Laser wire beam profile monitor in the spallation neutron source (SNS) superconducting linac

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Laser wire beam profile monitor in the spallation neutron source (SNS)superconducting linac

Y. Liu �, A. Aleksandrov, S. Assadi, W. Blokland, C. Deibele, W. Grice, C. Long, T. Pelaia, A. Webster

Spallation Neutron Source, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

a r t i c l e i n f o

Article history:

Received 17 June 2009

Received in revised form

15 September 2009

Accepted 8 October 2009Available online 22 October 2009

Keywords:

Laser wire

Beam diagnostics

Spallation neutron source

Beam profile monitor

Superconducting linac

Photodetachment

a b s t r a c t

The spallation neutron source (SNS) at Oak Ridge National Laboratory is an accelerator-based, neutron-

scattering facility. SNS uses a large-scale, high-energy superconducting linac (SCL) to provide high beam

power utilizing hydrogen ion (H�) beams. For the diagnostics of high-brightness H� beams in the SCL,

nonintrusive methods are preferred. This paper describes design, implementation, theoretical analysis,

and experimental demonstration of a nonintrusive profile monitor system based on photodetachment,

also known as laser wire, installed in the SNS SCL. The SNS laser wire system is the world’s largest of its

kind with a capability of measuring horizontal and vertical profiles of an operational H� beam at each of

the 23 cryomodule stations along the SCL beam line by employing a single light source. Presently 9 laser

wire stations have been commissioned that measure profiles of the H� beam at energy levels from

200 MeV to 1 GeV. The laser wire diagnostics has no moving parts inside the beam pipe, causes no

contamination on the superconducting cavity, and can be run parasitically on an operational neutron

production H� beam.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction

The spallation neutron source (SNS) commissioned recently atOak Ridge National Laboratory (ORNL) is the world’s mostpowerful short-pulse, neutron-scattering facility. SNS is anaccelerator-based neutron source, and its linac consists of acombination of a room temperature linac and a high-energypulsed superconducting linac (SCL) [1]. The current SCL consists of23 cryomodules with 81 superconducting cavities and is designedfor acceleration of pulsed hydrogen ion (H�) beams from 187 MeVto 1 GeV with a peak beam current of 38 mA. The design beampower is 1.44 MW in 1-ms pulsed mode with repetition rates of upto 60 Hz. In the SNS upgrade plan, an additional nine cryomoduleswill be added to the SCL to boost the H� beam energy to 1.3 GeVwith a beam power reaching 3 MW.

Measurement of H� beam profiles along the acceleration path inthe SCL is important to minimize the beam loss. The profile monitorsystem for the SCL was originally envisioned to be a carbon wirescanner system [2,3]. However, linac designers were concernedabout the possibility that carbon wire ablation, or broken wirefragments, could find their way into the superconducting cavitiesand cause them to fail [3,4]. A search for nonintrusive methods wasperformed in collaborations with Los Alamos National Laboratoryand Brookhaven National Laboratory [4,5]. After initial experimentson H� beam profile measurements using a Nd:YAG laser, the final

decision was made to replace the carbon wire scanner system with alaser profile measurement system, also referred to as laser wire, inthe SNS SCL [6]. The advantages of the laser profile monitor systemover the conventional wire scanner system are: (1) H� beam profilescan be measured during normal operations, as opposed to the100ms, 10 Hz duty factor restriction [2,3] needed to prevent damageto carbon wires; (2) there are no moving parts inside the vacuumsystem, thus reducing the possibility of a vacuum system failure; (3)the profile measurement can be conducted in a parasitic manner foran operational neutron production beam; and (4) a longitudinalbeam scan can be conducted by using a pico-second pulsed lightsource such as a mode-locked laser and adjusting the phasebetween ion and laser pulses [7].

An outline of the SNS laser wire system is shown in Fig. 1. The SNSSCL consists of 23 cryomodules where each of the first 11cryomodules houses 3 medium-beta cavities and each of theremaining 12 cryomodules houses 4 high-beta cavities. The SCLbeam line was designed to have a laser wire station after eachcryomodule. Currently, 9 laser wire stations have been commissionedalong the SCL beam line. The first 4 stations are located after each ofthe first 4 medium beta cryomodules, the next 4 stations after thefirst 4 high beta cryomodules 12 through 15, and the last station atthe end of the SCL. In this way, the profiles of the H� beam atdifferent energy levels (200 MeV–1 GeV) can be measured.

Compared with the laser wire systems implemented in otherfacilities [8–13], the system installed at SNS has a number ofunique features. First, the SNS laser wire beam profile monitorconsists of 9 measurement stations and can be readily extended to

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Nuclear Instruments and Methods inPhysics Research A

0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.nima.2009.10.061

� Corresponding author. Tel.: +1865 241 2063; fax: +1865 2419831.

E-mail address: [email protected] (Y. Liu).

