean escape time.

When the secondary production is considered, it is possible to write down aset of differential equations that connect the measured relative abundances to thesource composition. It comes out that the propagation time (inferred from instablenuclei) is t ≈ 20 My, while the matter traversed by cosmic rays is x ≈ 9 g cm−2.We can infer the average density of the medium n = x/(ctmH) ≈ 0.3 cm−3. As thedisk density is about 1 cm−3, it follows that cosmic rays must spend a fraction ofthe time in an empty region, called the diffusion halo.

The leaky box model is able to work with stable primary and secondary ele-ments, but it fails with unstable nuclei. In addition, the parameters of the modelhave no direct physical meaning. Because the charged particles are scattered bymagnetic irregularities, the correct propagation model is a diffusion model: thesteady state equation for element j is formula (1.45) of section 1.3 [11], that wewrite again:

∇·(K j∇N j − VcN j) − ∂

∂E

[∇·Vc

3Ek

(2m + Ek

m + Ek

)N j

]+

∂

∂E(b jN j) − 1

2∂2

∂E2 (d jN j) + Γ jN j =

q j +∑

mk>m j

Γk jNk

In the leaky box model all quantities are spatially averaged (so that convec-tion has no meaning), and the diffusion term is replaced by the escape term:∇·(K j∇N j) → N j/τe. Since this model is homogeneus, the mean time spent byCR in the Galaxy and the matter thicnkess x are correlated. This is not true inmodels keeping into account the halo.

As far as stable species are concerned, leaky box and diffusion models areequivalent [11]. This can be seen in the “weighted slab technique”: the generalsolution is written in the form:

N j(r) =

∫ ∞

0N j(x) G(r, x) dx (2.1)

then equation (1.45) decouples into two indipendent equations. The first one in-volves G(r, x) and depends only on the geometry of the problem and on the chosen

27

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diffusion scheme, but not on the species j. The other equation involves N j(x) andcontains the physics aspects of the propagation. Different models (leaky box,diffusion) correspond to different G(r, x), that is the path length distribution (theprobability distribution that a particle j crosses the matter x).

The leaky box model gives G(x) = exp(−x/λ)/λ, where λ = 〈x〉 is the aver-age quantity of matter traversed by CR. In diffusion models, for a wide class ofgeometries, the function G is given by an infinite series of exponentials involvingthe diffusion coefficients. The first exponential is sufficient (i.e. the leaky box isrecovered) only for small values of x.

2.1.3 Measurements of CR ions spectra

Direct measurements of the cosmic ray spectra in the solar system have been doneby balloon and satelite experiments. The most important are HEAO-3 [23], ACE[24], Voyager 1 and 2 [25] and Ulysses [26]. These measurements can be usedto constrain the parameter space of propagation models, as it was done by severalgroups. Recently, Donato et al. [27] and independently Moskalenko et al. [28]emphasized that, in order to have a good fit at the same time for the B/C and sub-Fe/Fe ratios, it is necessary to consider the effect of the local bubble (LB) wherethe Sun is collocated.

In particular, the study of the radioactive nuclei (the most important are 10Be,14C, 26Al, 36Cl, 60Fe) shows that in first approximation the Sun is within a shellof radius ∼ 50 pc with density ∼ 0.1 cm−3, surrounded by a shell with almostnull density extending up to radii ∼ 200 pc. Beyond this second shell, the averagedensity is 1 cm−3 [27].

This is consistent with the picture of the local interstellar medium consisting ofan asymmetric bubble with radius of 65–250 pc filled by hot (T ∼ 105–106 K) andlow-density (n . 0.005 cm−3) gas, surrounded by a dense neutral gas boundary(“hydrogen wall”), as derived from spettroscopic measurements [29, 30, 27, 31,32, 33].

The presence of this low density zone around the solar system does not af-fect the diffusion of stable ions, but the secondary nuclei abundances, producedby spallation, are perturbed. For radioactive species the effect is very important,because they sample a relatively small fraction of the volume in which stablenuclei propagate: the effect is well represented by an exponential attenuationexp(−rhole/`rad), where rhole is the radius of the underdense region around the Sun,and `rad =

√K(E)γτ0 is the radial distance from the source that a particle that is

28


0

0.1

0.2

0.3

0.4

0.1 1 10 100Kinetic energy, GeV/nucleon

B/C ratio

Voyager

Ulysses

ACE

HEAO−3

Chapell,Webber 1981

Dwyer 1978

Maehl et al. 1977

LIS

Φ = 450 MV

0

0.1

0.2

0.3

0.1 1 10 100 1000Kinetic energy, GeV/nucleon

Sc+Ti+V/Fe ratio

ACE

Ulysses

Voyager

ISEE−3

HEAO−3

Sanriku

450 MV

800 MV

LIS

Figure 2.2: Boron to carbon (left panel) and sub-Fe to iron (right panel) ratios:measurement can be fit at the same time by a diffusive propagationmodel that takes into account CR reacceleration and convection, anda “fresh” contribution of C and O nuclei in the local bubble. Thecomputed local interstellar spectrum is shown for comparison. De-tails about different parameters can be found in Moskalenko et al.[28].

following a random walk reaches on the average. K(E) is the diffusion coefficientand γ is the Lorenz factor of the nucleus with lifetime τ0 at rest [27].

Values 60 pc . rhole . 80 pc are suggested by 10Be/9Be and 36Cl/Cl ratiosmeasured by ACE, while the 26Al/27Al ratio seems not compatible. By enlarg-ing the rhole range to 100 pc it is possible to fit at least the Ulysses and Voyager26Al/27Al data [27].

The need for a local structure is motivated by Moskalenko et al. [28] in a dif-ferent way. They stress the fact that propagation models fail to fit simultaneouslythe B/C and sub-Fe/Fe ratios, and the antiproton flux, even in presence of reac-celeration. However, their numerical simulation (called GALPROP1) can fit ev-erything if one postulates that the local bubble (LB) contains “fresh unprocessed”component at low energy (figures 2.2 and 2.3). The presence of this 12C and 16Ocomponent would lower the local B/C ratio, because B is produced by spallation,that is not an important effect in the neighborhood of the Sun.

This is consistent with the idea that the local bubble [30] was probably pro-

1http://lheawww.gsfc.nasa.gov/users/imos/galprop.html

29

http://lheawww.gsfc.nasa.gov/users/imos/galprop.html

C

0.001

0.01

0.1 1 10 100

Flu

x, m

−2 s

−1 s

r−1 G

eV−

1

Kinetic energy, GeV

Antiprotons

Φ = 550 MV

BESS 95−97BESS 98MASS91CAPRICE98

TertiaryLIS

Figure 2.3: Cosmic ray antiproton(left panel) and ions spectra (rightpanel) measured by different ex-periments are compatible with adiffusion/reacceleration propagationmodel with contribution from the lo-cal bubble [28]. The measured spec-tra are sensibly different from the lo-cal interstellar spectra below 10 GeVper nucleon.

0.01

0.1

1 BoronLIS

ACEHEAO−3450 MV800 MV

0.1

1

CarbonLIS

E2 F

lux,

GeV

/nuc

leon

m−

2 s−

1 sr−

1

0.1

1

OxygenLIS

0.01

0.1

1

0.1 1 10 100 1000

IronLIS

Kinetic energy, GeV/nucleon

duced in a series of supernova explosions whose progenitor was an O-B star as-sociation2. The LB age is ∼ 10 My and it was produced by 10–20 SN explosions,with the last SN 1–2 My ago or 3 SN in the last 5 My. There is also evidence infavor of a nearby recent SN (at about 30 pc from the Sun) [28]. Thus it is veryprobable that particles coming directly from SN remnants still influence the localspectra and abundances of cosmic rays.

Table 2.1 shows the results obtained by Moskalenko et al. [28] about the rel-ative abundances to Si computed for the local bubble component and the galacticsources, compared to the measured solar system abundances.

2An O-B association is a large, very loose form of an open star cluster consisting of youngspectral type “O” and “B” stars. They cover large volumes of space, are loosely held together bygravity and have short lifetimes (a few million years) as a distinct object.

30

2.2 — Cosmic ray electrons

Z Solar LB Galactic Z Solar LB Galacticsystem sources sources system sources sources

6 9.324 3.850 4.081 18 7.070 × 10−2 3.283 × 10−2 1.915 × 10−2

7 2.344 6.500 × 10−1 3.022 × 10−1 19 3.718 × 10−3 2.317 × 10−2 * 6.392 × 10−3

8 19.04 6.317 5.235 20 6.451 × 10−2 8.333 × 10−2 5.887 × 10−2

9 8.901 × 10−4 0. 0. 21 4.169 × 10−5 1.367 × 10−2 * 1.730 × 10−4

10 3.380 6.667 × 10−1 6.328 × 10−1 22 2.958 × 10−3 5.817 × 10−2 * 3.166 × 10−3

11 6.028 × 10−2 9.767 × 10−2 3.575 × 10−2 23 2.817 × 10−4 2.433 × 10−2 * 0.12 1.070 1.385 1.050 24 1.318 × 10−2 6.200 × 10−2 2.481 × 10−2

13 8.310 × 10−2 1.583 × 10−1 7.794 × 10−2 25 6.901 × 10−3 1.800 × 10−2 2.309 × 10−2

14 1. 1. 1. 26 8.901 × 10−1 7.767 × 10−1 9.661 × 10−1

15 7.944 × 10−3 5.667 × 10−3 1.041 × 10−2 27 2.344 × 10−3 4.500 × 10−3 1.773 × 10−3

16 6.028 × 10−1 1.000 × 10−1 1.425 × 10−1 28 5.014 × 10−2 3.567 × 10−2 5.591 × 10−2

17 8.901 × 10−3 4.667 × 10−3 4.047 × 10−3

*) Upper limit.

Table 2.1: Elemental abundances normalized to Si given by the GALPROP pro-gram [28].

2.2 Cosmic ray electrons

Cosmic ray electrons are probably accelerated by the same engines that accelerateCR protons and nuclei (supernova explosions), but they differ significantly fromhadrons for what concerns the energy lost during the propagation through theinterstellar medium.

Because of their small mass and lack of strong interactions, electrons sufferlarge energy losses due to electromagnetic processes as synchrotron radiation,inverse Compton scattering, and bremsstrahlung. These losses effectively limitthe volume that can be pervaded by the elctrons that were emitted by a givensource: the measured spectrum must carry information on smaller scales than thestable elements.

Even though there are conceivable sources of primary positrons, like pulsars,primordial black holes or supersymmetric particles annihilation, the measuredfluxes are compatible with the simple hypothesis of complete secondary origin.In fact, the secondary production of e+ and e− by pion decay (the pions are pro-duced in the CR proton interactions with the interstellar medium) yields almostthe same amount of electrons and positrons, whereas the measured e+/e− fractionis about 10%. Thus electrons are mostly of primary origin, while the positronshave secondary origin and can be used to set constrains on the parameters of CRpropagation.

31

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2.2.1 Energy lossesBremsstrahlung is significant when electrons propagate through H regions (radioemission) or near X binaries (X-rays), and the emission power due to bremsstrahlungis proportional to the product of the ion and electron densities of the plasma, andto the square of the average ion charge:

−(

dEdt

)

brem= 4NeNionZ(Z + 1.3)r2

eαcgE (2.2)

where re is the classical electron radius, g is the Gaunt factor, and E = γmc2 is thetotal energy. In the cases of interest:

−(

dEdt

)

brem∝

γ ln γ fully ionized Hγ neutral H

(2.3)

If the electrons have a power law distribution in momentum with spectral index−η, the bremsstrahlung radiation has a power law spectrum with the same spectralindex −η [1].

Synchrotron radiation is the dominant process when CR electrons propagatethrough regions where a magnetic field of intensity H exists, the emission powerbeing proportional to Umag ∝ H2:

−(

dEdt

)

sync=

43σT cUmag γ

2 (2.4)

where σT = r2e8π/3 is the Thomson cross-section (re = e2/(4πε0mec2) = 2.818 ×

10−15 m is the classical electron radius) and Umag is the magnetic field energydensity. For an electron power law distribution in momentum with spectral index−η, the synchrotron radiation has a spetrum that depends on the average magneticfield intensity and a spectral index equal to −(η − 1)/2 [1].

Inverse Compton scattering is the dominant process in photon rich environ-ments, like the jets emitted by active galactic nuclei, and in case of low magneticfield and matter density, when the electrons have to interact at least with the cos-mic microwave background photons. If the energy density of the photon field isUrad:

−(

dEdt

)

i.C.=

43σT cUrad γ

2 (2.5)

32


Measurement Year Sun e−/e+ Emin Emax Ref.pol. sep. (GeV) (GeV)

MASS91 1991 + Y 7.5 46.9 [35]CAPRICE94 1994 + Y 0.54 34.3 [36]HEAT94 1994 + Y 5.45 66.4 [37]HEAT95 1995 + Y 1.20 66.4 [37]Nishimura 2000 1996, 1998 + N 30.0 3000 [38]BETS97+98 1997, 1998 + Y 13.9 112.6 [39]AMS-01 1998 + Y 0.15 35.7 [40]

Table 2.2: Cosmic ray electrons measurements. In addition to AMS-01, only ex-periments which published data tables are reported. Positive and neg-ative Sun polarities refer to epochs when the magnetic field emergingfrom the North Pole of the Sun points outward and inward, respec-tively [41].

A power law spectrum with spectral index −η for the electrons produces a powerspectrum in frequency due to inverse Compton scattering with spectral index equalto −(η − 1)/2 [1].

In conclusion, electrons suffer total energy losses

−(

dEdt

)

tot= aE2 + bE + c ln E , (2.6)

while electromagnetic losses different by ionization are usually not important forCR protons and nuclei. In the leaky box jargon, this can be translated into the ef-fective lifetime τloss ≈ 300 (E/1 GeV)−1 My. This corresponds to a mean diffusiveradial distance rloss ≈ 1 kpc (E/1 GeV)−1/2(K/0.03 kpc2 My−1)1/2 from the source[12].

Hence the measured CR electron spectrum gives information only about arather small volume around the solar system. For example, electrons with E > 10GeV should be very sensitive to the local bubble, while protons are sampling alarge part of the galactic disc (up to the Galaxy core [34]) and the halo.

On the other hand, electrons can be traced through the Galaxy thanks to theirelectromagnetic emission, and their interstellar density can be inferred from themeasurements of the synchrotron emission in the radio band. In this way we caninfer the average electron density in our and in different galaxies.

Figure 2.4 shows the inferred local interstellar spectrum (LIS) of the cosmicray electrons, obtained demodulating the spectra measured by recent experiments

33

C

1

10

10 2

1 10 102

103

Ek (GeV)

E3 F

(m

-2 s

r-1 s

-1 G

eV-1

)

AMS-01 e-

BETS97+98 (e- + e+)

Nishimura 2000 (e- + e+)

HEAT95 e-

HEAT94 e-

CAPRICE94 e-

MASS91 e-


Figure 2.4: Local interstellar spectrum of cosmic ray electrons measured by re-cent experiments between about 1 GeV and 2 TeV [16].

[16] (table 2.2). The spread of the data points could be due to systematic uncer-tainties arising from the correction for the residual atmosphere or for the detec-tor response. If these effects are not strongly energy dependent, it is possible torenormalize the spectra to the same value at fixed energy, in order to minimize thespread.

Figure 2.5 shows that it is possible to fit of the renormalized data set with a

34


10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

10 2

10 3

1 10 102

103

Ek (GeV)

F (

m-2

sr-1

s-1

GeV

-1)

AMS-01 e-

BETS97+98 (e- + e+)Nishimura 2000 (e- + e+)HEAT95 e-

HEAT94 e-

CAPRICE94 e-

MASS91 e-


178.2 / 80

(3 ± 1) < Ek /GeV < (2070 ± 750)

γLIS = 3.42 ± 0.02

NLIS = (340 ± 18) m -2 sr -1 s -1 GeV 2.42

Figure 2.5: Local interstellar spectrum of cosmic ray electrons. Data taken bydifferent experiments were renormalized to the AMS-01 flux at 20GeV, with the exception of CAPRICE94 [16].

single power law in kinetic energy, obtaining a spectral index of 3.4 between 3GeV and 2 TeV. Whereas several authors (see for example [42]) emphasize theidea that the electron LIS should have slope changes due to the interplay betweenpropagation by diffusion, energy losses and source distribution, figure 2.5 showsthat the overall data set does not strongly suggest any spectral index change.

In addition, the overall LIS has the same slope as the electron LIS inferredfrom AMS-01 alone, that extends down to 1.5 GeV, and the low energy flatteningof different experiments may be explained with a charge dependent solar modu-

35

C

lation effect [16]. Thus, the spectral change at 10 GeV foreseen by Moskalenkoand Strong [43] is not compatible with the inferred electron LIS obtained withthe most recent experiments. Instead, the electron LIS may suggest that the mea-sured cosmic ray spectra are due to a recent and nearby supernova (or perhaps afew SNe), whose remnant may even contain the solar system. This would alsoaffect the spectra of the CR ions, that would have a galactic and a local compo-nent. Future high statistics measurements of the ions spectra made by AMS-02(see chapter 4) and other experiments should be able to determine the relativeimportance of the two components.

36

Chapter 3

Cosmic antimatter

The discovery of “antiparticle” solutions of the Dirac’s equation (1929) was soonfollowed by the experimental discovery of the positron by Blackett and Occhialini(1932). Since then, it was experimentally established that whenever we create newparticles in laboratory, they come in two different forms that are well balanced,generically called “matter” and “antimatter”.

In particular, the creation (and the annihilation) of fermions is governed byfew conservation laws, the baryonic and leptonic numbers conservation being themost important. These laws say that if we create few fermions, each with a pos-itive baryonic (or leptonic) number, in the same reaction other fermions will becreated, each with negative baryonic (or leptonic) number, in order to keep thetotal baryonic and leptonic numbers constant. In the simplest case, this meansthat we cannot create a single fermion: we must create a couple of particle andantiparticle at least.

When we think about the creation of the present universe, our first attemptwould lead naturally to a symmetric cosmology in which matter and antimatter arepresent in the same amount, but astrophysical measurements say that we live in abig domain that seems to be completely made of matter. Of course, the possibilityexists that the universe is symmetric on average, but may consist of a collectionof homogeneus domains separated by “walls” filled with radiation only.

An important point is the estimation of the domain size. If they are of the scaleof galaxies or galaxy clusters, we may detect antimatter cosmic rays (CR) comingfrom the nearest domain. On the other hand, if some antistar exists in our Galaxywe may even detect antinuclei with Z > 2.

Nevertheless, antimatter cosmic rays do exist and are detected. The two speciesalready measured are antiprotons and positrons, both of secondary origin: they are

37

C

produced by the CR interactions in the interstellar medium (ISM) or in the Earthatmosphere, and by the annihilation of exotic particles, if any.

3.1 AntimatterWhat the word antimatter means is not simple, thus we start from its constituents:the antiparticles. If all the characteristics of an elementary particle (i.e. a particlewithout any internal structure), like its mass, charge, spin are known, then itsassociated antiparticle is like its specular image: it has the same mass, but oppositecharge and spin (and all the other quantum numbers).

3.1.1 CPT theoremIn modern Physics, particles (and antiparticles) are described by the RelativisticQuantum Theory of Fields, in which a couple of field operators are capable ofdestroying or creating one copy of each kind of particles in every given state.One can switch between a particle and the associated antiparticle using the chargeconjungation operator C:

C : ψ(r, t)→ ψ(r, t)

where ψ(r, t) represents a particle quantum field and ψ(r, t) is the correspondingantiparticle.

There are two other important discrete operators: the time reversal operator Tand the parity operator P (the spatial inversion):

T : t → −tP : r→ −r .

Even though in general there is no exact symmetry with respect to these opera-tors, the CPT theorem says that every quantum field theory, relativistically covari-ant, that admits a minimum energy state and obeys the principle of microcausality(requiring that independent measures can always be done on two spacetime pointswhich are outside each other’s light cone), is invariant under the action of C, Pand T together, without any dependence from the order they are applied.

The strict correspondence between particles and antiparticles is a result ofthe CPT symmetry. In particular, the fact that their masses are exactly equal isdue to the commutative property between CPT and the Hamiltonian operator. In

38

3.1 — Antimatter

addition the CPT composite operator is antiunitary: “it relates the S-matrix1 foran arbitrary process to the S-matrix of the inverse process with all spin three-components reversed and particles replaced with antiparticles” (quoted from [44],p. 183). This means that the following two probability amplitudes are equal (anoverline denoting antiparticles):

A(a1 + a2 + . . .→ b1 + b2 + . . .) =

A(b1 + b2 + . . .→ a1 + a2 + . . .)

(the demonstration of this theorem can be found in [45] and [44]).

3.1.2 Anti-systemsThe existence of antiparticles, obtained making C acting upon particles, does notguarantee the existence of bound systems made with antiparticles. In other words,the presence of the C symmetry alone does not imply that our system can simplybe replaced by another system with antiparticles in place of particles: to obtainthe anti-system we do need the more complex CPT symmetry, that involves alsothe spatial and temporal reflections, changing indeed the dynamics of the system(not only its composition).

The antimatter is composed by compound systems like anti-atoms, that aremade of a cloud of positrons surrounding a nucleus containing antiprotons and an-tineutrons. Due to the C invariance of the electromagnetic interactions, all chem-ical interactions would be the same as ordinary matter, allowing for macroscopicagglomerates.

Howewer, one important point is that the fundamental interactions (the elec-troweak interaction at least) appear neither to be symmetric with respect to theC and P operators, nor to the composite operator CP, as found by Cronin andFitch in 1964 (for the references to original works, see [44] or [46] and referencestherein).

The experimental discovery of the antimatter, in the sense of bound systemsof antiparticles, was done in 1965 by A. Zichichi and his collaborators at CERNand by S. Ting and his collaborators at Brookhaven [46]. Recently (1996), the

1In Quantum Field Theory, the scattering process is modeled as a very short and intense inter-action, that is able to change the particle state from the initial free motion to a generally differentfinal state (again a free wave). The S-matrix contains the probability amplitude of the transitionfrom any initial state to all the final states, thus representing the most complete description of thescattering process itself.

39

C

simplest antiatom, the antihydrogen, was obtained and studied at CERN and atFERMILAB (see [47] et references therein).

Thus we see that the antimatter is actually a very complex system, even ifthe CPT theorem guarantees that its behavior is exactly the same as the commonmatter: the hypothetical humans and things made completely of antimatter wouldbehave, in their anti-world, exaclty as the “normal” humans and things.

3.2 Cosmic antimatter

As far as high energy physics experiments are concerned, matter and antimatterare created in the same amount. The CPT symmetry holds up to a level of 10−12,electronic lepton number violations may occur only below 10−12 (whereas thelimit on the total lepton number, including all families, is below 10−10), and theexperimental tests on baryon conservation imply that violations (if any) must bebelow 10−6 [19].

What about the matter we see in the universe? If we trust that the conservationlaws hold true during all the history of the universe, we must admit that some-where there should be the antimatter that balances the matter we are consisting of.As an alternative, we could state that the baryonic and leptonic numbers were notconserved in the past, i.e. that unknown physical processes may have happenedduring the first phases of the universe evolution.

If the conservation laws were valid for the whole universe life, then it is im-portant to explain the presence of non annihilated matter.

Today we can evaluate the ratio between the cosmic background radiation(CBR) photons and the nucleons (plus antinucleons) number as η ∼ 10−10 [19].The CBR is the result of the annihilation of particles and antiparticles (in nearlythermal equilibrium in the very early phase of the universe) when the temperaturebecame low enough to break the coupling between radiation and fermions. If allthe matter in the universe is of a kind only, then η is the relative difference betweenthe amount of matter and antimatter at the epoch in which the radiation uncoupledfrom the fermions. On the other hand, if the symmetry is conserved, η is the valueof the local fluctuation in the quantity of matter and antimatter in that epoch.

40

3.2 — Cosmic antimatter

3.2.1 Can total annihilation be avoided?

The non zero value of η is a problem: if the universe is made of matter only (plusthe radiation) we have to understand the mechanism that produced such a littleasymmetry; if the universe is symmetric, we have to understand how fluctuationscould survive and generate the observable structures.

The first attempt to answer to the latter question was due to Alfven [48] (1965).He considered an “ambiplasma” (a fully ionized plasma consisting of protons,antiprotons, electrons and positrons) and the possible formation of homogeneuscells separated by the radiation emitted from “leidenfrost”2 leyers in which all theannihilations happen. Omnes [49] (1971) found that this layer is stable when themagnetic field is negligible: the annihilations cannot disrupt the separation walls.

Unno and Fujimoto [50] (1974) applied these results to a specific case, tryingto explain quasars as super massive stars composed of matter and antimatter. If theantimatter is a little fraction of the total mass, they showed that it would constitutea domain surrounded by the matter and separated by a leidenfrost layer, like abubble inside a star.

To explain how the leidenfrost layer can be able to keep separate matter andantimatter, Aly [51] (1978) computed the annihilation rate at the boudary in 3cases: radiative and plasma eras of Big Bang model, strong magnetic field, two in-tergalactic hot domains. In the meanwhile, Lehnert [52, 53] (1977, 1978) showedthat at interstellar densities no well defined boundary can form in presence ofneutral gas or in a unmagnetized fully ionized plasma. Only a magnetized am-biplasma could produce a leidenfrost layer, whose thickness is proportional toBT 1/2: for 105 < T < 108 K and B = 10−8 T, the wall thickness is about 107 m.

Thus the walls are very thin (of the order of magnitude of the Earth diame-ter) and pratically invisible for distant observers. In analogy with the geomag-netic field structure, that has well defined zones separated by current and neutralsheets that can be detected only by spacecrafts traversing them, Alfven [54] (1979)pointed out that the whole space is likely subdivided in cells.

Howewer, Dolgov [55] pointed out that the behavior of the domain walls couldbe different from the leidenfrost process, or more precisely it could be the oppo-site: instead of repulsion, the layer could attract matter and antimatter towardsthe annihilation region. Actually, because electrons, positrons and neutrinos havelarger mean free paths than the domain walls thickness, the energy and pressure

2“Leidenfrost” is the German term used to indicate the process in which the water drops“bounce” upon a hot layer without touching it, sustained by their own vapor pressure.

41

C

density of the annihilation region decreases, increasing the diffusion of matter andantimatter towards each other and amplifying the efficiency of the annihilation.

In the framework of the inflation the problem may even be ill-posed, becausethe size of any conceivable antimatter domain would have been enlarged so muchthat the domain boundaries are well beyond the radius of the visible universe.

3.2.2 Antimatter domainsIt seems possible that mechanisms exist that could produce the formation of sep-arated homogeneous domains during the cosmic evolution, thus allowing the uni-verse to be matter-antimatter globally symmetric. This is an important point, be-cause it does not require any conservation law breaking, but we need an estima-tion of the domain dimensions. In addition the possibility exists to have antimatterconfined into condensed bodies like antistars in our Galaxy.

Uniform domains. Steigman [56] (1976) considered homogeneous and uniformdomains filled with matter or antimatter and concluded that they should be at leastof the scale of galaxy clusters, due to the constraints coming from the measuredgamma rays flux. The diffuse gamma ray background flux with energy E > 100MeV, of the order of 10−5 cm−1 sr−1 s−1, was used by Steigman to infer upper limitsfor the antimatter fraction in the Local Cluster. For the hot H II intergalacticmedium, his upper limit is ∼ 10−7, while inside our Galaxy the limits are morestringent: 10−15 for galactic clouds and inter-cloud medium, 10−10 in the halo.

In a recent paper, Dolgov [55] emphasizes that, even if the baryon/antibaryonasymmetry may be non-uniform in space, allowing for large antimatter domainsto exist in the universe, still there is no definite theory: neither the size nor thedistance of the domains can be predicted with any certainty. If Steigman [56] es-timated that the minimum distance has to be 10 Mpc, Cohen et al. [57] imposeda much stronger limit, under the assumption of a baryo-symmetric universe, con-cluding that the antimatter domains have to be very distant from us, at least fewGpc.

A key point is the smoothness of the cosmic microwave background (CMB)radiation, that requires density fluctuations below 10−4 at scales larger than 15Mpc, thus implying that, if existing, matter and antimatter domains must be inclose contact. But the annihilations products will carry away very efficiently theenergy from the contact region, because electrons, positrons and neutrinos havelarger mean free paths than the domain walls thickness. Hence the energy and

42

3.2 — Cosmic antimatter

pressure density of the annihilation region decreases, increasing the diffusion ofmatter and antimatter towards each other and amplifying the efficiency of the an-nihilation (in contrast with the leidenfrost process) [55].

Had this processes happened after the hydrogen recombination, the domainwalls regions would have been strong gamma ray sources. Non observation ofthis background means that any antimatter region must be near or beyond thehorizon. If the annihilation took place before the hydrogen recombination, therewould be some effect on the CMB energy spectrum, but no interesting limit canpresently be inferred from this effect.

Dolgov [55] reviewed few different models, amongst wich it appears that aviable model that could account for the existence of domains smaller than the vis-ible universe is based on “isocurvature fluctuations”: the initial baryon/antibaryonasymmetry was zero and started to rise only relatively late, due to fluctuations inthe baryons density. Baryon (antibaryon) rich regions cooled faster and diffusingphotons from hotter regions had the effect to drag those regions away, thus pro-viding a way to get separated matter and antimatter domains. In this model theannihilations could be weak enough to create a universe consisting of possiblylarge domains separated by thin baryon and antibaryon voids. Again, how largeare those domains?

Condensed bodies. The diffuse cosmic gamma rays background cannot put anequally stringent limit to the amount of condensed antimatter bodies, like anti-stars or anti-planetoids. Steigman [56] inferred for the antistars number an upperlimit of 107 in our Galaxy (i.e. 10−4 of the total stars number). This less stringentlimit is due to the fact that if antimatter is confined into compact structures likeantistars, it is well separated from the matter environment and is able to survivelonger than in gas clouds.

An antistar is not expected to be a strong gamma ray emitter, at least if itdoes not cross a galactic cloud neither it impacts on other condensed bodies. Du-darewicz and Wolfendale [58] (1994) gave as lower limit on the distance of thenearest antistar about 30 pc, and give a 10−3 upper limit on the fraction of antis-tars in M31. Howewer, they emphasize that the fraction could be of order unityat the Hubble radius, having superclusters and anti-supercluters sufficiently wellseparated, in order to restore the matter-antimatter global symmetry, even thoughthey conclude that a perfect symmetry appears impossible.

Recently, Khlopov [59] suggested the possibility that antimatter stars couldhave survived since the beginning of galaxy formation: they should be searched

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for in the globular clusters. In fact, condensation of an antimatter domain cannotform an astronomical abject smaller than a globular cluster, and isolated antistarsformation in the surrounding matter is impossible, since the necessary thermalinstability would finally favor the total annihilation. Thus antistars can form inan antimatter domain only, and they must constitute today a whole antimatterglobular cluster at least.

In this case, the antistars in the Galaxy could be found in the roughly sphericalglobular clusters halo around the Galactic center. The number of globular clustersis ∼ 102 and each cluster contains about 106 old stars. In addition, the antistars arewell separated from the rest of the Galaxy, and the upper limit of 107 calculatedby Steigman under the assumption of a unifomr distribution may be well under-estimated. For example Khlopov [60] states that the maximum antimatter windcompatible with the observed γ-ray flux is about 105 solar masses, and the flux atthe Earth is somewhat lower of the present limits (of order of 10−6).

3.3 Can we detect cosmic antimatter?

There are few ways in which cosmic antimatter may show itself. Indirect waysare based on the detection of annihilation radiation, or on the measurement of thehelicity of photons and neutrinos emitted during non CP invariant processes. Thedirect way is the detection of antinuclei among cosmic rays.

3.3.1 Indirect ways

Matter-antimatter bodies collisions. Sofia and Van Horn [61] (1974) consid-ered the collision between a star and antimatter “chunks” (m ∼ 1012 kg) and foundthat the annihilations due to the stellar wind are not important and that the anni-hilation rate is limited by the rate at which the matter is swept out by the chunkdue to the stellar radiation. Thus the impact with the star cannot be avoided andthe chunk penetrates into the star for ∼ 106 m before eventually evaporating com-pletely.

The chunk would become a hot and expanding antimatter bubble that willreturn to the stellar surface due to buoyancy in ∼ 102 s. Annihilations producecharged and neutral pions, and they decay to electrons/positrons of 50–70 MeVand gamma rays of ∼ 70 MeV (“prompt” photons). These photons suffer ∼ 10scatterings prior to escape, degrading to energies of hundreds of keV.

44

3.3 — Can we detect cosmic antimatter?

The inverse Compton scattering of those e+/e− in the stellar atmosphere (∼ 104

K) will produce a number of ∼ 60 keV photons with time constant of ∼ 103 s(“delayed” photons).

The signature of such a collision would then be a precursor burst emissionline at ∼ 500 keV (e+/e− annihilation) with a ∼ 70 MeV continuum lasting 0.1–1s, followed by the main annihilation burst at ∼ 100 keV (10–100 s) and by theinverse Compton photons (E . 100 keV, τ ∼ 103 s). This signature is not verydifferent from the time evolution of many gamma-ray bursts (GRB).

The cross section for the chunk capture with relative velocity v at infinite by astar with mass M and radius R isσ ∼ π(2GMR)/v2. A star like the Sun, for v ∼ 104

m s−1 has σ ∼ 1023 m2, and during 1 year sweeps up a volume V = σvt ∼ 1034 m3.In the Galactic disk, a sphere of radius 100 pc (V = 1056 m3) contains about 105

stars, then there will be a collision every ∼ 1016 years (much greater that theUniverge age).

A similar way was followed by Sofia and Wilson [62] (1976), who consideredthe collision between antimatter asteroids and the Sun, while Alfven [54] (1979)considered star-antistar collisions, possibly ending in “ambistars”, i.e. stars withmatter and antimatter whose annihilations contribute with the thermonuclear fu-sion processes to the total emitted power.

The collision with small (r < 10 km) bodies in the Solar system and the en-counter of clouds with antimatter clouds were considered by Rogers and Thomp-son [63, 64] (1980, 1982). They found that very small antimatter objects in theSolar system would produce a gamma ray flux of the order of 10−10 cm−2 s−1,too low to be detectable. In addition, different clouds will not merge. Instead athin “leidenfrost” layer will form (∼ 109 m, compared to ∼ 1015 m scale lengthfor clouds), and annihilation will burn only a very small (∼ 10−12) fraction ofthe total mass, resulting in less severe constraints for gamma rays emission thanthose considered by Steigman [56] (but this argument may not be valid, as Dolgov[55] recently pointed out). Very recently, Fargion and Khlopov [65] consideredantimatter meteorites in the solar system, obtaining a limit of 10−9–10−8 on theantimatter to matter ratio.

Atually all the interactions between antistars and the matter in our Galaxyare very weak until they remain in a bound system like a globular cluster (this isindeed the reason why they could have survived until now). Thus it make sense[66] to consider the possibility that antistars escape from their cluster, wanderthrough the Galaxy and possibly interact with the galactic matter.

Following Binney and Tremaine [67], a star (or antistar) can escape from a

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cluster in two ways: ejection, in which the escape speed is gained in a singleclose encounter with another star, and evaporation, in which several distant en-counters produce a gradual velocity increase. The former process is negligiblewhen compared to the latter, whose characteristic time can be roughly estimatedas tev ≈ 100 tre, where the mean relaxation time tre = 3 × 107–2 × 1010 years for aglobular cluster. Thus the number of stars in a cluster is:

N(t) = N0 exp (−t/tev) (3.1)

and the time t1 elapsed before one star can escape is found by solving the equationN0 − N(t) = 1, that is:

t1 = −tev ln[(N0 − 1)/N0] . (3.2)

The number of stars in a globular cluster is N0 ∼ 106, thus we get t1 = 3 × 103–2 × 106 years.

Because this time is much shorter than the age of the Galaxy, it is very likelythat, if at least one of the galactic globular clusters is made of antimatter, there aremany (possibly thousands) antistars wandering near the roughly spherical volumein the center of the Galaxy occupied by the globular clusters.

Those antistars may interact wih a matter cloud, star or smaller compact body.An important effect that has to be considered when gaseous material is accret-ing into an antistar is that the equilibrium between the gravitational and radiationpressure is reached at higher power than the “Eddington luminosity”

LEdd =4πGMmpc

σT≈ 1.3 × 1038 M

M�erg s−1 (3.3)

(M� = 2 × 1030 kg is the solar mass) because when annihilation photons areconsidered, the Thomson cross sectionσT has to be substituted with the relativisticKlein-Nishina formula.

This cross section, for photon energies much higher than the electron rest massenergy (mec2 = 511 keV), can be approximated by

σKN ≈ πr2e

ε

(ln 2ε +

12

), ε � 1 (3.4)

where re = 2.82 × 10−15 m is the classical electron radius and ε = (~ω)/(mec2)is the ratio between the photon energy and the electron rest mass energy. For(50–70) MeV photons, typically produced by the decay chains of the charged

46


and neutral pions arising from the nucleon/antinucleon annihilation, the Klein-Nishina formula gives for the cross section 46–61 smaller values than the classicalThomson value (σT = 8πr2

e/3 = 0.665 × 10−28 m2 = 0.665 barn).Thus, the annihilation photons pratically do not contribute to the total radiation

pressure, which still depends on those photons coming from “standard” processessuch as thermal radiation from the stellar surface, e.m. emission from the accretiondisk or diffused photons coming from the nucleosynthesis in the stellar core. In-stead, the annihilation photons may escape almost freely, taking away a consider-able fraction of the total emitted energy: the net effect is that the power emitted bya matter-accreting antimatter-star can become much greater than the usual accre-tion case, especially in the gamma-ray regime, where normal stars have negligibleemission.

Hence, a possible search for matter-antimatter accretion systems could be car-ried on by comparing optical, X-ray and γ-ray luminosities of Galactic sources:the signature would be an excess of emitted power in the γ-ray range [68].

On the other hand, the rare star/antistar head-on collisions would produce anintense energy release for few seconds, due to the surface annihilations, beforemerging and reaching a (probably super-Eddington) stationary luminosity [66].These close encounters may appear as GRB.

Polarization of e.m. emission. With a completely different approach, Cramerand Braithwaite [69] (1977) stressed out that in addition to direct annihilation,antistars may be distinguishable by the polarization properties of their electro-magnetic emission. In fact the ordinary thermonuclear reactions which occur instars systematically convert protons into neutrons through the weak-interactionprocess of β+ decay and electron capture.

When positrons (β+) are emitted, they are preferentially in a “right” elicitystate of strength v/c. Their bremsstrahlung emission is then right-circularly polar-ized. The same is true also for the forward going annihilation photon. In antistars,antiprotons are converted into antineutrons, producing electrons in a “left” elicitystate. The photons produced by those electrons are then left-circularly polarized.

During normal star processes, the photons take roughly 106 years to diffuseout of the star and they loose the initial polarization state, but during supernovaexplosion the photons produced by the 56Ni decay chain could be detectable. 56Nidecays by electron capture to 56Co, which decays by electron capture or positrondecay to 56Fe. The emitted positrons will radiate through bremsstrahlung polar-ized photons at the surface of the ejected material. These gamma rays may then

47

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escape and be detectable. Hence, a measurement of their degree of polarizationcould tell us the nature of their origin.

Supernovae neutrinos. Finally, Barnes et al. [70] (1987) suggested that the ini-tial neutrino bursts from a supernova could reveal whether the source is made ofmatter or antimatter. In the first (2–10) ms the neutronization reaction e− + p →νe + n produces a ∼ 1052 erg burst of ∼ 10 MeV neutrinos, whose flux cuts off

abruptly when the infalling matter achieves sufficient density to trap them. Thisdense infalling matter comes to thermal equilibrium, in which all neutrino flavorsare produced. Neutrinos and antineutrinos, approximatively in the same number,carry away 99% of the binding energy of the newly formed neutron star.

The electron neutrinos (and antineutrinos) suffer more scatterings than muonand tau neutrinos, and escape with a mean energy of ≈ 10 MeV, roughly half thanthe muon and tau neutrinos mean energy. On the other hand, the produced νe (andνe) number is roughly twice the νµ or ντ numbers. The net effect is that the energyof thermal neutrinos is equally divided amongst the three flavors.

In water Cerenkov detectors, like (Super)Kamiokande and IMB, all neutrinoflavors may interact by ν− e scattering, while electron antineutrinos have an addi-tional channel, the inverse β-decay on the hydrogen nuclei (the interaction crosssection for oxygen is negligible): νe + p→ e+ + n.

The ratio between the νe emitted during the burst phase and the number ex-pected from the thermal phase is r = 0.01–0.03 and the expected counting rate forthe 10 MeV electron neutrinos and the 20 MeV muon and tau neutrinos followsthe proportion:

νep : (all thermal ν, ν)e : (burst νe)e = 10 : 1.1 : 3.3r . (3.5)

If the progenitor star is made of antimatter, an important difference arises withthis picture: the initial burst is due to the antineutronization reaction e++p→ n+νe

and the burst contains electron antineutrinos rather than neutrinos. The νe crosssection in water is 18 times higher than the νe one, and the proportion (3.5) has tobe replaced with:

νep : (all thermal ν, ν)e : (burst νe)p = 10 : 1.1 : 60r . (3.6)

Thus (6–20)% of all oberved events from an antimatter supernova are expectedto occur within the first few milliseconds. In addition, the (νep) reaction produceselectrons with nearly isotropic cross section, while the elastic scattering (νee) is

48


peaked forward. Hence the expected signature for an antimatter source is an initialburst in a water Cerenkov detector with isotropic distribution.

From supernova SN 1987A, located in the Large Magellanic Cloud at ∼ 55kpc from Earth, 11 and 8 events were registered by Kamiokande II and IMB re-spectively. Due the too low statistics, it is impossible to distinguish between theexpected ∼ 2 (νep) events in case of antimatter star and the expected ∼ 0.1 (νee)events corresponding to a matter progenitor star. The first event registered byKamiokande is forward peaked and if it is attributed to the burst it may provethat SN 1987A was produced by a matter progenitor star (see [70] and referencestherein).

3.3.2 Direct detection

Direct detection of CR antihelium nuclei would be a very strong indication ofthe existence of cosmic antimatter: He could be of primordial origin or even beproduced by the antiproton fusion in the core of an antistar. Antihydrogen is ofcourse expected as the most abundant element of antimatter domains, but sec-ondary p production in CR interactions with ISM is an overwhelming source ofbackground for any conceivable cosmic antimatter search. The measurements ofpositrons are even less significative for this search, because positrons (and elec-trons) are commonly produced during the CR propagation in the ISM, and inaddition they loose energy very rapidly, making impossible to probe distances ofcosmological interest.

Recently, Khlopov [59] suggested the possibility that antimatter globular clus-ters could have survived since the beginning of galaxies formation. The idea thatone antimatter globular cluster may be present in our Galaxy refreshed the interestinto the possible observation of cosmic antimatter effects.

There are several possible ways in which such an antimatter globular clustercould manifest itself: its e.m. emission may show anomalous circular polarizationat all wavelengths, unrelated to any linear polarization which may be present (seeCramer and Braithwaite [69]); their antistar wind would hardly produce detectablereactions with the galactic ISM but they may interact with matter clouds, stars[54] or smaller bodies [61]. But the most important effect may be the detection ofantinuclei with Z > 2, that were produced only in negligible quantities during theprimordial nucleosynthesis.

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3.4 Antimatter cosmic raysIf a non zero amount of antimatter did survive the primordial annihilation, it isreasonable to expect that its composition will be similar to that of ordinary mat-ter. Hence, we may think about antimatter domains as composed by protons,positrons, antihelium nuclei, few isotopes of antihydrogen and antihelium, veryfew heavier nuclei (most of which would be 7Li).

Antistars could have formed inside antimatter domains exactly in the sameway as ordinary stars formed in matter domains. Thus we may expect that nuclearreactions happen inside antistars, of the same kind (apart from photon polarizationand antineutrino production, as seen in §3.3.1) of “normal” reactions: proton-proton and C-N-O chains.

As for matter domains which contains stars and galaxies, antimatter cosmicrays would be produced and accelerated inside antimatter domains, and a fractionof them (that depends on particle momentum and distance from us) could escapefrom those domains and reach our Galaxy, where they would continue to diffusefor a long time before annihilation can happen, because the interaction length(∼ 60 g/cm2 for protons and antiprotons) is greater than the escape length (∼5 g/cm2).

Thus, a finite probability exists that cosmic ray detectors in the Solar systemmay reveal cosmic antimatter. Actually, such instruments would certainly de-tect antiparticles produced by the interactions of cosmic rays with the interstellarmedium. This background can be completely overwhelming for certain kinds ofcosmic antiparticles, but this is not the case for antihelium and heavier antinuclei.

3.4.1 Positrons and antiprotons

Protons are the most abundant particles amongst cosmic rays, and CR electronsare about 1% of protons. Very likely their antiparticles would be the most abun-dant species in antimatter domains, and we may expect that they would constitutethe greatest antimatter fraction among cosmic rays detected on the Earth.

Other sources of antiprotons and positrons are the reactions of cosmic rayswith the interstellar medium. In fact, among the secondary particles produced byenergetic inelastic scatterings between two protons (the most abundant speciesboth in CR and ISM) or a proton and a nucleus, the most abundant ones aremesons, like pions and kaons, and antiprotons. In addition, while neutral pionsdacay into energetic photons (Eγ = 70 MeV in the CMS), charged pions decay

50

3.4 — Antimatter cosmic rays

into muons and electron-positron pairs (also produced by muon decays), so thatthe secondary production of antiprotons and positrons is a quite common process.

Like electrons, positrons have short radiation length and suffer heavy en-ergy losses during propagation in the ISM, hence there is no possibility that CRpositrons be of cosmic origin: they are produced by the interactions of cosmicrays with the interstellar medium.

On the other hand, antiproton production is hardly disfavoured for energiesbelow 2 GeV for kinematical reasons, so that the secondary antiproton spectrumshould have a characteristic peak around 2 GeV (for higher energies, it is theprimary proton spectrum that goes down as ∼ E−2.8, while the p production yieldis almost constant). Thus, cosmic antiprotons (and antiprotons from exotic sourcesas dark matter particle annihilation [71]) may be searched at low energies or abovethe secondary peak. Figure 3.1 shows the experimental results.

3.4.2 Antihelium and antinucleiAfter hydrogen, helium is the most abundant species in the universe (about 25%of the total baryonic mass, and about 20% of CR particles are He nuclei. 4Henuclei are of cosmic origin (produced during primordial nucleosynthesis) and ofstellar origin (result of the proton-proton nuclear chain). After their acceleration,helium nuclei propagate through the Galaxy for a time similar to the proton prop-agation time (about 2 × 107 years), and may interact with the interstellar medium,producing by spallation the 3He isotopes.

Similarly, we expect that the greatest fraction of CR antinuclei (after antipro-tons) is constituted by antihelium isotopes. Actually, the possible detection of Hewould be a striking demonstration that antimatter plays a cosmic role, as annihila-tion remnants wandering through the Galaxy or in form of antistars: the secondaryproduction probability of 3He by cosmic ray interactions with the ISM was esti-mated to be of order 10−13 [73] and the probability for secondary 4He is muchlower.