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measure profiles at each of the 23 cryomodules (or 32 cryomodulesin the upgrade project) in the SCL, which makes it the world’s largestsystem of its kind. Next, a single light source is used to perform theprofile measurement at all laser wire stations. To track the H�

profiles along the acceleration path, it is necessary to measure beamprofiles at multiple locations in the SCL. Using a single light sourceproves to be economically and operationally more efficient thaninstalling multiple lasers. Furthermore, while the laser wire systemhas a number of advantages over the conventional wire scanners, adisadvantage is that the laser is not as radiation-resistant as a wirescanner actuator. This issue was overcome in the SNS laser wiresystem by placing the laser source far away from the beam line inthe HEBT Service Building and using a laser transport line (LTL) todeliver the laser beam to each measurement station.

Since the laser beam must be transported as long as 250 m tocover all the measurement stations, and the laser room is locatedat a different building from the SCL, the laser beam parameters(pointing stability, beam quality, and beam size) as well as themechanical vibration and temperature instability of the LTL willinevitably affect the laser beam size and position at themeasurement point. Thus, it is critical to investigate how thelaser beam uncertainties influence the performance of the laserwire measurement.

In the following sections, we start with a theoretical analysis ofour laser wire system by including realistic laser beam parametersin the photoneutralization modeling. The numerical simulationclearly reveals the influence of the key laser beam parameters onthe performance of the profile measurement. In Section 3, wedescribe the implementation of the laser wire system includingthe light source, laser transport line, laser wire station, detection,software platform, and diagnostics. Section 4 describes experi-mental results of profile measurement at different energy levels.Dependence of the measurement on the ion beam minipulseposition is experimentally investigated. Finally, the paper issummarized in Section 5.

2. Laser wire modeling and influence of laser parameters

2.1. Photoneutralization with a realistic laser beam

The principle of the laser wire profile measurement is based ona light–ion interaction process called photodetachment or photo-

neutralization. The irradiation of the ion beam with a laser light ata certain wavelength range causes photodetachment of electronsfrom negative ions and the measurement of the resulting electrondensity leads to the determination of the negative ion density. Fig.2 shows a schematic of the laser–ion beam geometry. We assumethat the ion beam propagates along the x-direction, the laserbeam propagates along the y-direction, and the ion beam profilescan is conducted along the z-direction. To achieve spatialresolution, the laser beam is focused by a lens L1 with a focallength f before the light–ion interaction.

The photodetachment process has been studied in a number ofprevious works [12–14] where the photodetachment yield wasexpressed as a product of the photon and ion densities. Based onthe notations in Refs. [12–14], we can describe the variation of thedetached electrons by

@ndetðx; y; z; tÞ

@t¼ cS0nlðx; y; z; tÞnbðx; y; z; tÞ ð1Þ

where ndet(x,y,z) is the number of photo-detached electrons perunit volume, c the light speed, S0 the photodetachment cross-section, and nl and nb the photon and ion densities, respectively.As the number of ions decreases when electrons are detached, theion beam density will change at a rate

@nbðx; y; z; tÞ

@t¼ �

@ndetðx; y; z; tÞ

@t¼ � cS0nlðx; y; z; tÞnbðx; y; z; tÞ: ð2Þ

In previous models, both ion and laser beams were assumed tohave a Gaussian distribution, i.e.,

nbðx; y; z; tÞ ¼Nb

ð2pÞ3=2sbxsbysbz

exp �ðx� bctÞ2

2s2bx

�y2

2s2by

�z2

2s2bz

" #

ð3Þ

nlðx; y; z; tÞ ¼Nl

ð2pÞ3=2slxslyslz

exp �x2

2s2lx

�ðy� ctÞ2

2s2ly

�z2

2s2lz

" #ð4Þ

where Nb (Nl) is the total ion (photon) number, b=v/c the ionbeam relativistic factor, and s the RMS beam size. In this paper,we revise Eq. (4) by considering the realistic laser beamparameters. Major revisions in our modeling include: (i) the laserbeam is well collimated on the surface of L1. This assumption isreasonable since the laser beam needs to be delivered to targets ofup to 250 m away and the beam divergence angle should besufficiently small; (ii) there exists a defocus Dy between the laser

LR Laser room

Laser wire station

Camera

MirrorLR

3254321 1712

Cryomodule number Power meter32

SCL

25 m250 m 160 m C1C2C3

CCLDTL

Ring

HEBT RTBT

SCL

SNS Baseline

CCLDTLTarget

13 14 15

Fig. 1. Outline of laser wire setup at SNS superconducting linac.

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beam focal plane and the ion beam center line; and (iii) when alaser beam is incident on the lens L1, it may have certain drifts(Dx, Dz) from the lens center at incidence angles (jx, jz).Furthermore, since the lens aperture is much smaller than itsfocal length, we assume Dx5 f, Dz5 f.

It is shown in Appendix A that, under the above assumptions,the photon distribution in the x–z plane becomes a function of y

and Eq. (4) can be rewritten as

nlðx; y; z; tÞ ¼Nl

ð2pÞ3=2slxðyÞslyslzðyÞ

exp �ðx� xsÞ

2

2s2lxðyÞ

�ðy� ctÞ2

2s2ly

�ðz� zsÞ

2

2s2lzðyÞ

" #ð5Þ

where xs and zs are laser beam position displacements defined inEqs. (A3) and (A4).