While antihelium may be of cosmic or (anti-)stellar origin, the detection ofantinuclei could be explained only as a demonstration that antistars do exist in ourGalaxy (or may be in some nearby galaxy). Among the possible isotopes, the bestcandidates for this antimatter search are 12C, 14N and 16O, because they are themost probable production results (after 4He) of nuclear reactions fueling antistars.

Figures 3.2 and 3.3 show the experimental upper limits found by balloon andspace experiments (AMS included, see §4.3) on the cosmic ray anti-helium to

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Figure 3.1: Experimental results on the CR antiproton flux [72].

helium flux ratio and antimatter (i.e. antinuclei) to matter flux ratio, respectively.

52

3.4 — Antimatter cosmic rays

(a)

(b) (c)

(c)(a) Buffington et al. 1981

(b) Golden et al. 1997

(c) Badhwar et al. 1978

(d) AMS−01 (1998)

(e) BESS (1993−2000)

(d)

(e)

Rigidity (GV)

An

tih

eliu

m/H

eliu

m F

lux

Rat

io (

95%

C.L

.)

10−7

10−6

10−5

10−4

10−3

10−2

1 10 102

Figure 3.2: Experimental results on the CR antihelium-to-helium flux ratio [74,75, 76, 77, 78].

53

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(b)

(c)

(c)

(c)

(c)

(d)

(d)

(e)

(a)

(a) Aizu et al. 1961(b) Greenhill et al. 1971(c) Golden et al. 1974(d) Smoot et al. 1975(e) AMS−01 (1998)

Rigidity (GV)

An

tim

atte

r/M

atte

r F

lux

Rat

io (

95%

C.L

.)

10−5

10−4

10−3

10−2

10−1

1 10 102

Figure 3.3: Experimental results on the CR antimatter-to-matter flux ratio foratomic numbers Z > 1 [79, 80, 81, 82, 83].

54

Chapter 4

The AMS experiment

The Alpha Magnetic Spectrometer (AMS) [84] is a particle detector that will beinstalled on the International Space Station (ISS) in 2005 (NASA shuttle flightUF-4.1) to measure Cosmic Ray (CR) fluxes for at least three years.

During the precursor flight aboard of the shuttle Discovery (NASA STS-91mission, 2–12 June 1998), the test detector AMS-01 was operated for about 180hours, collecting over one hundred millions CR events [77, 85, 40, 86, 87]. Sec-tion 4.2 below describes the AMS-01 detector, while the published Physics resultsfrom the STS-91 mission are summarized in section 4.3.

Section 4.4 describes the improved version of the detector, called AMS-02,that will operate aboard of the ISS. In addition to a refined silicon tracker and toredesigned time of flight (TOF) and anticoincidence systems, a proximity focus-ing ring imaging Cerenkov (RICH) detector will substitute the threshold Cerenkovcounter of AMS-01, and two additional subdetectors (a transition radiation detec-tor and an electromagnetic calorimeter) will be added to improve the proton toelectron separation capability of the instrument.

4.1 Particle identificationIn order to measure the fluxes of CR particles, the detector has to be able to mea-sure their charge, velocity and rigidity

R =pcze

= γβm0c2

ze, (4.1)

where p and ze are the relativistic momentum and the particle charge respectively,m0 is the particle rest mass, c is the speed of light in vacuo, the particle velocity is

55

T AMS

v = βc and γ = (1 − β2)−1/2 is the Lorentz factor.In principle, when z, β and R are known, it is possible to find the particle

rest mass m0 from the relation (4.1): the particle identification is complete. In realcases, the measurement uncertainties on z, β and R may allow mass discriminationbetween two given particle species only in some rigidity (or energy) range. Inparticular, it is easier to distinguish electrons from protons (mp ' 1837me) thanprotons from deuterons (md ' 2mp), and the latter are better separated than anyother nuclear isotopes of the same element.

4.1.1 Rigidity measurementA particle with charge z and rigidity R, moving through a region where a uniformmagnetic field B exists, will follow a helix with curvature radius

r =RBc

sin θ , (4.2)

where B is the field intesity and θ is the angle between the particle momentumand the magnetic field. If the field is not perfectly homogeneous, like the case ofthe AMS detector, the trajectory will be more complicated but, in any case, it willdepend only on the particle instantaneous rigidity and the local magnetic field.

Hence, if the field is known, in order to measure the particle rigidity one hasto reconstruct its trajectory, keeping into account the energy eventually lost inthe interactions with the detector (that will decrease the instantaneous curvatureradius).

The tracking system of AMS is a silicon detector with N planes (N = 6 forAMS-01 [§4.2.2], N = 8 for AMS-02 [§4.4.2]) placed in the inner bore of themagnet, that are able to measure the (x, y) coordinates of the crossing positionand the energy lost by the particle by ionization of the active material.

If the spatial resolution of the tracking system is σpos and the magnetic fieldstrength along the particle trajectory is smag =

∫B · d`, the relative uncertainty on

the rigidity is [88]:∆RR∝ Rσpos

smag

1√N + 4

(4.3)

(that is, the “deflection” η = 1/R is Gaussian distributed).It is customary to define the maximum detectable rigidity (MDR) the rigidity

for which the measurement uncertainty is 100% (that is ∆R/R = 1). The MDRfor AMS-01 for protons is 150 GV (see §4.2.2) and AMS-02 will reach 1 TV.

56

4.1 — Particle identification

When the particle rigidity is comparable with the MDR of the instrument (i.e. thedeflection tends to zero), it becomes likely that the wrong deflection sign will beattributed to the trajectory (“spillover”). The spillover is a problem for two rea-sons: first, it produces false “antiparticles” due to the wrong sign of the measureddeflection; second, it leads to a distortion of the measured rigidity spectrum, thatwill appear steeper due to the disappearance of events from the highest rigiditybins.

When the particle rigidity is known, in order to get its momentum it is neces-sary to measure its charge. The sign of the charge is found by looking at the trackcurvature and direction in the magnetic field, while the absolute value is given bythe energy lost in the active parts of the detector.

4.1.2 Charge measurementThe basic way to measure the particle charge is to measure its energy deposition inthe materials that constitute the active detectors. In AMS-01 this is possible withthe plastic scintillator counters of the TOF system (§4.2.3 and chapter 5) and thesilicon layers of the tracker (§4.2.2). With AMS-02, in addition to the TOF andtracker measurements, also the electromagnetic calorimeter (§4.4.7) the transitionradiation detector (§4.4.6) and the RICH (§4.4.5 and chapter 6) will measure theenergy lost by the particle traversing the detector.

The energy lost by a particle with charge z and velocity βc after a path lengthdξ = ρ dx inside a medium with density ρ, atomic and mass numbers Z and Arespectively, is given by the corrected Bethe-Bloch formula [5]:

− dEdξ

= KZA

z2

β2

[12

ln2mec2(βγ)2Tmax

〈I〉2 − β2 − δ2

](4.4)

where K = 0.307075 MeV g−1 cm2, 〈I〉 is the mean ionization energy of the medium,δ is the “density effect” correction (usually computed using the Sternheimer parame-trization [89, 90]), and

Tmax =2mec2β2γ2

1 + 2γme/M + (me/M)2 (4.5)

(Tmax ≈ 2mec2β2γ2 for all CR particles but electrons). The “shell correction” to(4.4) is omitted here because its small effect is sensible only at energies below theAMS range [5].

57

T AMS

For electrons and positrons the argument of the logarithm of formula (4.4)in the ultrarelatvistic case becomes proportional to γ3/2 [91], but the dominantprocess is the bremsstrahlung. The energy loss is described by equation (2.2), thatwe rewrite here in a simpler form:

(− dE

dx

)

el= NE0Φrad , (4.6)

where N is the atomic density (in cm−3) of the material, E0 is the initial electron(positron) energy and Φrad is a function of the material only [92].

Formula (4.4) can be used to infer the particle charge |z| from the energy de-position measurements of the TOF and tracker layers, and inside the calorimeter,if the particle velocity β is known. In order to measure the charge sign, it is nec-essary to have a measurement both of the particle direction and curvature. Thecurvature is measured by the tracker and its direction can be found by the TOFsystem.

4.1.3 Velocity measurementThe particle velocity can be measured in two ways by AMS-02: through the timeof flight measurement and the Cerenkov cone opening angle.

The first method is used by the TOF system: a particle with velocity v = βctakes a time t = `/v to go along the path ` = L/ cos θ between upper and lowerTOF planes (L is their distance and θ is the trajectory colatitude angle). Hence,the time of flight is:

t =L

βc cos θ(4.7)

and its uncertainty σt will be Gaussian. The uncertainty on β will be:

σ2β =

L2

c2

σ2

t

t4 cos2 θ+σ2θ sin2 θ

t2 cos4 θ

' L2

c2

σ2t

t4 cos2 θ, (4.8)

because the second term inside the parentheses can be safely neglected both inAMS-01 and AMS-02 thanks to the very good angular resolution of the tracker.

The time resolution of the TOF system is of order of 0.1 ns, hence the timemeasurement can be used to infer the particle velocity up to about β ≈ 0.95. Onthe other hand, a direct measurement of β can be done by the RICH detector ofAMS-02, that will have ∆β/β ≈ 0.1%.

58

4.2 — The AMS-01 detector

The Cerenkov radiation, produced by particles crossing a medium with ve-locity greater than the light speed in that medium, is emitted at an angle α withthe particle momentum that depends only on the particle velocity and the mediumrefractive index (§6.1):

cosα =1βn

. (4.9)

Hence the threshold below which there is no Cerenkov emission at all is βmin =

1/n, and the measurement uncertainty is:

σ2β =

σ2n

n4 cos2 α+σα sin2 α

n2 cos4 α. (4.10)

At very high energies, the particle velocity could in principle be measured bymeans of the transition radiation opening angle χ ' 1/γ = (1 − β2)1/2, hence:

σ2β =

χ2

1 − χ2σ2χ or σγ =

σχ

χ2 .

Howewer, this angle is very small and in pratical applications it is very difficult tobe measured. Instead, a common practice is to measure the energy deposition inthe detector, that has different shapes for particles above and below the threshold[93] (the transition radiation photons have energy that depends on the βγ of theincident particle and contribute to the detected signal in addition to ionizationenergy losses).

4.2 The AMS-01 detector

Figure 4.1 shows the detector AMS-1 that was flown aboard of the shuttle Dis-covery on 2–12 June 1998. The core of the instrument is a permanent Nd-Fe-Bmagnet enclosing the tracking system (six silicon planes) and an anticoincidencecounter (ACC) system. Above and below the magnet, four layers of scintillatorcounters give the fast trigger to the experiment and measure the time of flight(TOF) of the particles traversing it, while an aerogel threshold Cerenkov (ATC)counter allows to discriminate between protons and electrons up to a rigidity of3.5 GV.

59

T AMS

Figure 4.1: The AMS detector for the STS-91 mission (AMS-01).

4.2.1 The magnet

The AMS-01 permanent magnet is a Nd-Fe-B cylinder whose axis defines thedetector z-axis. It produces a nearly uniform field along a transversal direction,and the magnetic vector B defines the AMS x axis. The y axis is defined bycompleting the right-handed unit vectors triplet.

The cylindrical magnet shell has a magnetization vector with constant modu-lus and angular direction α in the (x, y) plane given by:

α = 2φ +π

2(4.11)

where φ is the longitude angle of cylindrical coordinates [94]. This configurationproduces an internal field of intensity:

B = Br lnri

ro(4.12)

60


Z Layers

Glue Layers

NdFeB Block

B

1 2 3 4 5 67

89

1011

12131415161718

1920

2122

2324

25

2726

2829303133323435363738

3940

4142

4344

4546474849505152

5354

5556

5758

596061 62 63 64

Z

X

Y

r1

ϕ

2r

Figure 4.2: The AMS-01 magnet block numbering (left) and field configuration(right).

Z (cm)

18001600140012001000800600400200

0 −60 −40 −20 0 20 40 60

B

(G)

x

Figure 4.3: The AMS-01 magnetic field Bx component as function of z.

where Br is the residual magnetic flux density of the ring and the inner and outerradii are ri = 55.7 cm and ro = 64.9 cm, respectively.

In order to build the magnet structure, the first step was to produce 2 cm thickNd-Fe-B layers with uniform magnetization M. Then a series of small cylider

61

T AMS

sections (≈ 5 × 5 cm2) were cut away with 64 different orientations with respectto M. Each block has then a uniform magnetization Mi and can be glued to blocksi− 1 and i + 1 in order to produce a ring with magnetization directions αi given byequation (4.11). The whole magnet is made up of several glued rings (figure 4.2),reaching the height of 80 cm.

The magnetic field produced in the bore of the magnet is roughly constant(Bx ≈ 1.6 kG) within ±30 cm along z axis, and decreases rapidly outside the bore(for |z| > 40 cm), reaching the level of 200 G for |z| ≈ 65 cm (see figure 4.3).

The nominal bending power of the magnet is BL2 = 0.14 T m2, when consid-ering the average Bx over |z| < 71.4 cm [94]. Its geometrical acceptance is 0.82m2 sr and its weigth is 1998 kg.

4.2.2 The tracking system

The silicon tracker is composed of 300 µm thick double-sided micro-strip sensorsof area 40.10×72.04 mm2, based on the design used by the micro-vertex detectorsof ALEPH and L3 experiments at CERN, that were successfully operated withthe Large Electron-Positron (LEP) collider (see [95] and [94]). The readout strippitches are 110 µm along the y direction (p-side) and 208 µm along the x direction(n-side), respectively the bending and non-bending directions.

The silicon sensors are grouped together in ladders (7 to 15 sensors) of dif-ferent length, assembled on 6 ultra-light honeycomb planes (see figure 4.4). Forvertical tracks, the total amount of matter of the 6 planes is about 0.02 − 0.03radiation lengths.

The tracker was not fully assembled for the test flight in 1998: in total therewere 28 ladders on the inner planes and 34 ladders on the outer ones. The ladderswere read by 168 electronic boards featuring charge measurements via a sample-and-hold technique with 64-channels readout chips whose linearity was good up to75 MIP signals. Analog output signals from such boards were sent to 12-bit low-power fast ADCs installed on the electronic boards in charge of data reductionand pedestal subtraction.

The particle crossing position is determined by a clustering algorithm thatfinds the “center of gravity” of the energy loss measured by a set of strips. Forexample, the x coordinate of the crossing position in a given plane is computedusing the formula:

x =ΣiAixi

ΣiAi, (4.13)

62


Figure 4.4: The AMS-01 tracker.

where Ai is the amplitude of the signal recordered by the strip at the position xi.

In order to select only small sets of strips for this weighted mean, the trackerdata reduction (TDR) electronics perform a search of “seed” strips using a thresh-old of 3.5σped, then consider all neighboring strips with signal greater than 1σped.

The n-side strips have a noise level about 50% higher than the p-side level, re-sulting in a signal-to-noise ratio for the non-bending direction (x) approximativelyhalf of that of the bending direction (y).

The rigidity resolution of the tracker (shown in figure 4.5) is limited by mul-tiple scattering at low energies (up to about 10 GeV for protons), while at highenergies it is limited by the magnet bending power and the tracker spatial resolu-tion. The momentum resolution is at the 7% level between 1 and 10 GeV/c, whilethe MDR is about 150 GV for protons.

63

T AMS

∆

Proton beam test

Data (Z=1)

MC

R (GV)

R/R

101010

0.2

0.4

0.6

0.8

1

2

Figure 4.5: The AMS-01 tracker rigidity resolution predicted by Monte Carlosimulations, compared to the measurements done with a proton beamand with CR protons.

4.2.3 The time of flight system

The TOF system [96] was completely designed and built in the INFN Laboratoriesin Bologna. Its main goals are to provide the fast trigger to AMS readout elec-tronics, and to measure the particle direction, velocity (β), position and charge.In addition, it had to operate in space with severe limits for weight and powerconsuption.

Each TOF plane consists of 14 counters (Bicron BC408 plastic scintillator)1 cm thick covering a roughly circular area of 1.6 m2. The scintillation light isguided to 3 Hamamatsu R5900 photomultiplier tubes (PMT) per side, whose sig-nals are summed together to provide a good redundancy and light collection ef-ficiency. The total power consumption of the system (112 channels, 336 PMTs)was 150 W, while its weight (support structure included) was 250 kg.

64


Figure 4.6: The upper two planes of the AMS-01 time of flight system.

Time of flight resolution. The single channel time resolution is [96]:

σ(x) =

√σ2

1

N+σ2

2x2

N+ σ2

3 , (4.14)

where x is the distance of the particle crossing point from the PMT, N is the num-ber of photons which convert into electrons (“photoelectrons” for brevity) on thePMT photocathode, σ1 depends upon the PMT signal shape and the trigger elec-tronics, σ2 takes into account the dispersion in the photon path lengths and theconstant term σ3 depends on the electronic noise at the low threshold discrimina-tor input and on the reference time dispersion on each channel.

The overall time resolution of a plane can be determined by measuring thetime of flight of ultrarelativistic (β . 1) particles between two given planes, aftercorrecting for the track length. The time dispersion is expected to decrease withthe nuclear charge Z, due to the large number of photoelectrons produced by nu-clei with high atomic number, until it reaches the minimum value σ3. Figure 4.7

65

T AMS

25

50

75

100

125

0 1 2 3 4 5 6 7 8 9 10

Charge

σ pl (

ps)

Figure 4.7: AMS-01 TOF: mean single plane time resolution as function of theparticle charge derived from STS-91 data [97].

shows the average single plane time resolution as function of the particle charge,using data from the STS-91 flight: the horizontal line show that the limiting levelσ3 is 88 ps [97].

The velocity resolution of the TOF system, σ(β)/β . 3%, allows to discrimi-nate p/e+ and p/e− up to a rigidity of 1.5 GV.

Particle separation. One of the main purpose of the TOF system is the mea-surement of the time of flight of the particles traversing the detector with a resolu-tion sufficient to distinguish upward from downward going particles: an “upward-going” helium nucleus wrongly labelled “downward-going” would be interpretedas an “downward-going” anti-He nucleus.

The average time of flight of the particles which traverse the detector is ofthe order of 5 ns, while the time measurement has a resolution σt . 120 ps,independent from the rigidity. Hence the distribution of β−1 for all STS-91 events(figure 4.8) shows two populations peaked at ±1, with Gaussian profiles towardszero (where no physical particle is expected). No ambiguous event was detected.Thus the probability to mistake the particle direction due to non-Gaussian effectsis well below 10−8, the level reachable with the STS-91 statistics.

In addition to the capability to separate downward-going from upward-goingparticles, one goal of the TOF system was to provide a special flag for ions at thetrigger level. Accordingly, it was designed to distinguish in a fast and efficientway cosmic ray protons from other nuclei.

66


Figure 4.8: The distribution of β−1 for all (unshaded) and selected He nuclei forthe antimatter search analysis (shaded) [98].

The TOF system provides a measurement of the absolute charge of the cross-ing particle in addition to the tracker, even if, due to the strong constraints aboutpower consuption, the TOF front-end electronics was not optimized for energydeposition measurements.

The charge measurement was realized through a “time-over-threshold” method,whose response is proportional to the logarithm of the deposited charge. Thismethod results in a good separating power (≈ 5 × 10−3) between singly and dou-bly charged particles but has a poor charge resolution for |Z| > 2.

The stability of the charge measurement was very good for all the 112 TOFchannels, but five channels, as shown in figure 4.9 [97].

4.2.4 The anticoincidence systemThe AMS-01 anticoincidence system has 16 plastic scintillator counters (of thesame material as the TOF ones) whose shape is a cylinder section, placed alongthe inner wall of the magnet, containing the 4 inner tracker planes (figure 4.10).Each paddle is 1 cm thick, 20 cm large and 80 cm high.

The counters are read by one photomultiplier in each side of the same type

67

T AMS

plane 1 plane 2 plane 3 plane 4C

harg

e di

sper

sion

(rm

s, %

)

TOF channel

1

20 40 60 80 100

10

Figure 4.9: TOF charge measurement stability during the STS-91 flight [97].

of the TOF ones (Hamamatsu R5600U), connected to the scintillator through abundle of optical fibers. Their signal is used as veto by the level-1 trigger logics,in order to avoid events produced by the interactions of CR particles in the magnetstructure (giving secondaries of opposite charges that are deflected towards upperand lower TOF planes).

As side effect, the ACC veto rejects also “normal” events whose interactionswith the TOF or tracker planes produced δ-rays hard enough to reach the ACCcounters. This introduces a detector inefficiency that depends upon the particlecharge and crossing positions. The maximum allowed energy for δ-ray electronsor positrons is Emax = 2β2γ2mec2 but their production spectrum is very steep(P(E) dE ∝ E−2 dE), so high energy δ-rays are rare [88].

Due to their small curvature radius (3 mm for a 10 keV electron in a 1 Tmagnetic field), δ-rays emitted at angles not too large with respect to the magneticfield direction will follow the field lines untill reaching a mirror point or a materialwhere they stop or annihilate. Their large range is thus a problem, because theycan decrease the detection efficiency in two ways: by hitting one of the ACCcounters (producing a veto at the trigger level), or by hitting one or two trackerplanes. The latter case may produce events that are not well fitted with a singletrajectory, hence they may be discarded by the “track quality cuts” during theoff-line analysis.

68


Figure 4.10: Part of the AMS-01 anticoincidence system.

4.2.5 The threshold Cerenkov counter

The threshold Cerenkov counter mounted below the magnet of AMS-01 (fig-ure 4.11) consists of two layer of 8 × 10 (upper) and 8 × 11 (lower) aerogel cellswith refractive index n = 1.035, directly attached to the universal support structure(USS, figure 4.12), not to the magnet like the other subdetectors.

Each 11×11×8.8 cm3 cell consists of eight 1 cm thick slabs, it is wrapped withthree 250 µm reflecting Teflon foils and it is viewed by one Hamamatsu R5900PMT placed right below (figure 4.13). A wavelength shifter is used to convert300 nm photons to 420 nm photons matching the maximum efficiency range ofthe phototubes. The upper plane cells are placed over the separation between thelower cells, in order to reach a good mechanical rigidity and to avoid “holes” inthe ATC acceptance.

The ATC is used to extend the separation capability between protons (antipro-tons) and positrons (electrons) up to 3.5 GeV. The number of photons produced

69

T AMS

Figure 4.11: The AMS-01 aerogel threshold Cerenkov counter layers (only halfof them is displayed).

by a particle with charge Z traveling for a distance Laero inside the aerogel (withvelocity β above the Cerenkov threshold) is:

Nph ∝ LaeroZ2(1 − 1

n2β2

), (4.15)

where n is the refractive index of the radiator. Aerogel was chosen because its re-fractive index n = 1.035±0.001 allows the discrimination of protons and electronsup to 3.5 GeV/c, still yielding an acceptable number of produced photons.

A calibration carried on with p ≥ 15 GeV/c protons (β ≥ 0.99) gave the meanvalues of the number of detected photoelectrons: Nphel = 3.51± 0.02 for the upperATC layer and Nphel = 4.02 ± 0.02 for the lower layer. The channel to channeldispersion is (10–15)%.

70


Figure 4.12: The AMS-01 detector inside the Universal Support Structure.

4.2.6 The AMS-01 trigger

The trigger is the digital signal that starts the data acquisition (DAQ) chain. Byextension, this terms is often used to represent the logic conditions required for itto be generated by the trigger electronics.

In high energy Physics experiments it is customary to define three types oftrigger logics, depending on the type of data they act on: the first level trigger(including a pre-trigger called fast trigger) is generated imposing conditions onfast signals only (i.e. on logic signals coming from discriminators), the secondlevel trigger is generated after the first level trigger if digitized data of any sin-gle subdetector satisfy the required conditions, and the third level trigger followsthe second level trigger signal when the digitized data of the whole detector arechecked against the desired set of conditions.