2.2. Numerical simulation of a laser wire profile measurement

The procedure of the numerical calculation is described inAppendix B. At SNS, the ion beam structure consists of 50-ps longmicropulses separated by �2.5 ns and gated into �650-nsminipulses separated by �350 ns. In the numerical calculation,we look into a single micropulse of the ion beam with a peakcurrent of 30 mA. The detached electron density is calculatedusing Eq. (B1) and the photodetachment yield (efficiency) iscomputed as a ratio between the detached electron number Ndet

and the total ion number Nb within one micropulse, as defined byEq. (B3). Unless otherwise mentioned, parameter values used inthe numerical calculations are given in Table 1.

We simulate the beam profile measurement process byscanning the laser light (together with the focus lens) across theion beam at a step size of 0.25 mm. The ion beam has a beam sizesby=sbz=2 mm while the actual laser beam size at the light–ioninteraction point is a function of the laser beam and opticsparameters as discussed later. At each position z, we calculate thephotodetachment yield Z. The distribution of Z(z) gives themeasured profile of the ion beam and the profile amplitudecorresponds to the peak photodetachment yield.

Table 2 summarizes the calculated peak photodetachmentyield at all 9 commissioned laser wire stations using a pulsed laser

beam with a pulse width of 10 ns and a pulse energy of 50 mJ. Ingeneral, as the energy level of the ion beam gets higher, thephotodetachment yield decreases due to a shorter light–ioninteraction time. Overall, �2% of the ions within a micropulseare neutralized.

2.3. Saturation effect

We first look into the effect of the laser pulse energy. When anion beam interacts with a laser beam, the ion density depletes aselectrons are detached by photons. Since the laser beam is focusedby a lens before the laser–ion interaction, the laser spot size at theinteraction point, i.e., slx in Fig. 2, can be as small as 10–20mm atthe focal plane. As a result, the photon density at the center of thelaser beam can be so high that all ions running into this part of thelaser beam will be completely photoneutralized. Once such acomplete ion depletion happens, further increase of the laserpower will not produce electrons proportionally. Fig. 3 showsprofiles (numerically) measured with different laser pulseenergies. The amplitude of the profile saturates as the laserpulse energy exceeds a few tens of millijoules, as shown in theinbox of Fig. 3. Since the complete depletion of the ion beam onlyoccurs when ions interact with the laser beam center (typically afew tens of micrometers), most parts of the ion beam only lose a

Ion beam

(xs, 0, zs)

Laser beamx

yz

f

Focus lens L1

�x

�x

2wi

(�x, 0, �z)

2�lx

�y

Fig. 2. A schematic illustration of light–ion beam interaction. Ion beam interacts at or close to the focal plane of the laser beam. wi: incident laser beam size, jx: incidence

angle, Dx (Dz): incidence laser beam drifts, f: focal length, Dy: defocus, xs (zs): beam shifts, slx: laser spot size at the light–ion interaction point.

Table 1Parameters used in numerical calculations.

Parameter Value Unit

Laser wavelength l 1.064�10�4 cm

Laser pulse width 10�8 s

Laser pulse energy 0.05 J

Laser pulse repetition rate 30 Hz

Laser beam initial diameter 2wi 1.5 cm

Ion beam current 0.03 A

Ion beam energy 109 eV

Ion beam micropulse width 3�10�11 s

Ion beam micropulse repetition rate 4.025�108 Hz

Ion beam waist sby=sbz 0.2 cm

Photon-ion cross-section 3.51�10�17 cm2

Lens focal length f 20 cm

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small portion of electrons due to photodetachment. Therefore,even at a saturation state, the photodetachment yield (calculatedover an entire micropulse) stays at a level of a few percent. Itshould be noted, however, that the laser pulse energies within aquite large range (50–1000 mJ) do not affect the measured beamprofile or the beam size.

The saturation effect has an important impact on a number ofparameters. Fig. 4 shows how the peak (photodetachment) yieldchanges as a function of (a) laser beam diameter (2wi in Fig. 2) and(b) lens defocus (Dy in Fig. 2) at different laser pulse energy levels.At lower pulse energies (10–20 mJ), the peak yield exhibits weakdependence on the beam diameter or defocus; while at higherpulse energies, the peak yield strongly depends on bothparameters. Such dependence is directly related to thesaturation effect. Eq. (A6) shows that the laser spot size slx (slz)is determined by wi and Dy. The effect of Dy is straightforward. Alarger value of Dy will result in a larger value of slx (and slz) whichreduces the effective laser pulse intensity, mitigates the saturationeffect, and therefore increases the photodetachment yield. The wi

dependence is more complicated since two terms in Eq. (A6)depend on the f-number (f#= f/2wi) in opposite ways. First, forvery large wi, f# is very small and the second term in Eq. (A6)dominates. In the presence of Dy, increasing wi will effectivelymitigate the saturation effect and enhance the photodetachmentyield. On the other hand, for very small wi (large f#), the first termin Eq. (A6) becomes the leading factor. In this case, furtherreduction of wi will expand the interacting laser beam size andraise the photodetachment yield. At low laser pulse energies,neither wi or Dy affects the photodetachment yield since there isno saturation.

It should be noted that the actual values of wi and Dy arelimited by a number of practical factors. wi is limited by theaperture size of the optics and, in particular, by the fact that thelaser beam diameter has to be sufficiently large to propagate overa long distance. In the actual system, wi varies between 7 and10 mm. The choice of Dy is limited by the damage threshold of thevacuum windows and another important factor discussed in thenext section.

2.4. Influence of laser beam drift

Laser beam drift on the focusing lens is a major concern due tothe long LTL in the SNS laser wire system. Eqs. (A1) and (A2)

Table 2Calculated peak photodetachment efficiency at each laser wire station.

Laser wire station # Beam energy (MeV) Relativistic factor b Distance from laser (m) Peak photodetachment yield (%)

1 205 0.57 249.1 2.33

2 223 0.59 243.3 2.30

3 250 0.61 237.4 2.27

4 276 0.63 231.6 2.25

12 470 0.75 182.2 2.13

13 504 0.76 174.9 2.11

14 547 0.78 167.0 2.10

15 589 0.79 159.2 2.08

32 875 0.86 25.0 2.02

Laser pulse energy was 50 mJ at 10 ns pulse width.

3

10 mJ 20 mJ 50 mJ 100 mJ 200 mJ

34

2012

0

Laser pulse energy (mJ)

Peak

Yie

ld (

%)

1

Yie

ld (

%)

0-4

Position (σ)

-2 0 2 4

100 200 300

Fig. 3. Numerical simulation of profile measurement with laser wire at different

laser pulse energy levels. Inset box shows the peak amplitude of the profile, i.e.,

peak photodetachment yield, changes as a function of laser pulse energy.

3

4

510 mJ 20 mJ 50 mJ 100 mJ 200 mJ

0

1

2

5 10 15 20 25

Peak

Yie

ld (

%)

15

2010 mJ 20 mJ 50 mJ 100 mJ 200 mJ

0 30

Beam Diameter (mm)

5

10

Peak

Yie

ld (

%)

00 5 10 15 20 25 30

Δy (mm)

Fig. 4. Calculated dependence of the peak photodetachment yield as a function of

(a) laser beam diameter 2wi and (b) lens defocus Dy at different laser pulse energy

levels. Dy=10 mm in (a).

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suggest that the change of the laser beam incidence angle can beconverted to the variations of beam position. Here we concentrateon the beam position drifts with an assumption jx=jz=0. Eqs.(A3) and (A4) show that Dx and Dz cause the laser beamdisplacements at the interaction point, xs and zs, respectively.According to Eq. (5), xs and zs offset the photon densitydistribution. Since the displacement xs is along the ion beampropagation direction, it only affects the timing of laser–ioninteraction and will not change photodetachment yield providingthe laser pulse is longer than the ion beam pulse. In the SNS laserwire system the pulse length of the laser beam is typically two tothree orders of magnitude longer than that of the ion beammicropulse. On the other hand, the displacement zs is in theprofile scan direction and any change in zs will work as a directoffset to the laser–ion interaction location. In other words, with anoffset zs, the laser beam will ‘see’ the ion beam density nb(z+zs) asthe measurement of nb(z). As a result, the variation of Dz (zs)during the profile scan process will cause dramatic fluctuations inthe measured profile.

Eq. (A4) indicates that the beam displacement zs is a product ofDz and Dy, i.e., the effect of Dz is ‘amplified’ by the amount of thelens defocus Dy. To quantitatively study this effect, we define ameasurement error as the difference between the profilemeasured at DzDya0 and a reference profile measured atDz=Dy=0, i.e.,

e¼

����������1�

XN

i ¼ 1

Zi

�����DzDya0

XN

i ¼ 1

ZijDzDy ¼ 0

����������

,ð6Þ

where Zi is the photodetachment yield at the ith measurementpoint and N the total number of points. Note that the abovemeasurement error calculates the absolute difference between atarget profile and a reference profile, rather than compares twoprofiles. Therefore, two identical profiles with different centers oramplitudes will result in a non-zero measurement error. Fig. 5(a)shows that the measurement error e varies in direct proportion toDzDy.

The linear relationship epDzDy can be used to control themeasurement error in our system design. Since Dz is subject to anumber of factors including the spatial jitter of the light sourceand mechanical vibrations in the LTL, it is unrealistic tocompletely eliminate such instabilities. Meanwhile, the lensdefocus Dy can be minimized by optimizing the position of thefocus lens as shown Fig. 2. To further demonstrate the effect of Dy,we have conducted a series of numerical simulations of the profilemeasurement as shown in Fig. 5. In the simulation, we assumedthat the beam spot varies arbitrarily, i.e., Dz in Eq. (A2) issimulated with a random number, within a range (�10 mm,10 mm) from the center of the focusing lens. At Dy=20 mm, oneobserves a profile with large fluctuations corresponding to a largemeasurement error. Such fluctuations are significantly reduced asDy is decreased from 2 cm to 5 mm. At Dy=2 mm, measurementfluctuations are barely noticeable. Note that, due to the saturationeffect, the photodetachment yield decreases as the interactionpoint approaches the laser beam focus, i.e., as Dy-0.