The AMS-01 trigger has no second level logics. The fast trigger (FT) logicsprocess the scintillator data and provide, in about 50 ns, the “time zero” for the

71

T AMS

aero

d PMd

PM LayersTeflon

WavelengthShifter (PMP)

PMT

L

PMT

dPMT

(3)

Light Guide

Figure 4.13: The AMS-01 ATC cell.

time-of-flight measurement. Then the first level trigger rejects events with hits onthe anticoincidence counter system and enhances the fraction of particles crossingthe tracker planes through the analysis of the pattern of hit counters in the upperand lower TOF planes (“matrix” condition). Finally, at the last level (the third onebecause global digitized data are checked) the trigger logics suppress spurious fasttriggers and find preliminary good tracks on the silicon tracker.

In order to characterize the effect of every trigger condition, during the STS-91 flight AMS-01 collected one event requiring the fast trigger alone every 1000“normal” triggered events. This sample (called prescaled events data set) can beconsidered unbiased with respect to the FT efficiency, to be measured in a differentway, and was used to measure the effect of all other trigger conditions on cosmicray protons, helium nuclei and electrons1 (figure 4.14).

The FT signal is generated when at least one counter side in 3 (over 4) differentTOF planes produces a signal above a threshold corresponding to ≈ 40% of aminimum ionizing particle (MIP) crossing the counters center. The efficiency ofthe fast trigger could be measured with the same data taken during the STS-91mission using two different ways: either by looking at events triggered by a givenset of 3 TOF planes and searching for a signal in the other (“spectator”) planethat would pass the required threshold, or using as unbiased sample the signals

1For ions with Z > 2 the prescaled events gave too low statistics.

72

4.3 — Results of the STS-91 mission

6

1 2 3 4 50

10

10718000

(100%)

714309

(99.5%) (85.1%)

610931 256000

(35.7%) (32.0%)

229776 100608

(14.0%)

all t

rigge

rs

4/4

TO

F p

lane

s (f

ast t

rigge

r O

K)

mat

rix c

ondi

tion

no a

ntic

oinc

iden

ce v

eto

leve

l 3 T

OF

OK

leve

l 3 tr

acke

r O

K

5

Pre

scal

ed e

vent

s

Figure 4.14: The AMS-01 trigger conditions applied off-line on prescaled events.

produced by particles that did not produce the trigger.The latter can be done by exploiting the characteristics of the TOF electronics,

sensitive to all particles impinging on the detector in an interval of about 16 µsaround the trigger signal. Up to eight hits can be registered by each channelwith a time resolution of 1 ns and a full charge measurement. The analysis ofthese unbiased data provided the instantaneous rate of particles, the dead time andaccidental rate, in addition to the total FT efficiency [99].

The background can be estimated by checking the consistency of the TOFdata and the trigger mask, and comes out to be about 0.5% of the fast triggers(due to electronics noise). This background is completely eliminated in the lastlevel trigger by requiring the coincidence of both sides of the same counter.

4.3 Results of the STS-91 mission

AMS-01 was successfully flown aboard of the space shuttle Discovery on June1998 for a ten days mission. The instrument was operating for about 180 hoursand collected over hundred millions events. The Collaboration has published theresults of the analysis about the cosmic antimatter limits [77] and the flux in the

73

T AMS

low orbit environment of protons [85] [86], electrons and positrons [40], and he-lium [87]. Results are summarized in ref. [100].

4.3.1 Primary CR spectraThe primary cosmic rays are dominated by the proton component, as seen in thefigure 4.15, that shows the primary spectra of protons, He nuclei, electrons andpositrons measured by AMS-01 [86, 87, 40]. The protons differential spectrummeasured by AMS-01 can be fit with a power law in rigidity for R > 10 GV withthe form

φ(R) = φ0 R−γ ( m−2 s−1 sr−1 MV−1) (4.16)

with [85]:

γ(p) = 2.79 ± 0.012 (fit) ± 0.019 (sys)

φ(p)0 = 16.9 ± 0.2 (fit) ± 1.3 (sys) ± 1.5 (γ) ( GV2.79 m−2 s−1 sr−1 MV−1) .

(4.17)

In addition, the He spectrum for 20 < R < 200 GV can be fit by a power law with[87]:

γ(He) = 2.740 ± 0.010 (stat) ± 0.016 (sys)

φ(He)0 = 2.52 ± 0.09 (stat) ± 0.13 (sys) ± 0.14 (γ) ( GV2.74 m−2 s−1 sr−1 MV−1) .

(4.18)

Figure 4.16 shows the comparison between the AMS-01 protons spectrum andfew recent balloon measurements. The agreement is very good between AMS-01and BESS (the most recent measurement), but elder instruments gave differentspectra, with experimental data points that are generally lower (even by a factor2) than those of AMS-01 and BESS [86].

The left plot of figure 4.17 shows the number of collected |Z| = 2 particlesas function of the rigidity: no antihelium has been found up to 150 GV. The cor-responding upper limit on the fraction of cosmic ray antihelium is shown in theright part.

Figure 4.18 shows the measured electron and positron spectra, with the simu-lated background from protons. While this background makes impossible to saysomething about the positron spectrum above 1.5 GeV, the measurement of theelectron spectrum is very good up to about 30 GeV. AMS-01 accumulated a bigamount of data, and the spectra of electrons and positrons have unprecedentedsmall error bars.

74


10−4

10−3

10−2

10−1

1

10

102

103

104

10−1

1 10 102

Ek /A (GeV)

F (

m−

2 sr−

1 s−

1 GeV

−1 A

)

AMS−01 protonsAMS−01 He nucleiAMS−01 electronsAMS−01 positrons

Figure 4.15: Primary fluxes of CR protons, He nuclei, electrons and positronsmeasured by AMS-01 [86, 87, 40].

The e− and e+ spectra are shown again in figure 4.19, where it appears clearlyhow the fraction of positrons depends on the energy.

75

T AMS

This experimentCAPRICE [12]LEAP [13]

This experimentBESS [14]IMAX [15]

Flu

x *

E K

2.5

EK (GeV)

a)

b)

2

3

4

5

6

7

2

3

4

5

6

7

20 40 60 80 100 120 140 160 180 200

Figure 4.16: AMS-01 proton flux compared with balloon experiments [86].

76

4.3 — Results of the STS-91 missionE

ven

ts

1

10

10 2

10 3

10 4

10 5

-150 -100 -50 0 50 100 150

HeHe2.86×106 events0 events

Sign×Rigidity GV

AMSSTS - 91

10-4

10-5

10-6

3 10 70

An

tih

eliu

m/H

eliu

m U

pp

er L

imit

RmaxGV

Excluded

AMSSTS - 91

|Z| = 2

Figure 4.17: The AMS-01 |z| = 2 sample [77] (left), and 95% C.L. upper limit tothe relative flux of antihelium to helium [77] (right).

e- + BackgroundBackground

e+ + BackgroundBackground

Ek (GeV)

Flu

x (m

sec

sr

MeV

)2

-1

10-6

10-5

10-4

10-3

10-2

10-1

1

10-6

10-5

10-4

10-3

10-2

10-1

10-1

1 10

Figure 4.18: AMS-01 electron and positron fluxes compared to the expectedbackground [40].

77

T AMS

e-e+

e/(

e+

+a)

+e

E (GeV)

-

k

E (GeV)k

)F

lux

(m

b)

2 sec

sr

MeV

)-1

10 -6

10 -5

10 -4

0

0.1

0.2

0.3

0.4

10

0.5

-3

0.6

10 -2

1

10 -1

1

1 10

Figure 4.19: AMS-01 primary fluxes of electrons and positrons (a) and relativeabundances (b) [40].

78


4.3.2 Secondary spectraThe wide range of geomagnetic coordinates sampled by AMS-01 during the STS-91 shuttle flight (θM < 75◦) allowed for a precise measurement of the dependenceof the secondary cosmic ray component on the geomagnetic field.

Figure 4.20 shows the measured upward and downward proton flux at differentgeomagnetic latitudes. It is evident that for small latitudes (i.e. in the equatorialregion) the primary component is damped at low energy by the Earth magneticfield, that reflects back the incoming particles with rigidity below a cut-off levelthat is near 10 GV. This level decreases for increasing latitudes.

Howewer, the spectrum shows a dip and starts to rise again below few GV. Inaddition, this second part of the spectrum is the same for upward and downwardprotons, indicating that it is due to particles that are looping in the geomagneticfield. Indeed below the geomagnetic cutoff, the secondary fluxes agree in therange 0 ≤ ΘM ≤ 0.8 [85]. It was possible to back-trace those particles to seeif they were coming from the atmosphere (hence secondary products) or fromoutside (primary component): they are particles of secondary origin, trapped inthe geomagnetic field.

Figure 4.21 shows the measured helium flux at different geomagnetic latitudes.It is again evident the damping below about 10 GV in the equatorial region, witha cut-off level that is decreasing with increasing latitudes. Also the He shows asecond spectrum of secondary origin, as can be inferred from the fact that most ofthe second component nuclei are 3He isotopes (figure 4.22).

Figures 4.23 and 4.24 show a similar effect for electrons and positrons: belowa geomagnetic latitude cut-off in rigidity, a second spectrum emerges that is dueto secondary particles looping in the Earth magnetic field.

79

T

AM

S

0.9 < θM <1.00.8 < θM <0.9

Upward

10-5

10-4

10-3

10-2

10-1

10-1

1 10 102

f)e)d)

c)b)a)

0.7 < θM < 0.80.6 < θM < 0.70.5 < θM < 0.60.4 < θM < 0.50.3 < θM < 0.4

Upward

Kinetic Energy (GeV)10

-11 10 10

2

0.2 < θM < 0.30 < θM < 0.2

Upward

10-1

1 10 102

1 < θM < 1.10.9 < θM < 10.8 < θM < 0.9

Downward

0.7 <θM <0.80.6 <θM <0.70.5 <θM <0.60.4 <θM <0.50.3 <θM <0.4

Downward0.2 < θM < 0.30 < θM < 0.2

Downward

Flu

x (m

2 sec

sr

MeV

)-1

10-5

10-4

10-3

10-2

10-1

1

Figure 4.20: AMS-01 measured proton spectra at different geomagnetic latitudes [85].

80


Rigidity (GV)

Flu

x (m

2 sec

sr

GV

)-1

0 < ΘM < 0.40.4 < ΘM < 0.80.8 < ΘM

10-3

10-2

10-1

1

10

10 2

1 10 102

Figure 4.21: AMS-01 measurements of helium flux at different geomagnetic lat-itudes [87].

81

T AMS

Rigidity (GV)

β

Primary Second

3He4He

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

10-1

1 10 102

Figure 4.22: AMS-01 3He and 4He measurements show that the secondary he-lium flux is dominated by 3He [87].

82


Ek (GeV)

Flu

x (m

2 sec

sr M

eV)-1

a) e- b) e-

c) e+ d) e+

0.0 < ΘM < 0.30.3 < ΘM < 0.60.6 < ΘM < 0.8

0.8 < ΘM < 0.90.9 < ΘM < 1.01.0 < ΘM

0.0 < ΘM < 0.30.3 < ΘM < 0.60.6 < ΘM < 0.8

0.8 < ΘM < 0.90.9 < ΘM < 1.01.0 < ΘM

10-5

10-4

10-3

10-2

10-1

10-5

10-4

10-3

10-2

10-1

10-1

1 10 10-1

1 10

Figure 4.23: AMS-01 measured downward fluxes of electrons (a,b) and positrons(c,d) [40].

83

T AMS

Ek (GeV)

Flu

x (m

2 sec

sr M

eV)-1

a) e- b) e- c) e-

d) e+ e) e+ f) e+

0.0 < ΘM < 0.3 0.3 < ΘM < 0.7 0.7 < ΘM < 1.0

0.0 < ΘM < 0.3 0.3 < ΘM < 0.7 0.7 < ΘM < 1.0

10-5

10-4

10-3

10-2

10-1

10-5

10-4

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Figure 4.24: AMS-01 measurements at different geomagnetic latitudes of down-ward (full circles) and upward (open circles) going electrons (a,b,c)and positrons (d,e,f) [40].

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Figure 4.25: The detector that will be installed on the ISS (AMS-02).

4.4 The AMS-02 detectorThe AMS-02 detector (figure 4.25) will be installed aboard of the ISS in 2005(NASA shuttle flight UF-4.1), where it will operate for at least 3 years. Scientificgoals of AMS-02 are:

• improved measurements of the antimatter fraction in cosmic rays;

• perform a search of exotic particle annihilation signatures over the wideenergy range (1–103) GeV in protons, electrons and γ-rays spectra;

• refine experimental results concerning CR spectra with a large acceptance,long duration mission.

This detector will have a very long exposure time (at least 3 years), it willtraversed by a significant sample of high energy particles, up to few TeV per

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nucleon. Hence its rigidity resolution must be improved with respect to AMS-01, in order to reach a MDR high enough to cover the range where a detectableflux of primary cosmic rays is expected in the whole time window.

The AMS-02 detector is based on a superconducting magnet generating ahigher magnetic field than the AMS-01 permanent magnet. In addition the sil-icon tracker will have a larger area, with 8 indipendent measurements instead of 6and improved spatial resolution.

The TOF system will be similar to AMS-01: the main differences are thenumber of counters, that has been decreased to save power and weight, and thePMT model, that must operate in a very high magnetic field. In addition, the shapeof the light guides was adjusted on each counter in order to minimize the anglebetween the residual field and the PMT axes. The same kind of phototubes willbe installed also on the ACC counters.

The ATC will be substituted by a RICH counter, in order to increase the ve-locity and charge resolution, and two completely new detectors will be added: aTRD on the top of AMS-02 and an electromagnetic calorimeter below the RICHwill improve the detector sensitivity to high energy electrons and γ-rays.

4.4.1 The magnet

The AMS-02 superconducting magnet [101] consists of a pair of large racetrackshaped Helmoltz coils that generate the majority of the dipolar magnetic field,plus 12 smaller racetrack coils circumferentially distributed (at angles ±60, ±72,±84, ±96, ±108, ±120 degrees) whose aim is to increase the magnetic field in-tensity and to reduce the stray field, in order to limit the torque resulting from theinteraction with the geomagnetic field (figure 4.26).

All coils, built in the United Kingdom, are situated inside a vacuum tank andoperate at 1.8 K with superfluid helium. The free bore of the system has a diameterof 1.1 m, while the external diameter of the vacuum tank is 2.7 m, with height of1.55 m.

The coils are electrically connected in series, and operate with a current of 459A in the “persistent mode”: once a constant current has been established, a super-conducting switch will cut away the power supply and the current will circulatewith zero energy dissipation. At this stage no power is required to mantain thecurrent loop.

Howewer, power will be required to turn on/off the current and to mantainthe system at low pressure. If any part of the superconducting material is heated

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Figure 4.26: 3D artist view of the AMS-02 magnet system [101].

above its critical temperature, the current energy will be dissipated by this portionof normal conducting material: a “quench” occurs. The dissipation will heat theother parts and all the energy will be very soon converted into head, potentiallycausing damages to the structure. The system has been designed to be able to startoperation again after a quench with a delay of three days.

The conductor is the same for all coils: a NbTi/Cu superconducting wire em-bedded in a high purity Al stabilizer. A total of 55 km of strand is required for thewhole system. The operating temperature is below 10 K, and it is reached with2500 liters of liquid helium (the He vessel is filled with superfluid He at 1.8 Kbefore the launch).

The coils are thermally connected to the He tank through pipes filled withpressurized superfluid He: this material has the highest heat conductivity amongall materials, and high density. Helium will circulate also through the coolingcircuit, and finally will be vented into space. The large volume of 2500 liters isneeded to be able to operate three years without refilling.

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4.4.2 The tracking system

The main differences between the AMS-01 and AMS-02 tracker are the numberof support planes (6 and 5 respectively) and read-out planes (6 and 8 respectively),the geometrical acceptance (from about 0.15 to 0.4 m2 sr), and the production ofthe Si modules.

The decrement of the number of supporting planes results in a diminutionof the matter traversed by the particles, hence of the probability that multiplescattering affects the trajectory fit. This is the main problem with momentummeasurements at low rigidities.

The increment of the number of read-out (x, y) planes allows for a better mea-surement of the energy loss and an improvement of the trajectory fit. In additionto a refinement in the ladders production and to the stronger magnetic field, the netresult is a better measurement of the particle momentum. The MDR of AMS-02will be in the range 1–2 TV.

The new technique for the construction of the silicon ladders was motivated bythe poor performances of the n-side read-out of the AMS-01 tracker [95]. Insteadof using four p+ blocking strips between two consecutive n+ read-out strips, thenew ladders have only three blocking strips on the n-side, resulting in a bettersignal-to-noise ratio. The p-side of the ladders is built along the same lines as theAMS-01 tracker.

4.4.3 The time of flight system

The time of flight system of AMS-02, developed in the laboratories of INFNBologna, will be similar to the TOF system of AMS-01. Two scintillator planeswill be placed above the magnet, and other two planes will be placed below. Thecounters of adjacent planes are orthogonal, in order to guarantee a certain granu-larity at the trigger level.

Due to the strong residual magnetic field in the phototubes zone, the new TOFwill adopt different PMTs (Hamamatsu R5946) and will have curved light guidesin order to minimize the angle between the field and the PMT axis. This willproduce a worse time resolution than AMS-01, but the new front-end electronicswill improve the charge resolution. More details in chapter 5.

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Figure 4.27: The structure of an ACC module [102].

4.4.4 The anticoincidence system

The Anti-Coincidence Counter (ACC) system, built in Aachen, form a barrelaround the Si tracker of AMS-02 [102]. Its purpose is to flag events produced byparticles crossing the detector from the side, by δ-rays or even showers producedby triggered particles, and by back-scattering of the electromagnetic calorimeter.In all cases, the detector would record informations giving bad track fit, and chargeand velocity resolution.

The ACC modules (figure 4.27) are plastic scintillators (Bicron BSC414) withemission in the range 380–420 nm, coupled with wavelength shifting fibers (ab-sorption at 400–410 nm, emission at 480–500 nm). White glass optical fibers areused to bridge the wavelength shifting ones to the phototubes, that are 1–2 m far

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from the scintillators.The 16 plastic paddles have a height of 83.2 cm and form a cylinder with an

inner diameter of 109.1 cm. Their thickness is 1 cm and their signal is read by16 PMTs, by both ends: each phototube sees two adjacent paddles, and the PMTcouples are interleaved.

Due to the high magnetic field intensity (≈ 0.16 T), fine mesh phototubes hasbeen chosen that are able to operate up to 0.3 T, provided that the angle betweentheir longitudinal axis and the magnetic field is less than 30 degrees. These cylin-drical PMTs are of the same kind as those used by the TOF system (HamamatsuR5946), and need to be installed in the region of the magnet vessel where the fieldis parallel to the x axis, i.e. near the y axis. They will be oriented in order to aligntheir longitudinal axis to the field direction.

The powering system and the read-out electronics are very similar for the TOFand ACC phototubes: the high voltage will be produced by an elevator placed inthe electronics crate, and each channel will be regulated from the top (2300 V)down to the desired tension. The ACC anodes will be sent to the scintillator front-end anticoincidence (SFEA2) board, that will send the discriminated signal to thetrigger electronics. Because the ACC signals will be used also to check for back-scattering from the calorimeter, they will be used at the first level trigger stage inconjunction with the signals coming from the TOF and ECAL systems.

4.4.5 The RICH detector

The AMS-02 detector will have a proximity focusing Cerenkov counter whoseaim is to improve the velocity resolution with respect to the TOF system, andto provide the AMS Collaboration with an additional charge measurement. TheRICH is developed by a team of researchers coming from institutions of six dif-ferent countries (INFN Bologna, ISN Grenoble, LIP Lisbon, CIEMAT Madrid,University of Maryland, and IFUNAM Mexico).

The instrument is placed below the lower TOF planes, whose support structureis keeping the RICH radiator. Particles crossing this layer with energy above theCerenkov threshold will cause the emission of optical photons (peaked at about430 nm), eventually reaching the pixel plane (directly or after being reflected bythe conical mirror), placed about half meter below the radiator. In the middle ofthe pixel plane there is a square hole, right above the calorimeter. More details inchapter 6.

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Figure 4.28: The structure of a TRD module.

4.4.6 The trasition radiation detector

The transition radiation detector (TRD), built in Aachen, is a gas detector thatmeasures the energy deposited by the X-rays produced by high energy chargedparticles crossing the radiator [93] (in addition to ionization losses). When theseparticles cross the boundary between two media with dielectric constants ε1 , ε2,they have a small (∼ 10−2) probability to emit transition radiation photons.

The AMS-02 TRD modules have 16 straw tubes with diameter 0.6 cm thatfollow a 2 cm thick radiator. The latter is a fleece of 10 µm fibers with 0.06g cm−3 density (figure 4.28). The gas mixture is Xe CO2 at 80%/20%, and thegold-plated sense wires are operated at 1600 V, reaching a 50% probability todetect with one module the transition radiation produced by the particle.

The TRD consists of 20 layers of straw modules interleaved with fibers andarranged in a conical octagonal structure. Outside this structure a grid of carbonfiber tubes makes support for gas tubes and cabling (figure 4.29). The top andbottom 4 layers are parallel to the x axis, while the middle 12 layers are parallelto the y axis.

In order to operate in space for 3 years, the TRD is equipped with a reservoirof 50 kg of gas, corresponding to 8100 liters of Xe and 2000 liters of CO2 at 1atm.

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Figure 4.29: The AMS-02 transition radiation detector.

4.4.7 The electromagnetic calorimeter

The electromagnetic calorimeter (ECAL), constructed by LAPP (Annecy, France),BISEE (Beijing, China), and INFN (Pisa and Siena, Italy), will identify, amongstall cosmic rays, electrons, positrons and γ-rays in the high energy range.

The ECAL is an imaging calorimeter consisting of 9 modules made of Pb andscintillating fibers (figure 4.30), whose area is 64.8×64.8 cm2 and the depth is 1.8cm (≈ 1.8 radiation lengths). Two adjacent modules are rotated by 90◦ and theirfibers follow x or y directions [103].

Fibers are read only at one end, by Hamamatsu R7600-00-M4 photomultipli-ers placed alternatively on each side. Each PMT window has 4 “pixels”, hencethe elementary cell of the calorimeter has 648 × 9 × 9 mm3 (or 9 × 648 × 9 mm3)size, corresponding to about 1 radiation length along z and 1 Moliere radius alongy (or x).

A charged particle impinging vertically on the ECAL will cross ≈ 16 radiationlength and the shower longitudinal profile will be sampled by 18 independentmeasurements. Depending on the primary particle energy, the signal collected byPMT ranges from few photoelectrons for a MIP particle to ∼ 105 photoelectronsfor 1 TeV electrons. The HV divider chosen by the collaboration saturates above

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Figure 4.30: The ECAL structure.

2000 pC of collected charge per pixel, corresponding to about 100 photoelectronsper pixel [103].

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Chapter 5

The AMS-02 TOF system

The long duration of the AMS-02 mission (at least three years) and the detectorlarge acceptance make it possible to collect a high statistics sample of particleswith energies of the order of 1 TeV per nucleon. For this reason, the permanentmagnet of AMS-01 has been substituted with a more powerful superconductingmagnet: this allows AMS-02 to have a maximum detectable rigidity for protonsof 1–2 TeV.

The higher magnetic field produces also a higher fringing field in the zonewhere the photomultipliers are placed. While the use of a shielding materialmakes it possible for RICH and ECAL to use the same kind of PMT that wasused by ACC and TOF in AMS-01, this would not be possible for the AMS-02ACC and TOF systems because the shielding boxes would be too heavy. Instead,a different model of phototube was chosen, that can operate with high magneticfields provided that its longitudinal axis is almost parallel to the field direction.