The numerical investigations are summarized as follows. (i)The profile amplitude saturates after the laser pulse energyexceeds a certain amount but the profile shape is not affected bythe laser power. (ii) In general, a larger laser beam size or lensdefocus result in higher photodetachment yield due to itsmitigation of the saturation effect. (iii) The laser beam drift inthe (ion beam) propagation direction is irrelevant to the profilemeasurement providing the laser pulse duration is sufficientlylonger than that of the ion pulse. (iv) The laser beam drift in theprofile scan direction can induce significant fluctuations on themeasured profile. (v) The measurement error caused by the laser

beam drift can be suppressed by appropriately aligning the opticsso that the ion beam interacts with a focused laser beam.

3. Laser wire system setup

3.1. Laser

Since the outer electron of the H� is bound by 0.75 eV, photonswith an energy above this threshold level (corresponding towavelengths o1.65mm) can be used to detach electrons from theH� beam. For our application, the most important properties ofthe light source are its spatial beam quality, linewidth and outputpower. High beam quality is critical for the beam transportationalong over 200 m. Single wavelength and narrow line width arerequired to avoid neutralization noise induced by the jitter of thelaser pulse. Based on our estimation, 5 MW of peak power willgenerate sufficient photodetachment yield for signal detection.Laser wavelength, on the other hand, is a parameter with moreflexibility. We chose the wavelength of 1064 nm that is near thepeak of the photoneutralization cross-section of H� ions. Inaddition, this wavelength has less propagation loss, exerts lessimpact on optics, and mitigates safety stringency.

A Q-switched Nd:YAG laser operating at 1.06mm was chosen asthe light source. The laser has a repetition rate of 30 Hz and apulse width of 7 ns. The maximum laser pulse energy is up to 1.5 J.Since the 7-ns laser pulses are significantly longer than the H�

micropulses, a narrowband injection seeder is included in thesystem to provide a smoother temporal profile and reduce thelinewidth to the 100 MHz order. The seeder reduces the jitter of

6

7

1

2

3

4

5

Err

or (

%)

60 2 mm 5 mm 2 cm

00

2

3

4

5

Yie

ld (

%)

0

1

-4

50 100 150 200 250

�z·�y (mm2)

-3 -2 -1 0 1 2 3 4

Position (σ)

Fig. 5. (a) Calculated measurement error e as a function of DyDz. (b) Simulation of

the profile measurement at different values of Dy. Large fluctuations appear in the

measured profile at Dy=20 mm. Fluctuations decrease as Dy gets smaller. No

fluctuation exists at Dy=0. In all simulations, the laser beam is drifting randomly

within (�10 mm, 10 mm) in the z-direction during the beam profile scan process.

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the Q-switched laser pulse from several nano-seconds to around1 ns. Since the SNS SCL ion beam micropulses have a period of�2.5 ns and a pulse width of �50 ps, a 1-ns laser pulse jitterensures that each laser pulse interacts with the same number ofmicropulses. Both the laser flashlamp and the Q-switching gateare externally triggered by the H� beam macropulse timing.

The light beam right after the laser has a beam size ofapproximately 8 mm (diameter) with a (full) divergence angle ofapproximately 1.1 mrad. A pair of lenses (focal lengths �100 and250 mm) are used to expand the beam size to about 17 mm with abeam divergence angle less than 0.1 mrad. The laser power can becontrolled by tuning the time delay between the flashlamp and Q-switch triggers. Yet this will cause a slight change to the beampointing direction and, therefore, a beam position drift at the laserwire stations located as far as 200 m away from the laser room. Inour system, this time delay is fixed and the laser power iscontrolled with a set of polarization elements. By using two sets ofhalf-wave plate and polarization beam-splitters, the output laserpulse energy can be continuously tunable from the millijoule levelto over 1 J. The wave plate is mounted on a rotary stage that isdriven by a picomotor actuator (New Focus 8401). A small sampleof the laser beam is monitored by a power meter in the laserroom. Both the rotary stage and the power meter are remotelyaccessible.

3.2. Laser transport line

The laser beam is carefully aligned so that it will deliveracceptable beam size and position at all 9 laser wire stations. Asshown in the previous section, the measurement error due tobeam drift can be compensated through the optimization of theposition of the focusing lens. However, because the upstreamoptics are over 200 m from the target, large drift will cause thebeam to miss the downstream optics altogether. The challenge isthen to keep the beam (spatial) jitter small enough so that thebeam is not steered off the downstream optics.

In our system, an active stabilization scheme has beenimplemented to help in this regard [15]. A mirror with picomotoractuators is installed in the entrance box of the tunnel to steer thelaser beam downstream. Meanwhile, the laser beam position ismonitored at three locations along the LTL (Fig. 1). At eachlocation, a camera is viewing either leaked light through a mirroror a small reflection of the light from a beam sampler. The firstcamera (C1 in Fig. 1) detects the laser beam position at theentrance of the SCL tunnel. The second and third cameras (C2 andC3 in Fig. 1), respectively, monitor the beam positions at thelocations about 140 and 220 m away from laser room. The imagesfrom those cameras are analyzed to extract the laser beam centerposition which, after comparing with the reference position,generates an error signal that controls the picomotor actuators tominimize the beam drift. The feedback speed is typically a fewhertz. The beam propagation efficiency of the LTL is finallychecked by measuring the laser power at the end of LTL. Wenormally achieve an efficiency of about 50% during the laser beamalignment.

3.3. Laser wire station

A geometric scheme of the laser wire instrument is shown inFig. 6 [6], and the schematic optics setup is shown in Fig. 7. Thelaser beam enters the vacuum chamber through a vacuumwindow (laser port) and is designed to interact with the ionbeam close to the focus point of the laser beam. After theinteraction, the laser beam hits the beam dump. A photodiode isinstalled at the center of the beam dump to receive a small portionof the laser beam. The photodiode output gives an indicationsignal of laser beam presence. When the H� beam interacts withthe laser light, a certain number of electrons are detached fromthe ion beam by the photons. The detached electrons are bent inthe vertical direction by a magnetic field and collected by anelectron detector (Faraday cup). The magnet and the electrondetector are placed downstream of the laser-ion interaction

Fig. 6. Diagram of laser wire station setup.

Y. Liu et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 241–253246

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section. A beam position monitor (BPM) is installed for diagnosticpurposes.

Each laser wire station contains a light pickup box where amotorized mirror slides in and out of the laser transfer path topickup or unblock the laser beam, a beam division box where aflip mirror is used to switch the laser beam between horizontaland vertical scans, and two beam scan boxes. Fig. 7 shows atypical pickup optics setup and a beam division setup togetherwith horizontal and vertical scan optics. Note there is a 901rotation between planes in (a) and (b).

Since the laser–ion interaction occurs near the focal plane ofthe lens, it is required that the focal plane has a certain extent offlexibility. This flexibility is achieved by simply changing theposition of the focusing lens. The function is accommodated inour setup by a translation stage that moves the lens L in Fig. 7(b)over � 1 cm in parallel to the laser beam. For the ion beam profilescan, however, the laser beam is translated across the ion beam.This is accomplished by translating the final steering mirror. Sincethe light passes through the focusing lens after striking the mirror,both SM and L are mounted and translated together. In this way,the effect of the lens upon the beam is unchanged throughout theprofile scan.

The laser beam arrives at each LW station with a beam sizeabout 14–20 mm (diameter) and is then focused into the vacuumchamber by a single lens. The lens has a focal length of 200 mmand is placed as close as possible to the vacuum windows so thatthe laser beam remains large when it passes through the vacuumwindow and, therefore, reduces the chance of laser-induceddamage on the window. The focused laser beam can increasethe spatial resolution of the measurement. An additional benefit isthat it minimizes the effect of unwanted reflections. As the beamexits the vacuum chamber, a small fraction of the light is reflectedback toward the ion beam. Even with uncoated windows, theamount reflected is only a few percent of the primary beam.But the signal level from this unwanted reflection can besignificant if the light is concentrated near the center of the ionbeam. Using a lens to couple the light into the vacuum chamber

ensures that the beam is diverging as it leaves the target. Itcontinues to diverge as it is reflected back toward the ion beam sothat the reflected energy is spread out over an area much largerthan that occupied by the ion beam. Thus, the signal contributionfrom unwanted reflections is quite small and is fairly constantthroughout the scan.

3.4. Detection

The detached electrons are bent in the vertical direction by adipole magnet. The C-shape dipoles are designed by ORNL. Theirdimensions are: 8 cm gap, 4.5 cm2 cross-section, 48 turns with acoil length of 44.2 cm per turn, and 7 cm effective length. Thisdesign results in a center magnetic field of 190 G and an integratedfield of 1330 G cm at a current density of 142 A/cm2 and amagnetomotive force of 615.6 A-turns.

The electrons are detected by a Faraday cup. The Faraday cup isheld vertically over the beam pipe. A large circular aperture ismade in the beam pipe, which allows the electrons to pass intothe cup. It was desired to have as big of an aperture as possiblewhereby the path and/or flight of the liberated electrons easilystrikes the cup inducing a current in the cup. A small ring keepsthe cup from shorting to the walls of the vacuum chamber.Connecting the cup is a short 50O transmission line and then atransition is made to a type N feed-thru. The advantage ofcollecting electrons vs. measuring the deficit in beam current are:1) the signal to noise ratio is better because of the large numbersof released electrons and 2) the simplicity of the electron collector,since the electron energy is well defined and the electrons are wellcollimated.