In order to minimize the angle between the PMT axis and the magnetic field,the ACC phototubes (connected to the scintillator paddles through optical fibers)were positioned in the two zones where they are approximatively parallel to thefield. On the other hand, the TOF system does not make use of any optical fiberto avoid photon losses, but each scintillator has four plastic light guides (LG) asshort as possible. Howewer, these LG have to be bended in order to minimize themagnetic field effects, at least for the PMTs of the inner TOF planes.

Due to the strict packing of the phototubes, the LG bending has been a com-plicated mechanical problem. Another problem was to design the scintillator sys-tem in order to minimize its weight (the allotted budget was decreased by 20%in 2002) still keeping the required large acceptance and trigger efficiency for aprecise antimatter measurement.

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The complicated geometry and the new kind of PMT make it difficult to obtainsimilar performances to the AMS-01 TOF. Howewer, the ion beam test carried onduring October 2002 at CERN showed that in absence of strong magnetic fieldsthe time resolution of the new counters is almost the same of the AMS-01 TOF,while the charge resolution will be improved thanks to a new design of the front-end electronics. The magnetic field mostly affects the time resolution, while it isnot expected to induce strong variations on the charge measurement.

5.1 The time of flight system of AMS-02

The time of flight (TOF) system of the AMS-02 detector has the following es-sential tasks. First, it has to send to the trigger box the signals used to create thefast trigger signal: this is the very first step of the data acquisition (DAQ) elec-tronics. This signal is used by the TOF electronics as the “time zero”, which thescintillator time signals are referred to.

Second, the particle time of flight is used to measured its velocity β = v/c,when the crossing positions (hence the track length) are known. The TOF coun-ters themselves should be precise enough to give, through the time difference oftheir two edge signals, the longitudinal position within few centimeters, allow-ing for the β measurement without the need for information coming from othersubdetectors. This spatial information is related to the particle producing the trig-ger, and is very useful to cross check the tracker and TRD track reconstruction,expecially when secondary hits are recorded by the latter subdetectors.

Third, the time of flight is used to distinguish between upward and downwardgoing particles. This is fundamental in order to separate particles from antiparti-cles. The sign of the particle charge is in fact given by two distinct measures: thetrack bending and its direction. After the TOF measurement of the particle direc-tion, the tracker measurement of the trajectory curvature is sufficient to distinguishbetween negative and positive electrical charges, that are deflected in opposite di-rections by the magnetic field.

Finally, the energy loss measurement is used by the TOF system to send to thetrigger box a special flag for ions events, that can be used at the first level triggerto disable the anticoincidence counters veto, that would suppress more stronglyhigher charges (whose flux is low). In addition, the TOF charge measurement isused (with the corresponding measurements by the other subdetectors) during theoffline analysis to separate light ions from protons and He nuclei.

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5.1 — The time of flight system of AMS-02

Figure 5.1: The Hamamatsu fine mesh R5946 photomultiplier tube.

While all the previous items are equally fundamental both for AMS-01 andAMS-02, the new TOF system design is different from the first one, due to moresevere constraints given by the stronger magnetic field in the photomultiplier tubes(PMT) zone and by the reduced allotted weight budget.

The strong magnetic field, whose intensity reaches 0.2 T for some PMT, makesimpossible to use the same PMT model of AMS-01 (Hamamatsu R5900, “vene-tian blind” dynodes), and forces us to adopt bended light guides in order to mini-mize the angle between the field direction and the PMT axis. The new PMT model(Hamamatsu R5946, “fine mesh” dynodes, figure 5.1) is bigger and heavier thanthe old device, thus the new counters have two (instead of three) PMT per side.In addition, it has a higher working voltage (2000 V instead of 800 V), making itnecessary to develop a different high voltage (HV) scheme.

The reduced weight budget (about 238 kg for the whole TOF system) imposesa different number of scintillator counters per plane with respect to the old 4 × 14scheme. In addition, to reach a geometrical aperture of 0.4 m2 sr, the externalcounters of each plane have a trapezoidal shape, and one additional PMT per sidein planes 1 and 4, where the magnetic field constraint is less severe.

The effect of the intense and spatially variable magnetic field in the PMT zone(figure 5.2), that forced the choice of a different PMT model and of bended light

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guides, combined with the reduced weight (lesser number of counters and dif-ferent shape), will give a worse time resolution with respect to AMS-01, due tothe increase of the transit time1 of the phototubes [104] and of its jitter. On theother hand, the TOF charge resolution will be better due to a refined design of thefront-end (FE) electronics (§5.4.1).

1The transit time is the time elapsed between the arrival of photons on the photo-cathode andthe anode current generation. It is related to the multiplication process between the dynodes.

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5.2 Magnetic field

The phototubes used by the TOF system of AMS-01, the “venetian blind” Hama-matsu R5900 model, are small and light, and need a relatively low voltage to work(below 900 V). Thus they are well suited for space applications. The maximummagnetic field intesity in the PMT zone of AMS-01 was about 300 G, then it wasdecided to use a ferromagnetic material to shield them: the PMTs were enclosedby 1 mm thick Permalloy boxes, whose effect was to reduce the field intensitydown to few Gauss, a level at which the R5900 model can work without problem.

On the other hand, the superconducting magnet of AMS-02 (§4.4.1) is about6 times stronger than the permanent magnet of AMS-01 (§4.2.1). In addition, thenew TOF planes are nearer to the magnet than the AMS-01 ones. The result isthat the fringing field in the PMT zone is much stronger than in AMS-01, reach-ing values of the order of 2.5 kG (ten times higher), with a complicate directiondistribution (figure 5.2).

In order to shield such an intense field, 1 mm thick boxes are not sufficient,because they would saturate. Thicker ferromagnetic boxes are not allowed by thesmall weight budget allotted for the TOF system. Thus one has to find phototubesof different technology with respect to the old PMTs, in order to allow them tooperate in regions with strong magnetic fields.

The new model selected for the TOF (and ACC) system of AMS-02 is thecylindric Hamamatsu R5946 “fine mesh” photomultiplier (figure 5.1). Its dynodeshave a mesh shape and are tightly packed. In addition it operates at quite highvoltages (about 2000 V), in order to reduce its sensibility to the magnetic field.This PMT can indeed work with the high intensity fields of AMS-02, but it showsa strong dependence on the angle between the field direction and the PMT axis.For example, figure 5.3 shows the measured PMT single photoelectron responsefor different values of the magnetic field intensity and direction.

In general, measurements carried on in Bologna with magnetic field up to 0.4T, about the single photoelectron response, the time resolution, the charge peakposition and its distribution, show that one should avoid angles larger than 20degrees as much as possible: for higher values, even for lower field intensitiesthan those expected for AMS-02, the PMT single photoelectron response and thePMT transit time jitter rapidly become no more acceptable [104]. On the otherhand, the gain and the charge resolution are not strongly affected for angles below20 degrees, that is the situation of planes 1 and 4, and of many phototubes of theother two planes.

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Figure 5.3: Measurement of the single photoelectron response of HamamatsuR5946 phototubes as function of the intensity and direction of themagnetic field [104].

In order to minimize the angles between the PMT axes and the field direction,that has strong spatial variations all around the scintillator planes, bended lightguides has been adopted, whose shape has been tuned keeping into account notonly the magnetic field, but also the tight packing between the TRD and the TOFmechanics (figure 5.4), that are both fixed to the same honeycomb layer.

Starting from the simulated field map in a three-dimensional spatial grid with5 cm step, with all Cartesian coordinates in the interval [0, 150] cm, I wrote aFORTRAN program to compute the mean field intensity and direction inside anygiven PMT, whose front window and rear panel centers are known.

In order to be able to work with positive and negative coordinates, the program

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Figure 5.4: The TRD and the upper two TOF planes of AMS-02 share the supportstructure.

first applies a symmetry transformation to the field components (the field is dipolarand symmetric around the x axis). Then it finds the nearest 8 grid points around thePMT window center and computes the weighted average of the field components(the weight is the inverse of the distance to the grid point). Finally, it computes thevalue of the acute angle formed by the field vector and the PMT axis. The resultis an ASCII file (see appendix B) with a table containing one row per PMT, wherethe columns are: the 3 coordinates of the PMT window center (in centimeters), the3 coordinates of the PMT rear center (in centimeters), the magnetic field intensityand its 3 components (in Gauss), the angle between the field vector and the PMTaxis (in degrees).

5.3 Mechanical designThe simulated field intensities and directions in the PMT positions were used toconstrain the mechanical design: the engineers proposed several different schemesfor accomodating all the PMTs in the small volumes that they were allowed to fitinto, and I checked these schemes against possible problems due to the magneticfield. After several iterations (that involved also the TRD support structure de-sign), the following final scheme of the AMS-02 TOF has emerged.

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5.3.1 The TOF planes

The time of flight system has 4 planes made of 1 cm thick plastic scintillatorpaddles of different shapes: the outermost counters have a trapezoidal (x, y) pro-jection, while all other counters have a rectangular shape. Figure 5.5 shows thetop-bottom view of all counters. The shape of the external counters was chosento match the desired geometrical aperture still satisfying the severe weight con-straints (20% mass reduction was decided at the beginning of 2002).

The four planes actually form two structures, as shown in figure 5.5, placedabove and below the magnet. Each structure has one plane with counters whoselongitudinal axis is parallel to the field direction inside the spectrometer (that de-fines the x axis), and counters along the y direction in the other plane, in order tohave a certain granularity at the trigger time. First and fourth planes have 8 coun-ters along the x axis, while second and third planes have 8 and 10 counters alongy, respectively (figure 5.6). Each couple of adjacent TOF planes is enclosed in acarbon fiber light tight envelope, and is connected to the electronics crates thanksto patch-panels installed on the envelope itself, where the powering and read-outcables are plugged.

The inner (non trapezoidal) counters are 12 cm large in order to accomodatetwo Hamamatsu R5946 phototubes per side, and each two adjacent parallel coun-ters have 0.5 cm overlap, in order not to have “holes” in the acceptance. Hence,at trigger time one has inner matrices of 6 × 6 and 6 × 8 of square (x, y) cellswith 11.5 cm sides, plus surrounding cells of larger granularity. About 90% of allacceptable tracks will cross the central square cells.

5.3.2 The TOF counters

Figure 5.7 shows a schematic view of a 12 cm large TOF counter. The sensitivematerial is an organic plastic paddle (polyvinyltoluene) whose scintillator light isinternally reflected until it reaches the two edges, where plexyglass light guidesbring it to the photomultipliers.

The light guides consist of five different parts: a straight “extender” that pro-longs the scintillator paddle is connected to two bended and twisted pieces thatend with “conical” junctions whose the PMTs are fixed to. Actually the exten-der and the two curved pieces come from the same plexyglass layer, that is firstcut along the separation of the bended guides, then it is heated and deformed asneeded. After this operation, the whole piece is heated again to avoid optical non-

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Figure 5.6: 3D view of the AMS-02 TOF scintillator paddles.

uniformities, and its surfaces are finally polished. All the conical parts are equaland they are glued to the bended light guides.

The phototube housing (figure 5.8) is a black box divided into two pieces,that enclose the PMT and the edge of the conical light guide. Between the guideand the PMT window a soft transparent pad is placed, that guarantees the neededoptical and mechanical couplings. In addition, the printed circuit boards (PCB)hosting the PMT voltage divider are fixed to the rear of the black housing throughdiamagnetic screws. In order to protect them against low pressure discharges, thePMT pins and the lower PCB are potted with Dow Corning 93-500, the sametransparent material used to build the optical pads. The rest of the electronics is

104


Figure 5.7: A sketch of a TOF counters of AMS-02.

Figure 5.8: The mechanical fixation of the PMT to the conical part of the lightguide is realized through the PMT housing.

coated with Nusil CV-1152 white material, while the light tightness is obtainedusing the black CV-1146-2 Nusil product.

The scintillator, extenders and light guides are wrapped by a thin mylar foils,that improves reflectivity and protects the surfaces from dust and small debris thatmay be produced by the enclosing carbon fiber 0.5 mm thick boxes, that providethe needed rigidity. Light tightness is provided by a large carbon fiber envelope0.7 mm thick that encloses the couple of adjacent planes and their phototubes.

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T AMS-02 TOF

Figure 5.9: The AMS-02 electronic crates placement. ‘S’ denotes the S-crates.

Each couple of TOF planes has to be considered a unique detector piece,whose signals and powering lines are connected to the electronic crates via ca-bles connected to the 4 patch-panels of the enclosing carbon fiber envelope.

5.4 Electronics

The time of flight and anticoincidence systems have front-end (FE) electronicsboards placed in four crates (called “scintillator crates” or “S-crates”) that aresituated in opposite corners (figure 5.9).

Each S-crate is doubly redundant: there are two identical copies of each mod-ule, connected to different power lines for redundancy. Only one half of the crateis turned on during normal operations. In case of problems, the half with the lesssevere problems is kept powered on, while the other will not be used.

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5.4 — Electronics

max 8 ns (clock cicle)

min 100 ns

no HT

250 ns after re−formation

max 220 ns

min 2500 ns max 5500 ns

Low Threshold

High Threshold (to pre−trigger logics)

Fast Trigger

Time expansion

TDC input

SFET timings

13 24

Figure 5.10: Timings of the SFET module.

5.4.1 Data acquisition

Analog data coming from TOF and ACC phototubes are digitized by the SFEx2boards and then collected by the scintillator data reduction unit SDR2 through se-rial links (“TOFwire” custom protocol). The SDR2 sends the data via “AMSwire”LVDS serial links to the 4 boards (called JINJ) on the next higher hierarchicallevel, where data coming from the four S-crates are put in the same structure asthe data from the other subdetectors.

The TOF anodes are sent to the scintillator front-end time (SFET2) redundantboard, that measures the arrival time of their signals with respect to the fast triggerand provide digital signals to the pre-trigger electronics when the analog signalspass a threshold corresponding to about 0.4 MIP (i.e. 40% of the average energylost by minimum ionizing particles).

The SFET2 is similar to the FE electronics of the AMS-01 TOF: the anodesignal is compared to two different thresholds (figure 5.10) and goes into two TDCchannels. The first, or “low”, threshold (LT) starts the “time expansion” logics,while the second, or “high”, threshold (HT) is used to produce the fast trigger andit goes in the “history” TDC channel. After LT, the SFET2 charges a capacitor

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and waits at most 250 ns for the FT and then discharges it fastly if this signal doesnot come in time. In case of FT, the capacitor is discharged over a circuit withgreater time constant, and the discharge time is equal to the time between LT andFT multiplied by 25. This information goes to the TDC “time expansion” channel.A fraction of the anode analog signal is used to measure the charge.

The anode channels of the ACC phototubes are connected to the SFEA2 re-dundant board, that sends digital signals to the trigger boxes (called JLV1A andJLV1B) when ACC anodes pass the 0.4 MIP threshold, and measures their charge.The SFEA2 board receives both ACC and TOF anodes: the latter are processedin the same way of SFET2, whereas the former lack the time expansion logics. Inaddition, anode charge measurement is carried on directly on SFEA2 for all theinput anodes.

In AMS-01, the anode and dynode charge was measured by TDC using thetime over threshold of a discharging capacitor, in order to reduce power consump-tion. The read-out dependence from the charge was logarithmic, resulting in apoor particle separation for Z > 3. On the contrary, AMS-02 will use a linear ADCcoupled with a sample-and-hold technique, identical to the method employed bythe RICH FE electronics. This charge measurement technique is linear over 12bit, and will be used both for anode and dynode signals, the latter being sent tothe SFEC2 boards (‘C’ for “charge”).

In addition to the threshold used for singly charged particles (the HT), theS-crate electronics provides the trigger boxes also with a special flag for Z > 2particles (super-high threshold, SHT). The pre-trigger logics that operate on Z ≥ 1and Z > 2 digital signals is hosted by the S-crate itself. For each half TOF planeconnected to the crate, three logical levels are sent to the trigger boxes: the logicalOR of all Z ≥ 1 signals (CP or “charged particle” flag), the same thing excludingthe outermost counters (CT or “central charged particle”), and the logical OR ofall the Z > 2 levels (BZ or “big Z”). These signals are used by the trigger boxesto generate the fast trigger (CP) and the level 1 trigger (CT and BZ).

5.4.2 Slow control

Slow control commands are foreseen to change the PMT voltage, to turn on/off theS-crate boards, to control and monitor the scintillator power distributor (SPD) box,to read the temperature sensors. Two universal slow control modules (USCM) areplaced in each S-crate, connected to different power lines.

Commands from the control center (called POCC) will reach the USCM in

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5.5 — The beam test

the S-crates through a dedicated connection (CAN bus). The USCM will forwardany command to the boards it refers to, and will send back status, powering andtemperature information (again via CAN bus).

The connections of each USCM to the SDR2 and the high voltage controllerare realized with one Le Croy bus per USCM (plus a double connection withthe SPD controller for redundancy): there is no crossing point in S-crates. Thecommands that change the powering of SFEx2 boards are sent from USCM toSDR2, then SDR2 forwards them through TOFwire to the desired board.

5.4.3 Powering

The S-crate contains the scintillator high voltage (SHV) redundant module, thatconsists of two high voltage elevators (HVE) connected to different power lines.Each HVE feeds 24 linear regulators (LR) that can be set at voltages between−2300 V and −1300 V with a 8 bit DAC (hence the minimum step is about 4 V).One, two or three ACC/TOF PMTs can be connected to the same LR.

The low voltage DC/DC converters are placed outside the S-crate, in the scin-tillator power distributor (SPD) box. The SPD receives two indipendent 28 Vlines, connected to two separate families of DC/DC converters, providing the S-crate with +5 V, ±5 V, +3.3 V. These LV lines are connected to the S-crate mini-backplane through screwed wires.

5.5 The beam test

Two AMS-02 TOF counters and one AMS-01 counter were tested at CERN onOctober 2002 with standard NIM and CAMAC electronics, on the ion beam pro-vided by the SPS facility. The primary Pb beam was directed against a Be target10–30 cm long (target T4), producing secondary particles and nuclei with chargespanning a very wide range: Z = 1–82 (see chapter 7).

The H8 selection line was tuned to obtain secondaries with A/Z = 2 (4Heand almost all stable nuclei up to iron), A/Z = 7/4 (mostly 7Be), and A/Z = 1(protons). For what concerns the scintillators, all primary particles were at theirminimum ionization plateau (that is at Lorenz factors γ > 3).

This section shows first results from the analysis of TOF data, from the runs002–014.

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5.5.1 Selection cutsIn order to study in a self consistent way the data obtained with the three TOFscintillators tested at SPS, it is necessary to apply a number of cuts to the sample.The three counters (a plastic scintillator from Eljen Technologies, one from Bi-cron, and a Bicron TOF counter dismounted from AMS-01) are large comparedto the beam spot, whose diameter is about 3 cm. Hence they picked up a lot ofsecondary particles that are off the beam axis.

The first effect that can be easily isolated is the deviation of the mean countertime

ti =ti,left + ti,right

2(5.1)

from the value that corresponds to the sum of the delays between the TDC startand the arrival of the signals from both ends of the same counter: the beam spotis at the center of the three scintillators, while secondary off-axis particles hit thecounters over the whole area.

As figure 5.11 shows, the wrong mean time measurements are a small fractionof the total number of events. A Gaussian fit reveals the mean values 〈ti〉 and thestandard deviation. As first set of cuts, it is required that events not consistent with〈ti〉 within one standard deviation are discarded.

Then one can consider the half difference between the time measured in bothends of the same counter (omitting the index i):

∆t =(t + x/v) − [t + (L − x)/v]

2=

xv− L

2v(5.2)

where t = ti is the particle crossing time for counter i, L is the counter length, v isthe effective light speed inside the scintillator, and x is the distance of the crossingposition with respect to one of the two sides.

Apart from a constant term (L/2v), ∆ti gives the longitudinal coordinate xalong the scintillator (v ≈ 15 cm ns−1 has been measured in the INFN laboratoriesin Bologna). The time resolution of the counters (§5.5.3) is of the order of 0.1ns, hence the beam particles give a fixed time difference, because the spot radiusis approximatively equal to the spatial resolution σx ≈ 1.5 cm of the countersobtained with the half time difference measurement.

In general, off-axis particles will give a different value for ∆t, hence they canbe discarded by requiring that the half time difference is within one standard de-viation from its mean value for each counter (figures 5.12, 5.13 and 5.14). Acouple of secondaries that hit the counters in symmetric positions with respect

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11010 210 310 410 510 6

20 30 40 50 60 70 80 90 100 110 120

Entries 1339713

C3 time (ns)


Figure 5.11: Mean time measured by the three TOF scintillators under ion beamtest (runs 2–14). Only events within 1 standard deviation from theGaussian mean are kept.

to the beam spot cannot be rejected by this condition, but they produce a wrongmeasurement of the mean time, hence they are discarded by the other condition.

In order to be able to study the charge resolution of the scintillators, I imposeda constraint also on the relative time of flight between each couple of counters.This condition discards slow secondaries with crossing positions near enough tothe beam spot that they cannot be resolved using the half time difference alone.

Figures 5.15, 5.16 and 5.17 show that after the mean time and half time differ-

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Entries 907842

C1 time diff. (ns) − mean time cut

606180 events within 1 σ

(cut eff. = 66.77%)

Figure 5.12: Half difference between the time measurements of both sides of theEljen scintillator (runs 2–14) without cuts (upper panel) and withthe mean time cut (lower panel). Only events within 1 standarddeviation from the Gaussian mean are kept.

ence conditions the all-particle time of flight has a distribution that can be fitted bya Gaussian with standard deviation of 160–180 ps. Howewer non Gaussian con-taminations are recognizable by eye. Discarding also the events with time of flightmeasurements outside one standard deviation from the mean values it is possibleto obtain a quite clean sample of appreciable statistics (25.6% of the consideredevents), that will be useful to study the charge resolution.

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(cut eff. = 64.55%)

Figure 5.13: Half difference between the time measurements of both sides of theBicron scintillator (runs 2–14) without cuts (upper panel) and withthe mean time cut (lower panel). Only events within 1 standarddeviation from the Gaussian mean are kept.

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(cut eff. = 65.15%)

Figure 5.14: Half difference between the time measurements of both sides of theAMS-01 TOF scintillator (runs 2–14) without cuts (upper panel)and with the mean time cut (lower panel). Only events within 1standard deviation from the Gaussian mean are kept.

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P1 0.1502E+06 334.4P2 −2.321 0.2210E−03P3 0.1776 0.2452E−03

C1−C2 (ns)

No cut: 1336762times cut: 342516TOF cut: 241520

(eff. = 25.62%)

Figure 5.15: Time of flight between the first two counters (runs 2–14) withoutcuts (upper panel) and with mean time and half time difference cuts(lower panel). Only events within 1 standard deviation from theGaussian mean are kept.

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P1 0.1605E+06 352.4P2 −10.73 0.2891E−03P3 0.1664 0.2351E−03

C1−C3 (ns)


(eff. = 25.6%)

Figure 5.16: Time of flight between the first and last counter (runs 2–14) withoutcuts (upper panel) and with mean time and half time difference cuts(lower panel). Only events within 1 standard deviation from theGaussian mean are kept.

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Entries 342516 0.1181E+05/ 14

P1 0.1696E+06 389.8P2 −8.415 0.1889E−03P3 0.1556 0.2356E−03

C2−C3 (ns)


(eff. = 25.59%)

Figure 5.17: Time of flight between the second and third counter (runs 2–14)without cuts (upper panel) and with mean time and half time dif-ference cuts (lower panel). Only events within 1 standard deviationfrom the Gaussian mean are kept.

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±1.3

38.2

±0.9

39.7

±1.3

41.4

±1.6

42.7

±2.8

Figure 5.18: The charge peaks of the first counter can be seen up to Z = 13for the left side (upper panel) and Z = 20 for the right side (lowerpanel).

5.5.2 Charge peaks

The most important information gained with the beam test are about the chargeresolution of the AMS-02 TOF counters.