The electron collector was designed such that it neitherelectrodynamically couples well to the minipulse structure ofthe linac current nor to the harmonic dependence of themicropulse structure of the linac current. A calculation of theelectrodynamic coupling from the beam to the electron collectoris shown in Fig. 8. The system is configured so that the salient

H -scan

from LTL

M

SM

L

FM

H scan

SM

LBD

PD

LTL

M

V-scan

W

W

SM

z

y

z

x

Fig. 7. Schematic of (a) pickup mirror and (b) beam division optics at each laser wire station. LTL: laser transport line, M: mirror, L: lens, FM: flipper mirror, SM: scan mirror,

W: vacuum window, BD: beam dump, PD: photodiode.

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bandwidth is below 50 MHz, and it is observed in this plot that thecoupling is less than �70 dB. The signal from the electroncollector passes through a Bias-T capable of 7100 V as shown inthe flowchart in Fig. 8(b). No bias is used, however, as the largeaperture and geometry of the collector captures all secondaryelectrons. The signal then passes through two stages ofamplification and low pass filtering. The amplifiers arenecessary for two reasons. First, they buffer the two low passfilters, and second, they raise the signal to about 600 mV, wellabove the noise floor of the ADC. The low pass filters are installedto broaden the pulse and reduce the bandwidth, thereby reducingthermal noise from the measurement and allowing slowersampling rates on the ADC. The combination of collector designand low-pass filtering guarantee that no undesired harmonicstructure is interfering with the collected signal.

3.5. Orbit distortion compensation

The magnet used to collect electrons introduces a severalmillimeter vertical orbit distortion on the H� beam making itunacceptable for parasitic use during a normal production run. Toallow for parasitic operation, we localize the orbit distortion byusing vertical dipole correctors downstream to create a closedbump. An existing application, Knobs, allows one to specify acollection of process variables to vary together in fixed, pre-determined ratios (which is appropriate for linear, stablesystems). The typical orbit distortion introduced after compensa-tion is only a few tenths of a millimeter (noise level) which isacceptable for parasitic operation during a production run.

3.6. Data acquisition platform

The laser wire profile monitor data acquisition (DAQ) systemhas five main components: (1) the hardware trigger whichsynchronizes the laser and DAQ components to the H� beam,(2) the LabVIEW software which controls the acquisition of datafrom multiple sensors (photodiodes, cameras, and laser positiondetectors) from each laser wire station, (3) the laser lighttransport drift compensation system, (4) the laser power/position

monitor and control, and (5) the laser protection andsafety (LPS) system. Individual components of the above compo-nents have been tested and integrated under a main controlplatform.

4. Profile measurement results

4.1. Beam scan procedure

The profile of the H� beam in the SCL has been measured at all9 stations (serially). The measurement was conducted parasiti-cally on a neutron production beam. At SNS, the H� beam consistsof approximately 50-ps long micropulses separated by �2.5 nsand gated into minipulses of 650 ns long. The period ofminipulses, or a turn, is determined by the SNS accumulationring beam path length and the beam energy. The minipulses arebunched into macropulses with a length of 1 ms and a repetitionrate of 60 Hz. The firing of the laser flash lamps is locked to aprecursor signal (timing signal) for the macropulse with a certaintime delay t1 while the laser Q-switch trigger is synchronized tothe flash lamp firing signal with a second time delay t2. The lengthof t2 directly affects the pulse energy of the laser. In theexperiments, t2 is usually fixed at a value to provide themaximum laser output. Meanwhile, t1 determines the phaserelationship between the laser and ion pulses, i.e., the turnnumber of the minipulse within a macropulse. During the profilemeasurement, t1 at each laser wire station was appropriatelytuned so that the same minipulse (within each macropulse) of theion beam was scanned at all laser wire stations. The timing for thedetector was adjusted to ensure the maximum detectionefficiency.

Fig. 9 shows an example of the detached electron signaldetected by the Faraday cup. Both the amplitude and the areaintegration (typically over 100 ns) of the electron signalcorrespond to the electron number detached by a laser pulse. Itwas verified that both variables result in the identical profile. Theprofile of the ion beam was obtained by scanning the laser beamacross the ion beam and recording the amplitude (or the areaintegration) as a function of the laser beam position. Prior to the

-65

-75

-70

-800

Cou

plin

g M

agni

tude

(dB

)

ElectronCollector Bias T ADC+13 dB +13 dB

Frequency (MHz)

100 200 300 400 500

Fig. 8. (a) A calculation of the electrodynamic coupling from electron beam to electron collector. (b) Flowchart of signal processing in the electron collector circuit.

Y. Liu et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 241–253248

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profile scan, the detector output at the laser beam off state wastaken as the background noise level and this value wasautomatically deducted from the measured profile.