The energy lost dE/ dx by a particle with atomic number Z is proportional toZ2 (see equation (4.4) on page 57), but the emitted scintillation light is propor-tional to dE/ dx only for small values of the energy loss. In general, the signalQ measured by the ADC is the time integral of the PMT current pulse, i.e. it is

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.619

.3±0

.721

±1.2

22.6

±124

±1.6

25.4

±126

.7±2

.428

.3±1

.5

Figure 5.19: The charge peaks of the second counter can be seen up to Z = 13for the left side (upper panel) and right side (lower panel).

proportional to the emitted scintillation light, and can be written:

Q =A dE

dx

1 + B dEdx + C

(dEdx

)2 =aZ2

1 + bZ2 + cZ4 (5.3)

(the first equality is the Birks’ formula [105]). Hence a plot of the square root ofthe ADC signal (after the cuts already discussed) gives the particle charge at thefirst order, as seen in figures 5.18 and 5.19.

While the gains of the four PMTs mounted on the Bicron scintillator was al-most balanced, figure 5.18 shows that this was not the case for the Eljen counter.Actually, the latter was tested with a high- and low-gain couple of PMTs in eachside (left to right ratio 3 : 2). Howewer, this is not important for the charge res-

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T AMS-02 TOF

olution (apart from the ADC overflow for Z > 13 of the left side dynodes of theEljen counter): because the PMTs are similar, the charge resolution depends onlyupon the light yield of the scintillator.

These results strongly supported the choice of the Eljen scintillator (figure 5.18)instead of the Bicron one (figure 5.19), thanks to the Eljen higher photostatistics.The Eljen product will allow to measure the particle charge up to atomic numberZ ≈ 20, providing important cross check of the tracker, RICH and ECAL chargemeasurements.

In order to correctly measure the particle charge, formula (5.3) has been usedto fit the ADC peaks (figures 5.20, and 5.21), obtaining the ADC pedestal andthe three parameters of (5.3). Then the relation was inverted to get a plot of thereconstructed particle charge Z (a real number) for each counter side. Finally,the mean of the four measurements has been used as best estimate of the particlecharge (again a real number, figure 5.22).

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0.1544 / 9P1 19.35 2.417P2 0.8996E−02 0.4686E−02P3 −0.2058E−04 0.2398E−04P4 113.4 6.829

Q = C1LD − ped. (ADC ch.)

Q =P1 Z

2

1 + P2 Z 2 + P3 Z

4

ped. = P4

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h.)

1.503 / 16P1 9.425 0.7058P2 0.6131E−02 0.1406E−02P3 −0.8641E−05 0.3235E−05P4 109.3 4.287

Figure 5.20: ADC channels correspondence to particle charge for the left (upperpanel) and right (lower panel) dynodes of the Eljen counter. Fit withBirks’ law.

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60708090

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0.1934 / 9P1 6.527 1.009P2 0.7548E−02 0.4933E−02P3 −0.1436E−04 0.2316E−04P4 90.28 4.144

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0.1794 / 9P1 8.008 1.169P2 0.7672E−02 0.5415E−02P3 −0.1500E−04 0.2783E−04P4 79.14 3.121

Figure 5.21: ADC channels correspondence to particle charge for the left (upperpanel) and right (lower panel) dynodes of the Bicron counter. Fitwith Birks’ law.

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Figure 5.22: Side charge measurements (upper panel) and mean charge (lowerpanel). For higher charges than Z = 13 only the right side of thefirst counter is available. 123

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0.1633E+05/ 59Constant 0.3883E+05 92.68

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Constant 0.4546E+05 105.7

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Figure 5.23: All-particle time of flight distribution for runs 2–14. The stan-dard deviation is dominated by singly charged particles. The singlecounter time resolution is 100–120 ps.

5.5.3 Time resolutionWhen a criterion is known to find the best estimate of the particle charge, it ispossible to study the time of flight resolution of the three counters. First, the cutson the mean time and the half time difference are applied, then one can study theresolution of the difference between ti and t j with i, j = 1, 2, 3 and i < j.

Figures 5.23 and 5.24 show the three possible differences without charge se-lection, the former without any other cut, the latter with the two following cuts:the time of flight between the first two counters has been plotted after the rejectionof events with (t1 − t3) and (t2 − t3) outside one standard deviation from their meanvalues. The large tails of figure 5.23 disappear when applying this cut. Using

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2550. / 10Constant 0.3236E+05 93.07

Mean -2.321 0.1892E-03

Sigma 0.1080 0.1746E-03

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Constant 0.3563E+05 98.83

Mean -8.393 0.1567E-03Sigma 0.1059 0.1592E-03

C2-C3 (ns)

Figure 5.24: All-particle time of flight distribution for runs 2–14, after TOF cuts.The standard deviation is dominated by singly charged particles,and it is of the order of 100 ps.

σ2i j = σ2

i + σ2j , the resulting single counter resolution is given in the following

table:

Time without TOF with TOFres. cuts (ps) cuts (ps)σ1 125 ± 3 74 ± 1σ2 111 ± 2 79 ± 1σ3 90 ± 2 71 ± 1

Figure 5.25 shows the average standard deviations of the Gaussian fit of thetime of flight between the three possible couples of TOF counters, as function

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of the most probable particle charge. In order to select the particles with atomicnumber Z, it was required that the four sides of the AMS-02 counters give dynodesignals in the Z-th ADC peak within one standard deviation.

As foreseen, the time of flight resolution improves with increasing particlecharge, reaching a limiting level dominated by the electronic noise. This levelwas between 50 and 60 ps for the standard electronics used during the ion beamtest at CERN.

The SFET2 design keeps the value of 50 ps as the maximum allowable elec-tronic jitter. Howewer, the presence of a strong magnetic field, even if its directionis almost parallel to the PMT axis, worsen the time resolution of the HamamatsuR5946 phototubes: the standard deviation will increase almost at the same rate ofthe phototube transit time, depending on the PMT position and orientation in themagnetic field (§5.2).

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P1 0.6055E-01 0.1764E-02P2 0.5720E-01 0.1165E-02

σt = P1/Z + P2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 1 2 3 4 5 6 7 8 9 10Z

Tim

e re

solu

tion

(ns

)

5.578 / 7P1 0.3987E−01 0.1652E−02P2 0.5277E−01 0.1246E−02

σt = P1/Z + P2

Figure 5.25: Average time resolution of the three counters as function of charge,without (upper panel) and with (lower panel) cuts on TOF. The timeresolution gets better with increasing atomic number: the limitinglevel of 50–60 ps is the electronics noise.

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T AMS-02 TOF

128

Chapter 6

The AMS-02 RICH subdetector

The AMS experiment is able to identify cosmic ray particles through the measure-ment of the energy lost in active materials, the trajectory curvature and the particlevelocity. The energy losses in media are proportional to the square of the charge(§4.1.2), hence their measurements can be used to determine the atomic numberZ of the incident nucleus. From the track curvature one can find the particle rigid-ity (§4.1.1) and hence the momentum, in combination with the knowledge of thecharge. Finally, the velocity measurement (§4.1.3) is necessary to find the particlemass from its momentum.

The proximity focusing ring imaging Cerenkov counter (RICH) of AMS-02will be able to measure the cosmic rays velocity β = v/c with a 0.1% uncertaintyfor βc < β < 1, and the particle charge up to Fe, through the measurement of theCerenkov opening angle and the number of emitted photons, respectively. Thesefeatures, in addition to providing redundant charge measurement in combinationwith the TOF and the tracker, are needed to study the isotopic composition of thecosmic rays.

6.1 The Cerenkov emission

When charged particles cross a medium with refractive index n > 1 with velocity vgreater than the light speed in that medium (v` = c/n, where c is the light speed invacuo), they emit Cerenkov radiation. The photons are produced uniformly alongthe path (if n is constant), and they are emitted at a fixed (if also the variation of vis negligible) angle θc with respect to the particle momentum direction, while theazimuthal emission is uniform.

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T AMS-02 RICH

The Cerenkov angle θc is given by the formula:

cos θc =1

nβ, (6.1)

hence it reaches its maximum value

θc = arccos1n

(6.2)

for ultrarelativistic particles (i.e. β ' 1). On the other hand, the lowest value forthe velocity is given by the condition cos θc = 1 (i.e. θc = 0): the threshold speedis

βc =1n. (6.3)

In addition, the mean number of emitted photons by a particle with charge Zeis

NZ = Z2N1 ∝ Z2 L(1 − 1

n2β2

), (6.4)

where N1 is the average number of photons emitted by a singly charged particlecrossing the same medium, that depends on the path length L = d/ cos τ throughthe radiator of thicnkess d, on the particle velocity v = βc and azimuthal angle τ,and on the refractive index n of the radiator. Because β2 ≈ 1, N1 is pratically notdependent on the particle velocity.

6.1.1 Particle energy loss in the radiatorThe energy lost by a non relativistic particle with charge ze that crosses a mediumwith atomic number Z and atomic number density N is well described by theformula found by Bethe in 1930 (from Jackson [91], in Gauss’ units1):

dEdx

= 4πNZz2e4

mv2

[ln

(2γ2mv2

~〈ω〉)− v

2

c2

], (6.5)

where m and v are the mass and velocity of the particle respectively, and 〈ω〉 isthe average electron frequency of the medium, defined by the following geometricmean:

Z ln〈ω〉 =∑

i

fi ωi , (6.6)

1In Gauss’ units, the Maxwell’s equations in vacuo are: ∇·E = 4πρ, ∇×B = (4π/c)J +

(1/c)∂E/∂t, ∇×E + (1/c)∂B/∂t = 0, ∇·B = 0.

130

6.1 — The Cerenkov emission

where the “oscillation intensities” fi satisfy Ne =∑

fi.For ultra-relativistic particles the Bethe formula overestimates the energy loss,

and one needs to add a correction due to the dielectric polarization of the medium(“density effect”): thanks to the relativistic beaming, the charged particles feel theelectric field also of distant atoms. This effect was pointed out by Fermi in 1940and it is more important in the treatment of the scattering with large impact param-eter b, while for small b one can still neglect the field produced by distant atoms.The tipical scale between small and large impact parameters (hence between theBethe approximation and the Fermi correction) is the inter-atomic distance a.

For large impact parameters, one can find the total electromagnetic field insidethe medium produced by the different atoms by using the Fourier transform of thecharge and current densities in the dielectric and solving the Maxwell equationsin the Fourier space, with coordinates (ω, k). Then it is possible to compute theenergy variation due to a single diffusion process, and finally compute the averagevalue. This calculation is well explained by Jackson [91]. Here we only quote theresult (Fermi formula):

(dEdx

)

b>a=

2π

(ze)2

v2 Re∫ ∞

0iωλ∗a K1(λ∗a) K0(λa)

(1

ε(ω)− β2

)dω (6.7)

where ε(ω) is the dielectric “constant”, K0 and K1 are the modified Bessel func-tions of order 0 and 1 respectively, and the “wavelength” λ is defined by the rela-tion

λ2 =ω2

v2

(1 − β2ε(ω)

). (6.8)

The usual density effect correction is found when considering the limit |λa| �1. In this case, the Fermi formula (6.7) becomes similar to the Bethe expression(6.5), with the exception of the exponent of γ in the logarithm, that is 1 insteadof 2. This reduces the “relativistic increase” (figure 6.1) after the minimum in theenergy loss curve as function of βγ = P/mc:

(dEdx

)

b<a=

(ze)2ω2p

c2 ln(1.123c

aωp

), (6.9)

where ωp = 4πNZe2/m is the electronic plasma frequency.If we are interested into the energy released far from the trajectory, we can

consider the opposite limit, |λa| � 1. In this case one can use the asymptotic

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T AMS-02 RICH

0.5

1.0

2.0

5.0

10.0

20.0

50.0

−dE

/dx

(MeV

g−1

cm2 )

1.0 10 100 1000 10 0000.1

Minimumionization

−100 ×shellcorrect.

Complete dE/dx

dE/dx without δ

dE/dx ∝ β−5/3

Radiative effectsbecome important

π ± on CuI = 322 eVdE/dx ∝ β−2

∝ β−2

βγ

Approx Tmax

Tcut = 0.5 MeV

∝ β−5/3

Figure 6.1: Energy loss of singly charged particles (pions) as function of the rel-ativistic momentum βγ = P/mc [106]. The explanations refer to theenergy loss written in the form of equation (4.4).

behavior of the Bessel functions and find that the term inside the integral of theFermi formula will approach the expression:

integral in (6.7) ∝−i

√λ∗

λ

ω(1 − 1

β2ε(ω)

)exp [−(λ + λ∗)a] . (6.10)

Usually λ has a positive real part, and the exponential produces a rapid cut-off for large distances: all the energy is deposited along the particle trajectory.Howewer, there can be cases when λ is a pure imaginary number (actually Reλ ≈0, because a tiny dissipation is always present). In such cases, the asymptoticexpression (6.10) becomes independent from a: part of the energy goes to infinityas electromagnetic radiation (Cerenkov radiation). From equation (6.8), we seethat this happens if ε(ω) is real and β2ε(ω) > 1 (anomalous dispersion, figure 6.2),that is when

v >c√ε(ω)

. (6.11)

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6.1 — The Cerenkov emission

��

��

ω

ε(ω

)

β21

ω0

1

Figure 6.2: The shadowed region is the Cerenkov zone. Emitted radiation withfrequency ω is possible only if the dielectric “constant” ε(ω) > β−2

(anomalous dispersion).

6.1.2 Cerenkov radiationThe condition (6.11) states that when a charged particle crosses a material withreal dielectric “constant” ε(ω) with velocity greater than the phase velocity vph(ω) =

c/√ε(ω) of the electromagnetic radiation with frequencyω, the polarization of the

medium induces the emission of Cerenkov radiation with the same frequency.In this case we have λ = −i|λ| and the asymptotic expression (6.10) does not

depend on a. Hence the Fermi formula now represents the emitted energy per unitpath and can be written [91] in the form

(dEdx

)

rad=

(ze)2

c2

∫

ε(ω)>1/β2ω

(1 − 1

β2ε(ω)

)dω (6.12)

(in Gauss units) given by Frank and Tamm in 1937 as interpretation of the emis-sion found by Cerenkov in 1934. The function inside the integral is of course thedifferential spectrum of the Cerenkov radiation:

(d2E

dω dx

)

rad=

(ze)2

c2 ω

(1 − 1

β2ε(ω)

)(6.13)

for all values of ω in the shadowed region of figure 6.2.

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T AMS-02 RICH

pitch = 37 mm

aerogel thickness = 30 mm

600 mm

670 mm

468 mm

114 mm

LG height = 31 mm

ECAL hole 630 mm

radiator

supporting foil

foil thickness = 1 mm

Figure 6.3: The proximity focusing RICH detector of AMS-02.

Usually a medium has more than one region with anomalous dispersion (likethe zone in figure 6.2), and the emission is concentrated in frequency bands justbelow the critical frequencies (ω0 in figure 6.2). For ultrarelativistic particlesβ−2 ≈ 1 and such bands can be very large.

The Cerenkov radiation is emitted around the particle line of flight with anangle that depends on its velocity and on the medium refractive index n(ω) =√ε(ω):

cos θc(ω) =1

β n(ω)(6.14)

so that the criterium β2ε(ω) > 1 is equivalent to the condition that the cosine isreal. In addition, the Cerenkov radiation is totally polarized in the plane contain-ing the particle momentum and the propagation direction [91]. Due to the for-mula (6.14), light of different colors will be emitted with slightly different angles(chromatic dispersion), but this effect is reduced when using media with refractiveindex very near to one.

6.2 The RICH designThe AMS detector is a large acceptance cosmic ray spectrometer, where the mea-sured particles have trajectories with a quite large range of incidence angles andcrossing positions. Hence, a “traditional” ring imaging Cerenkov (RICH) detec-tor would not be adequate, because of the need of almost collinear particles, or aknown vertex position. Instead, a “proximity focusing” RICH counter is used tomeasure the particle velocity and charge, because of its large angular and spatialacceptance.

134

6.2 — The RICH design

n>1

n=1

radiator

pixels plane

charged particle

photons

Figure 6.4: Schematic representation of the proximity focusing RICH detector.

In order to reach momenta above 10 GeV/c per nucleon, the solid radiatorwith the smallest refractive index was chosen: silica aerogel. Central tiles of Na Fwill be used to cover the momentum gap between the TOF and the aerogel βmeasurements. In order to increase the geometrical acceptance, a conical mirrorwill be used to reflect the photons emitted at large angles towards the pixels plane.The PMT plane has a square hole just above the ECAL, in order to reduce thematter thickness in front of this detector. The RICH is shown in figure 6.3.

6.2.1 Large acceptance proximity focusing RICH detector

A proximity focusing RICH is a detector where the radiator is a (usually thin)layer of transparent material, and is separated from the photon detector by a regionwith refractive index very near to one (in AMS this region will be in vacuo, hencen = 1), as sketched in figure 6.4.

The Cerenkov photons are emitted only inside the plane of the radiator, fromwhich they escape and propagate until reaching the pixels of the light detector.The refractive index of the radiator determines the opening angle of the Cerenkovcone, that is one of the fundamental parameters that affect the β resolution. Theother important parameters are the pixel size and the width of the gap between theradiator and the pixel plane, i.e. the detector angular resolution.

Real detectors have few problems, due to the finite number of detected pho-tons, to the approximation n(λ) = n (chromatic dispersion), to the radiator thick-ness and opacity.

The number Ndet of detected photons that can be used in the data analysis is

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T AMS-02 RICH

given by the number NZ of emitted photons (proportional to the square of the par-ticle charge, equation 6.4), minus the number Ni.r. of internally reflected photonsinside the radiator, minus the Nmiss photons missed by the pixels due to geomet-rical effect or quantum efficiency, minus the number NR.s. of photons scattered atlarge angles by impurities or microstructures in the radiator (Rayleigh scattering):

Ndet = NZ(τ) − Ni.r.(τ) − Nmiss(τ) − NR.s.(τ) . (6.15)

The dependence on the particle incidence azimuthal angle τ is due to the pathlength L = d/ cos τ of the particle through the radiator of thickness d, and to theangular distribution of the photons.

The path length is related to the transmission T by the empirical formula [107]

T (L, λ) = 0.96 exp(−C

Lλ4

)(6.16)

where L is usually expressed in centimeters and λ is in micrometers. The param-eter C is called the clarity of the radiator (C is usually expressed in µm4 cm−1).The scattering length Ls at wavelength λ is given by the relation: Ls(λ) = λ4/C.

Both the emitted number of photons and the Rayleigh scattering are propor-tional to L: for materials that are affected by this problem one may improve Ndet byincreasing the thickness d of the radiator only up to a limit given by the Rayleighscattering. This is the case of the silica aerogel that will be used in AMS-02,whose radiator thickness is limited to 2–3 cm.

The photons are emitted at angle of θc with respect to the particle direction,hence they reach the radiator surface with angles between τ − θc and τ + θc withrespect to the normal, and may be totally reflected in some cases (when the direc-tion is above the total reflection angle). In addition, the photons escaping from theradiator will have angles between τ−θ and τ+θ, where θ is the Cerenkov angle inthe vacuum gap, given by Snell’s law: sin θ = n sin θc. When reaching the pixelswith large incident angles, they may be reflected instead of being detected.

Finally, another effect is due to the radiator thickness d and to the reconstruc-tion algorithm, that makes the assumption that all photons are emitted in the midpoint of the radiator. This effect, with the chromatic dispersion, may produce anumber Nbkg of detected photons outside the area where the algorithm is search-ing them. Such “background” photons should be subtracted from the number ofdetected photons given by equation (6.15), because they cannot be used to recon-struct the event.

136


0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14

θ (

degr

ees)

NaF (n=1.34)

Agl (n=1.050)

Agl (n=1.030)

c

P (Gev/c/nucleon)

Figure 6.5: Cerenkov angle as function of the momentum per nucleon, for differ-ent radiators.

6.2.2 Radiator

For better understanding of the cosmic rays propagation inside the Galaxy, it isvery important to measure the relative abundances of primary and secondary nu-clei as function of the energy per nucleon (as seen in chapter 2). In particular,the knowledge of the relative abundances of secondary to primary elements (likeLi, Be, B versus C, for example) is extremely important to study the cosmic rayspropagation in the Galaxy.

Few balloon measurements of the B/C ratio exist below few GeV per nucleon(see figure 2.2), but with large uncertainties due to the poor statistics. One ofthe Physics goals of AMS-02 will be the study of this ratio with high statisticsfrom few hundred MeV/c per nucleon up to 10–15 GeV/c per nucleon, that is theinteresting range to put constraints on propagation models.

Figure 6.5 shows the Cerenkov angle of photons emitted inside Na F and aero-gel, for particle momenta up to 15 GeV/c per nucleon. The Cerenkov thresholdis lower for Na F, that has a refractive index of n = 1.34, but the achievable res-olution on θc makes impossible to go beyond 5 GeV/c per nucleon. On the otherhand, the aerogel can be used to measure β up to 12–15 GeV/c per nucleon, buthas a threshold at momenta above the TOF useful range. Hence the interesting

137

T AMS-02 RICH

A B C

θc

ECAL HOLE

AGL AGLNaF

Pixels planePixels plane

Figure 6.6: Composite radiator plane: the central Na F square is surroundend byaerogel tiles [109]. In case of no Na F, a particle ‘B’ entering theECAL hole would not be detected due to the small Cerenkov coneaperture. Instead, particle ‘C’ crosses Na F and is detected.

momentum window can be covered by using two radiators: sodium fluoride andaerogel with n = 1.03 [108].

The radiator layout will be the following: a central square of Na F 34.5 cmlarge and 0.5 cm thick, surrounded by aerogel tiles 3 cm thick (figure 6.6). Inaddition to a larger momentum window, this configuration increases the RICH ef-fective acceptance, because of the ECAL hole in the pixels plane. In fact, particlescrossing an aerogel radiator in the middle part and impinging on the calorimeterwould produce photons that would not hit any pixel, while the Na F has largerCerenkov angles, increasing the probability that photons are detected [110] (fig-ure 6.7 shows an example).

The β measurement made by RICH will allow AMS-02 to separate positronsfrom protons and electrons from antiprotons up to 10–12 GeV/c [111] (figure 6.8),thanks to the low refractive index of the aerogel. This will allow to study withlarge acceptance the antimatter fraction of cosmic rays over the range where mostof the flux is found. For higher energies, ECAL and TRD will become fundamen-tal for the e/p separation.

138


AGL30 Na F

Beryllium cP = 1.2 GeV/ /nucl.

Figure 6.7: Beryllium event producing Cerenkov radiation on aerogel n = 1.03and Na F n = 1.34 radiators [110].

Momentum (GeV/c)

RIC

H β

0.96

0.97

0.98

0.99

1

1.01

0 2 4 6 8 10 12 14 16 18 20

Figure 6.8: Simulated positron to proton separation for AMS-02, thanks to theRICH β measurement [111].

139

T AMS-02 RICH

Figure 6.9: A picture of the mandrel on the lathe, during surface polishing. Pic-ture taken by the author on September 2002.

6.2.3 Mirror

The geometrical acceptance of AMS-02 is very large (about 0.4 m2 sr), hence theparticles will cross the RICH radiator over all its area with angles ranging from0 up to about 40 degrees. In order not to loose photons generated at large angleswith respect to the z axis, a multi-layer conical mirror will be used to reflect suchphotons towards the pixel plane.

The mirror has the shape of a truncated orthogonal cone, with reflecting in-ner surface. The carbon fiber structure was designed in Italy by INFN Bolognaand Carlo Gavazzi Space SpA, that took care of the realization of the mandrel.Howewer, the final mirror will be built in USA by the CompositeMirrors company,and the conical structure will be assembled starting from 120 degrees sectors.

The first phase of the mirror construction is the realization of the mandrel:this is the “negative” of the final product, that will be the starting point for thedeposition of the different layers. The mandrel surface will determine the mir-ror geometry and reflectivity, because after detaching the mirror from it, only aprotecting layer will be deposed on the inner surface of the conical sectors.

140


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

150°45°90°

measurement point

RM

Sro

ug

hn

ess

[nm

]

Figure 6.10: Measurement of the mandrel surface roughness with three orienta-tions of the incident/reflected light beam plane. The RMS averagedover 90 measurement points is 2.3 nm along the cone directrix (0deg); for 45 deg it is 8.0 nm; for 90 deg it is 4.4 nm. The highestRMS value at 45 deg is due to the small residual scratch.

The aluminum mandrel was lathe machined (figure 6.9) to get the desired con-ical geometry within the allowed tolerances, computed by requiring that the max-imum systematic deviation from the ideal situation would produce angular de-flection not greater than 3 mrad (i.e. no sensible pixel mismatch on the detectingplane).

Its surface was then polished using very fine grained sand and a vibratingrubber head: the whole surface got this treatment many times, progressively de-creasing the root mean square deviations from the ideal smooth geometry. Unfor-tunately, during one of the last passes, a larger sand grain was trapped between therubber head and the surface, producing a visible rippling scratch over the wholemandrel. Howewer, after the final passes the surface rugosity was decreased belowthe needed values. The roughness was measured with an optical instrumentationusing the dispersion of an incident LASER beam: the measured RMS deviationalong three different directions with respect to the cone directrix (figure 6.10) arevery good (compared to the Cerenkov wavelength of 400–450 nm), even though

141

T AMS-02 RICH

Figure 6.11: A picture of the RICH PMT assembly [109].

the scratch was not perfectly erased.The carbon fiber structure of the mirror (1 mm thick) will be deposited layer

by layer on the mandrel while the latter is rotating (“filament winding” technique).In this way, layers with different fiber orientations with constant tension will be“glued” together. After detaching from the mandrel, aluminum will be depositedon the mirror internal surface, covered by a protection coating with quartz or mag-nesium fluoride.

The mandrel was sent in December 2002 to CompositeMirrors, that shouldprovide us the first 120 deg sample in April 2003, whose optical properties has tobe tested in Europe.

6.2.4 Photomultipliers and light guidesThe AMS-02 RICH will use 680 Hamamatsu R7600-00-M16 photomultipliers,the 16 channel version of the “venetian blind” PMT adopted by the TOF, ACCand ATC systems of AMS-01, for a total of 10880 9 × 9 mm2 pixels. They havea gain G ≈ 2 × 106 with voltage of 750–900 V, small enough cross-talk betweenpixels and quite similar gain and efficiency over the 16 channels. Figure 6.11shows the assembly of the PMT, enclosed in (half of) the magnetic shielding box,with light guides in front of it and the front-end (FE) electronics on the oppositeside.

In order to reduce the dead space between pixels, solid light guides (LG) wereplaced in front of the phototubes. Figure 6.12 shows a schematic view of theRICH light guides, that bring photons to their pixel through internal reflection.

142


Figure 6.12: The RICH light guides bring pho-tons to pixels through internal re-flection.

10

10

10 3

2

1

150 200 250 300ADC counts

Figure 6.13: Typical single photoelectron spectrum [112].

The PMT calibration is carried out by looking at the “single photoelectronspectrum”, that is the ADC histogram obtained when only few photons reach thecathode (figure 6.13). A pulsed LED is used to generate photons during the dataacquisition. This spectrum has a characteristic shape: the high pedestal peak on

143

T AMS-02 RICH

the left is followed by an asymmetrical charge distribution.As simple approximation, this spectrum can be considered the Poisson distri-

bution of events with zero, one, two or more photoelectrons. Each photoelectronis then multiplied by the PMT dynodes until a sizeable current pulse is producedby the anode. The PMT response to a single photoelectron can be approximatedby a Gaussian charge distribution. Hence, the single photoelectron spectrum canbe considered a convolution of the Gaussians corresponding to 1, 2, . . . , n photo-electrons, where the Poisson distribution determines the relative weights.

A fit of the single photoelectron spectrum will reveal the pedestal positionp0, and the mean p1 and standard deviation σ1 of the Gaussian corresponding toexactly 1 photoelectron. By definition, the PMT gain G is the (average) number ofelectrons produced by the anode following the multiplication of one photoelectron[113]:

G =(p1 − p0)QADC

e(6.17)

where QADC is the charge per ADC count and e is the electron charge.Because the expected number of photons per pixel is zero or one for protons,

increasing with the square of the incident particle charge up to few hundreds foriron nuclei, one of the most important parameters is the pixel single photoelectronresolution

φ =σ1

(p1 − p0), (6.18)

that is related to the charge resolution of the detector (the lesser is φ the better isphoton counting, hence the better is the charge measurement).

A more complicate statistical treatment of the single photoelectron spectrum[114] brings to the following probability distribution:

P(x) ' e−λδ(x) + (1 − e−λ)e−λ

S λλx/S

Γ(x/S )Θ(x) (6.19)

where we make use of the Dirac’s distribution δ(x), the Euler’s Gamma functionΓ(x) =

∫ ∞0 e−ttx−1 dt and the Heavyside’s step function Θ(x). With this approach,

the parameter λ and the scale factor S are used to write the gain G ≈ S (1 + λ) andthe single photoelectron response φ ≈ √λ/(1 + λ).

6.2.5 Magnetic shieldingThe fringing field of the AMS-02 superconducting magnet is of the order of 100–300 G in the RICH PMT plane. This is not as high as the field that forced the

144


Figure 6.14: Magnetic field (in Gauss units) in the RICH PMT plane.

adoption of a different kind of phototube for TOF and ACC: the problem canbe solved by putting a shielding material around the PMT. Howewer, the limitedweight budget forces a solution where the heavy ferromagnetic shield materialis minimized. In practice, shielding boxes of different thickness will be used inthe different parts of the PMT plane, according with the simulated field map (fig-ure 6.14).

One important effect was discovered making tests with arrow of boxes insolenoidal magnetic fields [115]: while a single box made of soft iron or VA-COFLUX 50 with 0.8 mm thick walls is a perfect shield for a transversal field of300 G, when 6 boxes are aligned along the field direction a collective effect growsup that lowers the screening of the central boxes.

The simulation of this boundary conditioned magnetostatic problem is not aneasy task: whereas the external field is very simple and can be computed analyt-ically after defining the currents, the field in the zone where the strictly packed

145

T AMS-02 RICH

Data d s Magnetic field (G) at given position(mm) (mm) 1 2 3 4 5 6 7 8 9

real 0.8 4.4 43 97 144 144 156 150 130 105 55sim. 0.8 4.4 54 110 145 160 160 160 145 110 54real 1.0 4.0 30 71 102 125 130 127 107 72 35sim. 1.0 4.0 34 91 120 140 140 140 120 91 34

Table 6.1: Comparison between measurements carried on in Bologna with tworows of 9 boxes inside Helmholtz coils and the ROXIE simulation.Each box has thickness d and it is distant s from the next one. Theagreement is within 10–20% (measurement uncertainties are of theorder of few Gauss).

Figure 6.15: Helmholtz coils used in Bologna to test two rows of 9 shieldingboxes, reconstructed with ROXIE.

boxes are placed must be computed with a finite element method. With the helpof S. Russenschuck, one of the authors of the ROXIE2 program, and M. Aleksa,both working in the CERN LHC magnet division (AT division, MEL group), I wasable to simulate the behavior of 1–3 rows of boxes, and to reproduce the measuredeffect within 10–20% (table 6.1 shows an example).

At the same time, test boxes with 0.6 mm, 0.8 mm, 1.0 mm, 1.2 mm thick

2http://roxie-web.web.cern.ch/roxie-web/

146

http://roxie-web.web.cern.ch/roxie-web/


Figure 6.16: ROXIE finite element model of a grid of 3× 9 ferromagnetic boxes,with horizontal Al bars. Boxes and bars thicnkess: 1 mm. Reflec-tion symmetry with respect to x and y applies.

walls were produced and tested in Bologna using two Helmholtz coils (figures6.15 and 6.16). The mechanical design of the RICH PMT plane was then changedin order to cope with the shielding problem: thin (0.6 mm) boxes are used wherethe field intensity is not very high, whereas thicker boxes are used in the mostcritical parts. The worst situation is found in the large rectangular grids that areparallel to the x direction, where the rows have 17 PMTs. Here the central boxesare the thickest ones (d = 1.2 mm), and thin material is used for the outer boxes.In addition, an increased gap between adjacent phototubes has been designed inorder to reduce the collective effects (figure 6.17).

The superconducting magnet is well simulated in vacuo by ROXIE (figure 6.18),obtaining values that agree with the official field map from the magnet producerwithin roughly 1%. The presence of the diamagnetic materials that constituteAMS-02 does not sensibly affect the field map. Howewer, the RICH PMT planeand the ECAL phototubes just below the RICH have ferromagnetic shieldingboxes that will affect the magnetic field. The nearest PMTs to the magnet arehalf a meter below the lower TOF plane, hence their shielding will not sensiblyaffect the field inside the tracker (i.e. no appreciable effect on rigidity resolution).

On the other hand, the field map just outside the core of AMS-02 will besomeway distorted: this will affect the trajectory of the exiting particles from thespectrometer, and that of back-splash particles from ECAL and RICH. Presentlythere is no hope to be able to simulate the effect of thousand shielding boxes in a

147

T AMS-02 RICH

Figure 6.17: Rectangular grid of shielding boxes, with different thickness alongthe x axis [109]. Nearly at the center of the structure, a thickersupport layer is used, to increase the spacing and to facilitate theshielding effect.

Figure 6.18: The AMS-02 superconducting magnet, simulated by ROXIE.

148


known magnetic field, because of the complexity of the numerical methods. Onlyreal particles will make it possible to reconstruct the field configuration below thespectrometer.

6.3 The beam testThe heavy ion beam test carried on at CERN SPS, on October 2002 (see chap-ter 7), has been very useful to compare the results of Na F and different kinds ofsilica aerogel tiles. At the same time, it was a very important validation test forthe RICH simulation, and a test-bench for the read out electronics.

The selection line was tuned to obtain 20 GeV/c per nucleon secondaries withA/Z = 2 (4He and almost all stable nuclei up to iron), A/Z = 7/4 (mostly 7Be), andA/Z = 1 (protons). Special runs were carried on with protons of lower energies,to study the velocity resolution of the RICH prototype (proton energy: 5, 7, 9, 11,13 GeV). Figure 6.19 shows the image on the pixel plane of the Cerenkov ringproduced by a 20 GeV/A Li nucleus.

6.3.1 The RICH prototypeFigure 6.20 shows the grid of photomultipliers that has been used to assembly theRICH prototype (also known as “MiniRICH”). The 96 PMTs are strictly packed(the light guides touch the neighboring ones), and the front-end electronics is thefinal one. The radiator mechanics is able to support tiles of different geometries,that can be placed from few centimeters to half a meter away from the pixel plane.

6.3.2 The radiatorsOn the beam test, five different aerogel samples (three from Matsushita, one fromInstitute of Catalysis, Novosibirsk University) and one sodium fluoride radiatorwere used by the RICH prototype. The characteristics of the different aerogelsamples are summarized in table 6.2.

The charge resolution of the RICH is quite good: figure 6.21 shows the recon-structed charge distribution for run 312, using a n = 1.03 sample from Novosi-birsk, while figure 6.22 shows the Gaussian fit to the He events (selected usingdata from scintillators).

149

T AMS-02 RICH

Figure 6.19: Li event observed at CERN SPS [109].

Radiator Clarity d Nexp1 σ(Z = 2)

and n ( µm4/cm) (cm)NM 1.05 1.3 × 10−2 2 8.3 ± 0.2 0.21NM 1.03 1.2 × 10−2 2 5.7 ± 0.1 0.24OM 1.03 1.5 × 10−2 3 6.1 ± 0.1 0.23Nov 1.03 7.6 × 10−3 3 8.9 ± 0.1 0.20Nov 1.04 1.3 × 10−2 3 8.5 ± 0.1 0.20

Table 6.2: Comparison between different radiators with thickness d on He beam.New Matsushita samples (“NM”) with refractive indices 1.05 and 1.03were tested along with an old Matsushita (“OM”) sample with n =

1.03, and two aerogel tiles from Novosibirsk (“Nov”) with n = 1.03and n = 1.04 [116]. “Nov 1.04” is the only hydrophobic sample,whereas all the other ones are hydrophilic.

150


279

mm

341 mm

Figure 6.20: MiniRICH PMT plane with light guides, top view.

151

T AMS-02 RICH

Z0

20

40

60

80

100

2010 15 255

Figure 6.21: Charge distribution seen by the RICH prototype with aerogel fromNovosibirsk (n = 1.03) [116].

Run 312 − Nov 1.03

charge

FIT:µ=2.00σ=0.20

1

10

10 2

0.5 1 1.5 2 2.5 3 3.5

Figure 6.22: Charge distribution for He nuclei of the Novosibirsk n = 1.03 sam-ple [116]. Dots are real data, the histogram is the simulation. Thefits gives the resolution of 0.2 charge units.

152

Chapter 7

Ion beam test at CERN SPS

In order to understand the behavior of the AMS-02 detector, a very complex sim-ulation has been developed by the Collaboration1. The computer program is basi-cally divided into two sections: first, the simulation of the analog signals producedby each subdetector and of their “digitization” by the front-end electronics is fol-lowed by the storage of the “raw data” on disk; second, the raw data are elaboratedin order to get both low level (like the energy deposited in a given active part ofAMS-02) and high level informations (for example the particle momentum). Theuser can choose to generate files containing raw data, to read directly real or sim-ulated raw data from disk and process them, and to make both steps for eachsimulated event.

The most delicate part of the simulation is the first one: the physical pro-cesses of all particles that may interact with active and passive parts of the detec-tor have to be well understood and reproduced. This is done with the help of theGEANT 3.21 well tested FORTRAN framework [117] or of its updated C++ ver-sion Geant42. Howewer, extensive tests have to be done with detector prototypesin order to check the consistency of the simulation and to quantify the systematicdeviations from the observed beavior.

The best way to validate the detector simulation is to use particle beams withknown properties, like particle charge, mass and momentum, and to look at thedetector response under these well controlled conditions. The use of an externaltrigger makes possible to obtain absolute efficiencies as function of the particleenergy, charge and direction, whereas the data analysis should be able to show thebackground produced by misidentified particles, bad energy or velocity measure-

1http://ams.cern.ch/AMS/analysis.html2http://wwwinfo.cern.ch/asd/geant4/geant4.html

153

http://ams.cern.ch/AMS/analysis.html

http://wwwinfo.cern.ch/asd/geant4/geant4.html

I CERN SPS

ments, etc. In the specific case of AMS, that is a spectrometer with great accep-tance and large energy range, the number of degrees of freedom is very high: it isnecessary to sample the input parameters space in a systematic way. For example,AMS-01 was tested on a ion beam at GSI with 600 different incident directions[100].

The AMS-02 subdetectors have been tested using particle accelerators duringthe last few years: a 20 layer TRD prototype was tested in summer 2000 at CERNwith 5–250 GeV/c singly charged particles (electrons, muons, pions and protons)[93]; the ECAL prototype was tested at CERN in 2001 [118]; the RICH prototypewas tested at CERN in October 2002 together with a tracker prototype and a cou-ple of TOF counters. This chapter deals with the ion beam test carried on with theSPS accelerator at CERN, on October 14–19, 2002.

7.1 Experimental setupThe ion beam test of the RICH prototype was carried on at CERN on October2002 using a 20 GeV/c per nucleon Pb beam accelerated by the Super Proton Syn-chrotron (SPS), colliding with a Be target (in T4, see figure 7.1). The secondaryfragments (all nuclei up to Pb, mostly with the same momentum per nucleon asthe primary beam [119]) were filtered through the H8 selection line, obtaining a≈ 3 cm large ion beam with given A/Z ratio (i.e. defined rigidity).

The RICH prototype (figure 7.2) was placed in the NA45 area, together withfew “parasitic” detectors. Among the latter ones, two AMS-02 subdetector pro-totypes were tested: six tracker ladders in front of the RICH prototype and twoTOF counters behind it. The particles of the secondary beam had a spill flat topof 12.7 s over a cycle of 19 s. During the “spill on” phase, the trigger rate wasranging from hundred to few thousand Hz, depending on the tuning of the selec-tion line, that was set at values A/Z = 2, A/Z = 3/2, A/Z = 7/4, A/Z = 1 for eachradiator type.

7.1.1 RICH prototype

The AMS RICH prototype is a proximity focusing Cherenkov imager consistingof 96 units of 16-anode PMTs (1568 readout channels). It has been tested usingthe secondary fragments beam obtained from a 20 GeV/c per nucleon primarySPS Pb beam. Data were collected during a 4 days run with nuclear elements

154

7.1 — Experimental setup

Search(near thecryostat1rst floor)

T10NA48

NA50

R21-06

R22-26B5

T6

T4T4

B2

R22-07B3

R22-01B2

R22-04B1

R22-03B3

T2T2R22-05

R22-02B2

B1

241107MBNH

2411283MTNH

0400032MTNH

0200032MTNH

2309283MTSH

230907MBNH

GALERIESGALERIES

Chain H4Chain 11

Chain H6

Chain H2Chain H2Exp

Chain T2

Chain H8Exp

Chain P0

Chain M2Chain T6

Chain H2

Chain H4

Chain H6

Chain H8

Chain P0Chain M2

Chain M2

Chain M2

Chain T6

EHN2

TCC8ECN3

TDC8

TCC2

G L 8 1 8

G L 8 1 5

G L 8 1 4

G L 8 1 3

G L 8 1 1

entre EHN1 et BA81

ZÔNES CONTROLEESPAR LE PCR

B . C h a u c h a i x : m i s e à j o u r l e 1 3 / 0 3 / 2 0 0 0N O R T H A R E A A C C E S S

Chain H6BChain H6C

041 528041 542

( MBE 2103 Tot.; TED 2103; TBSE 2106 )

NA59NA49

H2AH4AH4B

H6AH6B

H6C

NA45H8A

H8B

TAXMOT

TDVIO(3)TDVIO(2)

TDVIO(1)

Chain H8Chain T4

.Search

TDXMIO(1)

.MSNH04122

B1R22-08

MSNH04129

B2R22-20

B4R22-64MCAH

041124

B1R22-14.2

B2R22-15.2

MBNV042049

B1R22-14.1

B2R22-15.1

MBNV042067

MBNV042079

MBNV042061

MBNV022053

MBNV022083

MBNV021065

MBNV021083MBNT

062074

MCA062119

MCV061067

MBNH061109

MCAH022117 B5

R22-17

B2R22-09

B3R22-10

B3R22-12

B4R22-11

PPEPPX

PPEPPX

PPE

PPX

Passerelle

PPXPPE

PPEPPX

PPX

Dump

PPE

PPXPPX

PPE

PPGE81PPX

PPEPPE

PPXPPE PPX

PPGE82

PPE

PPX

PPE PPX

PPE

PPXPPE

PPE

PPX

PPEPPX

PPXPPE

PPEPPX

à l'étagePasserelle

PPG842

PPG831

PPGE832TT83

PPG850

PPG841

PPG

PPEPPE

PPXPPX

TT84

02- 02102501- 021023

TAXMOT04- 02202503- 022023

TAXMOT06- 04202005- 042018

TAXMOT08- 04302007- 043018

TAXMOT13- 05205412- 062052

TAXMOT15- 06105414- 061052

NA57ALICE Tests

Dump

DumpPPE

PPXPPG

PPGX81

PPGX82

PPGX82

TT85

PPG851.5

PPG851.6

Access point TCC8PPG851

PPG852.4

PPG852.5

Access point ECN3PPG852

GHN300PPG300.1

PPG300.2PPG300.3

PPG300.4

PPG812Access point TDC8

from BA81

B4MBW043096

R22-26B5

MBW043082

PPG851.7

PPG851.8 (acces via ECN3)

TDC85

PPE

PPG

GL300

Chain P0 TCC8P42/(P62)

P41/P61K12

P4/P6

M2

M2

P4

P6NR31-04

NR22-21

PPEPPE

PPXPPX

PPX

PPXPPG

H8H8 H6

H6

H4 H2

H4 H2

M2

NR22-23B3 TT82

TT81

PPGX81

B6

TCC2

Chain 16Chain 14

Chain 12

Chain T6

Dump

Free Access

PPE

Chain 10

Figure 7.1: SPS North Area. 155

I CERN SPS

Figure 7.2: RICH prototype inside vacuum chamber, facing up during a radiatorchange. The radiator support is above the picture (not shown). CERNSPS, NA45 area, October 2002.

having A/Z = 2 mass to charge ratio, going from deuterium (D) up to the Fegroup, including all intermediate isotopes (most notably He, Li, Be, B, C, N, O,Al and Ca). Other beam line settings have been used to select different A/Z values,like 7/4 (to study 7Be) and 3/2 (for 3He). In addition to the data taken to study thecharge resolution, special runs were carried on with protons between 5 and 20GeV/c, to study the β resolution.

The response of the prototype has been studied for various radiators (chap-ter 6): Silica aerogels with refractive index 1.03 and 1.05, and sodium fluoride(Na F). Cerenkov rings associated to ions over the covered mass range have beenobserved, with average number of photons ranging from 4–7 for Z = 1 elements,up to several thousands for high atomic numbers. The charge and mass resolutionsare being evaluated from the analysis of the 5 million recorded events.

156

7.1 — Experimental setup

Trigger*BusyR

Def. closed

Def. open

LV1

Busy

BusyT OS

24SC

AL

ER

32 bit

Signal cond.

TriggerBusyT

20 HzInterspill

Timer

LV1Tracker cratein exp area

Busy

LV1

Interspill

EventNumber

NumberEvent

40 m

RICH Crate in counting room

Tracker Crate in counting room

Figure 7.3: Combined RICH/tracker trigger scheme for the ion beam test [120].

7.1.2 Tracker prototype

The time window allocated for the RICH prototype by the SPS coordinators wasexploited also by the tracker and TOF collaborations, that installed “parasitic”experiments in the NA45 area. The data acquisition procedure was developedin order to guarantee that the three separate DAQ setups could operate in a syn-chronized way without risk of collisions: the general trigger was given by theRICH collaboration, who provided also a scaler giving a unique label to the cur-rent event.

The general trigger logics gave two outputs: the general trigger and the generalbusy signals. The former was used by the RICH, tracker and TOF DAQ setups asthe necessary signal for data recording. The latter was used to inhibit the DAQprocedures. In order to be able to run synchronized, each setup was sending itsown busy signal to the main trigger logics (on the RICH side): the general busywas a logic of the RICH busy, the tracker busy and the TOF busy.

The RICH 32 bit CAMAC scaler was modified by the tracker group fromGeneve University: the reset possibility was denied by suppressing INHIBIT andCLEAR signals, the 8 high significant bits were suppressed, and the resulting24 bit words were transmitted to the tracker setup (and then forwarded to the

157

I CERN SPS

TOF setup) via LVDS cables [120]. Figure 7.3 shows the RICH/tracker combinedtrigger logics.

Six tracker ladders were crossed by the ion beam, each of them being a double(x, y) read-out plane with pitch of 110 µm along the y axis (the AMS bendingdirection) and 208 µm along x.

7.1.3 TOF counters

Two AMS-02 TOF counters and one AMS-01 TOF counter were placed in a blackbox and positioned behind the RICH prototype, in the NA45 area. The beamaxis was first positioned at the counters center, but runs were also taken with therelative beam position being at +10 cm, −10 cm and −20 cm with respect to thecounters center.

The first TOF counter was a scintillator from Eljen Technologies with 4 Hama-matsu R5946 PMTs. The second counter was a Bicron scintillator with 4 PMTsof the same kind. The third counter was the 1.07 TOF counter, dismounted fromAMS-01. One of the goals of the ion beam test was to select the best scintillatoramong the two products, comparing them to the old one (from Bicron).

Figure 7.4 shows the DAQ setup used by the TOF group: the coincidence ofall three scintillators gave the “local trigger” and the coincidence between thissignal and the general trigger was used to start the acquisition. The local busylevel was sent to the general trigger (on the RICH side), exactly in the same wayof the tracker busy.

Standard CAMAC electronics were used to build up the setup, with NIM mod-ules.

7.2 Preliminary results

Data analysis is still in progress for RICH, TOF and tracker. The first resultsabout RICH were given in chapter 6 and the first results about TOF were given inchapter 5. Here we show a plot of the correlation between the charge measuredby RICH and TOF3 (figure 7.5) and the tracker spatial resolution for He and Benuclei4 (figures 7.6 and 7.7). The tracker spatial distributions are fitted with the

3Courtesy of F. Giovacchini.4Courtesy of G. Ambrosi.

158

7.2 — Preliminary results

200

s

TD

C

0 1 2 3 4 5st

art

0 1 2 3 4 5 6 7 8 9 10 11ga

te

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nit

end

mar

ker

out

in

50−

100

nsT

ime

Uni

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end

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in250−

600

ns

µ

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/out

10%

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ener

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er

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ral v

eto

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ral t

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2 310 4 5 6 7 8 9

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ms)

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ns

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159

I CERN SPS

2

4

6

8

10

12

14

16

18

2 4 6 8 10 12 14 16 18

ENTRIES 15025

TOF charge

RIC

H c

harg

e

Figure 7.5: Preliminary consistency check between RICH and TOF charge mea-surements.

sum of two Gaussians. The first plot refers to an inclined ladder, hence has alwaysa wider distribution. The result is that σx ≈ 30 µm and σy ≈ 10 µm.

160

7.2 — Preliminary results

Figure 7.6: Preliminary plot of the tracker spatial resolution along x (left panel)and y (right panel), for He nuclei.

Figure 7.7: Preliminary plot of the tracker spatial resolution along x (left panel)and y (right panel), for Be nuclei.

161

162

Appendix A

Abbreviations

ACR Anomalous Cosmic RaysADC Analog to Digital ConverterAMS Alpha Magnetic SpectrometerAU Astronomic Unit (1 AU = 1.496 × 108 km)BZ Big Z particle digital signalCAMAC Computer Automated Measurement And ControlCAN Controller Area Network (bus)CMB Cosmic Microwave BackgroundCMS Center of Mass SystemCP Charged Particle digital signalCR Cosmic Ray(s)CT Central charged particle digital signalDAC Digital to Analog ConverterDAQ Data AcQuisitionDC During CurrentDRM Diffusive Reacceleration ModelECAL Electromagnetic CALorimeterFE Front-End (electronics)FIP First Ionization PotentialFT Fast TriggerGRB Gamma-Ray BurstHV High VoltageHVE High Voltage ElevatorHVPS High Voltage Power SupplyISM Inter-Stellar Medium

163

A A. A

ISS International Space StationLASER Light Amplification by Stimulated Emission of RadiationLED Light-Emitting DiodeLEP Large Electron-Positron colliderLG Light GuideLIS Local Interstellar SpectrumLR Linear RegulatorLT Low ThresholdLV Low VoltageLVDS Low Voltage Differential SignalingLVPS Low Voltage Power SupplyMC Monte CarloMDR Maximum Detectable RigidityMIP Minimum Ionizing ParticleNIM Nuclear Instrument ModulePCB Printed Circuit BoardPMT PhotoMultiplier TubePOCC Payload Operation Control CenterRICH Ring Imaging CHerenkovRMS Root Mean SquareSAA South Atlantic AnomalySDR2 Scintillator Data Reduction boardSFEA2 Scintillator Front-End Anticoincidence boardSFEC2 Scintillator Front-End Charge boardSFET2 Scintillator Front-End Time boardSHT Super-High ThresholdSHV Scintillator High Voltage redundant moduleSN SupernovaSPD Scintillator Power Distributor boxSPS Super Proton SynchrotronTDC Time to Digital ConverterTOF Time Of FlightTDR Tracker Data ReductionTRD Transition Radiation DetectorUHECR Ultra High Energy Cosmic RaysUSCM Universal Slow Control ModuleUSS Universal Support Structure

164

Appendix B

TOF PMT positioning and field

PMT Fx Fy Fz Rx Ry Rz B Bx By Bz θ(cm) (cm) (cm) (cm) (cm) (cm) (G) (G) (G) (G) (deg)

101n1 -71.26 -48.5 66.49 -75.95 -48.50 68.2 1739.8 1538.3 -462.5 -668.4 -15.8101n2 -71.26 -43.00 66.49 -75.95 -43.00 68.2 1776.3 1618.6 -514.8 -520.0 -17.0101n3 -71.26 -37.49 66.49 -75.95 -37.49 68.2 1815.0 1695.8 -534.3 -364.5 -18.8102n1 -70.55 -31.51 66.00 -75.55 -31.50 66.0 1913.2 1825.2 -532.7 -212.2 -17.3102n2 -70.55 -26.00 66.00 -75.55 -25.99 66.0 1972.0 1908.8 -489.9 -72.8 -14.4103n1 -70.55 -20.01 64.50 -75.55 -20.00 64.5 2372.0 2315.7 -486.8 165.1 -12.4103n2 -70.55 -14.50 64.50 -75.55 -14.49 64.5 2465.0 2417.1 -329.8 354.2 -11.2104n1 -70.55 -8.51 66.00 -75.55 -8.51 66.0 2091.0 2066.7 -170.1 269.1 -8.8104n2 -70.55 -3.00 66.00 -75.55 -3.00 66.0 2096.6 2073.8 -58.8 302.5 -8.5105n1 -70.55 3.00 64.50 -75.55 3.00 64.5 2578.8 2519.2 70.9 546.6 -12.3105n2 -70.55 8.51 64.50 -75.55 8.51 64.5 2547.7 2491.0 204.0 494.3 -12.1106n1 -70.55 14.49 66.00 -75.55 14.50 66.0 2090.4 2062.2 280.9 195.4 -9.5106n2 -70.55 20.00 66.00 -75.55 20.01 66.0 2039.5 1994.9 421.5 46.1 -12.1107n1 -70.55 25.99 64.50 -75.55 26.00 64.5 2336.3 2260.2 588.6 59.5 -14.8107n2 -70.55 31.50 64.50 -75.55 31.51 64.5 2279.0 2181.2 653.0 -100.4 -17.0108n1 -71.26 37.49 67.99 -75.95 37.49 69.7 1776.3 1657.6 520.5 -370.0 -18.6108n2 -71.26 42.99 67.99 -75.95 42.99 69.7 1738.9 1581.5 500.7 -521.6 -16.8108n3 -71.26 48.50 67.99 -75.95 48.50 69.7 1701.8 1500.2 448.0 -667.’ -15.8101p1 71.26 -48.50 66.49 75.95 -48.50 68.2 1739.8 1538.3 462.5 668.4 15.8101p2 71.26 -42.99 66.49 75.95 -42.99 68.2 1776.3 1618.7 514.8 519.8 17.0101p3 71.26 -37.49 66.49 75.95 -37.49 68.2 1815.0 1695.8 534.3 364.5 18.8102p1 70.55 -31.50 66.00 75.55 -31.50 66.0 1913.3 1825.3 532.7 212.2 17.4102p2 70.55 -25.99 66.00 75.55 -25.99 66.0 1972.1 1908.9 489.8 72.9 14.5103p1 70.55 -20.00 64.50 75.55 -20.00 64.5 2372.0 2315.7 486.8 -165.1 12.5103p2 70.55 -14.49 64.50 75.55 -14.49 64.5 2465.4 2417.3 329.8 -354.6 11.3104p1 70.55 -8.51 66.00 75.55 -8.51 66.0 2091.0 2066.7 170.1 -269.1 8.8104p2 70.55 -3.00 66.00 75.55 -3.00 66.0 2096.6 2073.8 58.8 -302.5 8.5105p1 70.55 3.00 64.50 75.55 3.00 64.5 2578.8 2519.2 -70.9 -546.6 12.3105p2 70.55 8.51 64.50 75.55 8.51 64.5 2547.7 2491.0 -204.0 -494.3 12.1106p1 70.55 14.49 66.00 75.55 14.50 66.0 2090.4 2062.2 -280.9 -195.4 9.5106p2 70.55 20.00 66.00 75.55 20.01 66.0 2039.5 1994.9 -421.5 -46.1 12.1107p1 70.55 25.99 64.50 75.55 26.00 64.5 2336.3 2260.2 -588.6 -59.5 14.8107p2 70.55 31.50 64.50 75.55 31.51 64.5 2279.0 2181.2 -653.0 100.4 17.0108p1 71.26 37.50 67.99 75.95 37.50 69.7 1776.3 1657.5 -520.5 370.1 18.5108p2 71.26 43.01 67.99 75.95 43.01 69.7 1738.8 1581.3 -500.6 521.9 16.8108p3 71.26 48.51 67.99 75.95 48.51 69.7 1701.8 1500.1 -448.0 667.2 15.8

165

A B. TOF PMT


201n1 -43.00 -74.47 66.13 -43.00 -78.01 69.66 2086.4 -321.1 708.1 -1936.1 -26.4201n2 -37.49 -74.47 66.13 -37.49 -78.01 69.66 2070.4 -649.0 697.3 -1838.2 -30.1202n1 -27.28 -80.43 73.69 -23.74 -82.93 76.19 1323.3 -869.3 414.3 -907.7 -15.4202n2 -20.97 -80.43 73.69 -17.43 -82.93 76.19 1285.4 -1001.3 337.4 -732.1 -14.8203n1 -15.78 -82.61 68.84 -12.24 -85.67 70.60 1431.0 -1244.8 333.7 -621.9 -24.3203n2 -9.47 -82.61 68.84 -5.93 -85.67 70.60 1394.5 -1347.3 171.1 -316.3 -33.0204n1 -4.28 -84.18 64.22 -0.74 -87.70 64.53 1652.0 -1645.0 80.2 -128.6 -42.0204n2 3.23 -82.78 64.10 7.76 -84.88 64.28 1746.8 -1718.0 -160.5 271.7 -32.0205n1 -4.20 -80.87 73.81 -8.90 -81.97 75.12 1221.3 -1198.9 97.2 -211.0 30.7205n2 3.13 -81.43 74.47 -0.97 -83.27 76.67 1200.0 -1199.8 -10.8 21.0 33.9206n1 9.47 -84.11 70.34 5.93 -87.17 72.11 1283.1 -1236.0 -162.4 304.0 32.6206n2 15.78 -84.11 70.34 12.24 -87.17 72.11 1315.0 -1150.7 -296.4 563.1 24.7207n1 20.97 -79.41 74.14 17.43 -81.44 77.04 1318.0 -1024.3 -325.6 762.8 10.0207n2 27.28 -79.41 74.14 23.74 -81.44 77.04 1363.1 -890.1 -399.7 951.9 9.9208n1 37.50 -74.47 67.63 37.50 -78.01 71.16 1901.8 -599.4 -615.8 1696.5 30.8208n2 43.01 -74.47 67.63 43.01 -78.01 71.16 1912.1 -302.3 -623.0 1782.3 27.3201p1 -43.00 74.47 66.13 -43.00 78.00 69.66 2086.5 -321.2 -708.1 -1936.2 -26.3201p2 -37.49 74.47 66.13 -37.49 78.00 69.66 2070.4 -649.1 -697.2 -1838.3 -30.0202p1 -27.28 80.43 73.69 -23.74 82.93 76.19 1323.3 -869.3 -414.3 -907.7 -15.4202p2 -20.97 80.43 73.69 -17.43 82.93 76.19 1285.4 -1001.3 -337.4 -732.1 -14.8203p1 -15.78 82.61 68.84 -12.24 85.67 70.61 1430.9 -1244.8 -333.7 -621.9 -24.2203p2 -9.47 82.61 68.84 -5.93 85.67 70.61 1394.4 -1347.2 -171.1 -316.4 -33.0204p1 -4.28 84.18 64.22 -0.74 87.70 64.53 1652.0 -1645.0 -80.2 -128.6 -42.0204p2 3.23 82.78 64.10 7.76 84.88 64.28 1746.8 -1718.0 160.5 271.7 -32.0205p1 -4.21 80.87 73.80 -8.90 81.97 75.11 1221.4 -1199.1 -97.3 -211.0 30.7205p2 3.13 81.43 74.47 -0.97 83.27 76.66 1200.1 -1199.9 10.8 21.0 33.8206p1 9.47 84.11 70.34 5.93 87.17 72.10 1283.2 -1236.0 162.5 304.0 32.6206p2 15.78 84.11 70.34 12.24 87.17 72.10 1315.0 -1150.8 296.4 563.1 24.7207p1 20.97 79.41 74.14 17.43 81.44 77.04 1318.0 -1024.3 325.6 762.8 9.9207p2 27.28 79.41 74.14 23.74 81.44 77.04 1363.1 -890.1 399.7 951.9 9.9208p1 37.49 74.47 67.63 37.49 78.01 71.16 1901.7 -599.6 615.8 1696.4 30.8208p2 43.00 74.47 67.63 43.00 78.01 71.16 1912.1 -302.5 623.0 1782.3 27.3

166

A B. TOF PMT


301n1 -59.53 -71.43 -73.69 -63.07 -73.93 -76.19 1397.1 489.6 271.8 1280.0 -36.6301n2 -53.22 -71.43 -73.69 -56.76 -73.93 -76.19 1484.6 292.1 344.3 1414.3 -43.0302n1 -43.00 -74.47 -66.13 -43.00 -78.00 -69.66 2086.5 -321.2 708.1 1936.2 -26.3302n2 -37.49 -74.47 -66.13 -37.49 -78.00 -69.66 2070.4 -649.1 697.2 1838.3 -30.0303n1 -27.28 -80.43 -73.69 -23.75 -82.93 -76.19 1323.4 -869.2 414.3 907.8 -15.4303n2 -20.97 -80.43 -73.69 -17.44 -82.93 -76.19 1285.4 -1001.2 337.4 732.1 -14.8304n1 -15.78 -82.61 -68.84 -12.24 -85.67 -70.61 1430.9 -1244.8 333.7 621.9 -24.2304n2 -9.47 -82.61 -68.84 -5.93 -85.67 -70.61 1394.4 -1347.2 171.1 316.4 -33.0305n1 -4.28 -84.18 -64.22 -0.74 -87.70 -64.53 1652.0 -1645.0 80.2 128.6 -42.0305n2 2.69 -83.53 -64.16 6.79 -86.39 -64.41 1679.0 -1655.4 -151.4 -236.3 -41.5306n1 -4.21 -80.87 -73.80 -8.90 -81.97 -75.11 1221.4 -1199.6 97.3 211.0 30.7306n2 3.13 -81.43 -74.47 -0.97 -83.27 -76.66 1200.1 -1199.9 -10.8 -21.0 33.8307n1 9.47 -84.11 -70.34 5.93 -87.17 -72.10 1283.2 -1236.0 -162.5 -304.0 32.6307n2 15.78 -84.11 -70.34 12.24 -87.17 -72.10 1315.0 -1150.8 -296.4 -563.1 24.7308n1 20.97 -79.41 -74.14 17.43 -81.44 -77.04 1318.0 -1024.3 -325.6 -762.8 9.9308n2 27.28 -79.41 -74.14 23.74 -81.44 -77.04 1363.1 -890.1 -399.7 -951.9 9.9309n1 37.49 -74.47 -67.63 37.49 -78.01 -71.16 1901.7 -599.6 -615.8 -1696.4 30.8309n2 43.00 -74.47 -67.63 43.00 -78.01 -71.16 1912.1 -302.5 -623.0 -1782.3 27.3310n1 53.71 -73.43 -72.18 57.25 -75.93 -74.68 1568.5 317.0 -418.7 -1478.0 41.7310n2 60.02 -73.43 -72.18 63.56 -75.93 -74.68 1438.9 585.3 -307.7 -1278.0 33.0301p1 -59.53 71.43 -73.68 -63.07 73.93 -76.18 1397.3 489.7 -271.9 1280.1 -36.6301p2 -53.22 71.43 -73.68 -56.76 73.93 -76.18 1484.8 292.1 -344.4 1414.5 -43.0302p1 -43.00 74.47 -66.13 -43.00 78.01 -69.66 2086.4 -321.2 -708.1 1936.1 -26.4302p2 -37.49 74.47 -66.13 -37.49 78.01 -69.66 2070.4 -649.0 -697.3 1838.2 -30.1303p1 -27.28 80.43 -73.69 -23.74 82.93 -76.19 1323.3 -869.3 -414.3 907.7 -15.4303p2 -20.97 80.43 -73.69 -17.43 82.93 -76.19 1285.4 -1001.3 -337.4 732.1 -14.8304p1 -15.78 82.61 -68.84 -12.24 85.67 -70.60 1431.0 -1244.8 -333.7 621.9 -24.3304p2 -9.47 82.61 -68.84 -5.93 85.67 -70.60 1394.5 -1347.3 -171.1 316.3 -33.0305p1 -4.28 84.18 -64.22 -0.74 87.70 -64.53 1652.0 -1645.0 -80.2 128.6 -42.0305p2 2.69 83.53 -64.16 6.79 86.39 -64.41 1679.0 -1655.4 151.4 -236.3 -41.5306p1 -4.20 80.87 -73.81 -8.90 81.97 -75.12 1221.3 -1198.9 -97.2 211.0 30.7306p2 3.13 81.43 -74.47 -0.97 83.27 -76.67 1200.0 -1199.8 10.8 -21.0 33.9307p1 9.47 84.11 -70.34 5.93 87.17 -72.11 1283.1 -1236.0 162.4 -304.0 32.6307p2 15.78 84.11 -70.34 12.24 87.17 -72.11 1315.0 -1150.7 296.4 -563.1 24.7308p1 20.97 79.41 -74.14 17.43 81.44 -77.04 1318.0 -1024.3 325.6 -762.8 9.9308p2 27.28 79.41 -74.14 23.74 81.44 -77.04 1363.1 -890.1 399.7 -951.9 9.9309p1 37.50 74.47 -67.63 37.50 78.01 -71.16 1901.8 -599.4 615.8 -1696.5 30.8309p2 43.01 74.47 -67.63 43.01 78.01 -71.16 1912.1 -302.3 623.0 -1782.3 27.3310p1 53.71 73.43 -72.19 57.25 75.93 -74.69 1568.3 316.9 418.6 -1477.8 41.7310p2 60.02 73.43 -72.19 63.56 75.93 -74.69 1438.7 585.2 307.6 -1277.8 33.0

167

A B. TOF PMT


401n1 -73.01 -48.52 -66.49 -77.7 -48.52 -68.20 1721.2 1533.3 -472.9 622.9 -16.1401n2 -73.01 -43.01 -66.49 -77.7 -43.01 -68.20 1759.9 1611.7 -523.9 474.6 -17.7401n3 -73.01 -37.49 -66.49 -77.7 -37.50 -68.20 1800.1 1686.7 -542.7 317.8 -19.9402n1 -72.30 -31.51 -66.00 -77.3 -31.51 -66.00 1884.7 1798.7 -539.0 162.0 -17.4402n2 -72.30 -25.99 -66.00 -77.3 -26.00 -66.00 1933.3 1868.5 -496.3 15.9 -15.0403n1 -72.30 -20.01 -64.50 -77.3 -20.01 -64.50 2414.3 2335.7 -525.8 -311.0 -14.7403n2 -72.30 -14.49 -64.50 -77.3 -14.50 -64.50 2512.2 2436.8 -336.7 -509.7 -14.1404n1 -72.30 -8.51 -66.00 -77.3 -8.51 -66.00 2066.2 2032.5 -169.6 -330.7 -10.4404n2 -72.30 -3.00 -66.00 -77.3 -3.00 -66.00 2077.6 2045.4 -58.5 -359.8 -10.1405n1 -72.30 3.00 -64.50 -77.3 3.00 -64.50 2580.0 2501.9 70.8 -626.0 -14.1405n2 -72.30 8.51 -64.50 -77.3 8.51 -64.50 2557.3 2480.3 205.7 -587.9 -14.1406n1 -72.30 14.49 -66.00 -77.3 14.49 -66.00 2044.4 2007.2 277.7 -271.7 -11.0406n2 -72.30 20.00 -66.00 -77.3 20.00 -66.00 1981.7 1931.5 428.6 -113.3 -12.9407n1 -72.30 25.99 -64.50 -77.3 25.99 -64.50 2346.1 2259.5 613.2 -151.6 -15.6407n2 -72.30 31.50 -64.50 -77.3 31.50 -64.50 2275.7 2174.4 670.6 31.6 -17.2408n1 -73.01 37.49 -67.99 -77.7 37.49 -69.70 1764.6 1651.7 529.4 324.4 -19.5408n2 -73.01 43.00 -67.99 -77.7 43.00 -69.70 1725.9 1578.2 510.7 477.0 -17.5408n3 -73.01 48.52 -67.99 -77.7 48.51 -69.70 1687.8 1500.3 460.4 621.2 -15.9401p1 73.01 -48.52 -66.49 77.7 -48.52 -68.20 1721.2 1533.3 472.7 -622.9 16.1401p2 73.01 -43.01 -66.49 77.7 -43.01 -68.20 1759.9 1611.7 523.9 -474.6 17.7401p3 73.01 -37.50 -66.49 77.7 -37.50 -68.20 1800.1 1686.7 542.7 -317.8 19.8402p1 72.30 -31.51 -66.00 77.3 -31.51 -66.00 1884.7 1798.7 539.0 -162.0 17.4402p2 72.30 -26.00 -66.00 77.3 -26.00 -66.00 1933.3 1868.4 496.3 -15.9 14.9403p1 72.30 -20.00 -64.50 77.3 -20.00 -64.50 2414.3 2335.7 525.8 311.0 14.7403p2 72.30 -14.49 -64.50 77.3 -14.49 -64.50 2512.2 2436.8 336.7 509.7 14.1404p1 72.30 -8.51 -66.00 77.3 -8.51 -66.00 2066.2 2032.5 169.6 330.7 10.4404p2 72.30 -3.00 -66.00 77.3 -3.00 -66.00 2077.6 2045.4 58.5 359.8 10.1405p1 72.30 3.00 -64.50 77.3 3.00 -64.50 2580.0 2501.9 -70.8 626.0 14.1405p2 72.30 8.51 -64.50 77.3 8.51 -64.50 2557.3 2480.3 -205.7 587.9 14.1406p1 72.30 14.49 -66.00 77.3 14.49 -66.00 2044.4 2007.2 -277.7 271.7 11.0406p2 72.30 20.00 -66.00 77.3 20.00 -66.00 1981.7 1931.5 -428.6 113.3 12.9407p1 72.30 25.99 -64.50 77.3 26.00 -64.50 2346.1 2259.5 -613.2 151.6 15.7407p2 72.30 31.50 -64.50 77.3 31.51 -64.50 2275.7 2174.4 -670.6 -31.6 17.3408p1 73.01 37.49 -67.99 77.7 37.49 -69.70 1764.6 1651.7 -529.4 -324.4 19.5408p2 73.01 43.00 -67.99 77.7 43.00 -69.70 1725.9 1578.2 -510.7 -477.0 17.5408p3 73.01 48.51 -67.99 77.7 48.51 -69.70 1687.9 1500.4 -460.4 -621.1 16.0

NB. Fi are the cartesian coordinates of the central point of the PMT window; Ri

are the coordinates of the PMT rear center; B is the magnetic field intensity; Bi

are the magnetic field components; θ is the acute angle between the field directionand the PMT axis.

168

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