Once the measurement station and the ion beam location aredecided, the profile scan is conducted in horizontal and verticaldirections. The scan range on both axes is 46 mm and this value islimited by the translation stage as well as the aperture size of thevacuum viewport. Since the typical ion beam size is only a fewmillimeters, a 20-mm scan range is sufficient to cover the H�

beam even with possible halos. The translation stage can move ata step size of as small as 1mm, but usually a scan step of 0.25 mmresults in a reasonable resolution of profiles. At each measure-ment point, 10 to 20 samples are continuously taken and theaverage, as well as the standard deviation, is computed in realtime and the results are recorded in the data file. To avoidaccidental measurement errors which usually return a signal atthe background noise level due to a laser trigger or a detectortrigger failure, a threshold scheme is employed to automaticallythrow away abnormal data and conduct a make up measurementduring the profile scan process. Recent improvements in thesoftware have increased the sample rate to near 15 Hz allowing atypical scan including 40 measurement points to be completed inabout 2 min for a 60 Hz neutron production H� beam.

4.2. Measurement of H� beam profiles

We have measured the H� beam profiles at the beginning,center, and end of the SCL. The measurement was conductedon a 60 Hz, neutron production beam with an averagepower of 620 kW. Fig. 10 is a snapshot recorded from the SNSbeam status broadcast channel (available publicly at http://neutrons.ornl.gov/diagnostics/channel13/Ch13.html) during theweek when the laser wire measurement was performed. Theneutron production beam shows a very steady output powerwithin the measurement time window, which clearly verified theparasitic nature of the laser wire diagnostics.

Fig. 11 depicts the horizontal (Y-direction in Fig. 2) and vertical(Z-direction) profiles measured at laser wire stations 1, 4, 12, 15,and 32. The corresponding H� beam energy levels are recorded inTable 2. At lower (ion beam) energy laser wire stations, weobserve relatively large fluctuations on the profiles. Suchfluctuations become smaller at higher energy laser wire stations.This is because the laser beam shows more spatial instabilities atlower energy laser wire stations than at high energystations.

Gaussian function fitting has been conducted on all measuredprofiles. At low and medium energy stations, both the horizontal

0

-0.2

-0.4

-0.6

Det

ecto

r O

utpu

t (V

)

-0.8

Time (ns)0 200 400 600 800 1000

Fig. 9. Photodetachment signal detected by the electron collector following the interaction of a laser pulse with the ion beam. The pulse width (�20 ns) is due to the

bandwidth of the lower-pass filters (Fig. 8) and the small peak at the right side is a result of the reflections between the amplifier and the detector.

Fig. 10. A snapshot of SNS beam status during October 5–October 7, 2008. Laser wire measurement time window is indicated with shadowed region.

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0.4

0.5

0.6Az = 0.44

Z0 = 20.6 mm

σz = 3.2 mm

0.5

0.6

0.7

0.8Ay = 0.61

Y0 = 22.1 mm

σy = 2.9 mm

0

0.1

0.2

0.3

1Ay = 0.88

0.5Az = 0.36

0

0.1

0.2

0.3

0.4

0

0.2

0.4

0.6

0.8

Out

put (

V)

σy=2.2 mm

0

0.1

0.2

0.3

0.4

Out

put (

V)

σz = 2.3 mm

0.2

0.3

0.4

0.5

0.6

Out

put (

V)

Ay = 0.45

Y0 = 24.9 mm σy = 2.7 mm

0.2

0.3

0.4

0.5

0.6

0.7

Out

put (

V)

Az = 0.59

Z0 = 22.1 mm σz = 2.1 mm

0

0.1

0

0.1

0.4

0.5

0.6

0.7

0.8Ay = 0.61

Y0 = 24.5 mm σy = 2.1 mm

0.3

0.4

0.5

0.6Az = 0.46

Z0 = 23.7 mm σz = 1.7 mm

0

0.1

0.2

0.3

0.4

0

0.1

0.2

0.3

0.8

1

0.8

1

0

0.2

0.4

0.6

Out

put (

V)

Single-Gaussian function fit Single-Gaussian function fit

0

0.2

0.4

0.6

Out

put (

V)

Out

put (

V)

10 30 10 20 30

Position (mm)

40Position (mm)

Out

put (

V)

Out

put (

V)

20 40

Double-Gaussian function fitDouble-Gaussian function fit

Out

put (

V)

Z0 = 27.8 mm Y0 = 25.8 mm

Fig. 11. Measured profiles at different laser wire (cryomodule) stations. (a), (b): station 1; (c), (d): station 4; (e), (f): station 12; (g), (h): station 15; and (i), (j): station 32. Left

column graphs are horizontal (Y-direction in Fig. 2) and right column graphs are vertical (Z-direction) profiles. In all figures, dots are measured results, solid lines are single-

Gaussian, and broken lines are double-Gaussian function curves. Ay (Az): amplitude, Y0 (Z0): beam center position, sy (sz): beam size.

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and vertical profiles were well fitted with a single-Gaussian curve.The fitting result was evaluated with a fitting error that is definedas the ratio between the sum of squares error and the total sum ofsquares, i.e.,

Ef ¼XN

i ¼ 1

½yi � gðxiÞ�2

XN

i ¼ 1

½yi � y�2,

ð7Þ

where xi is the position, yi the measured value, y the average overall points, g Gaussian function, and N the number of scan points.Parameters of the Gaussian function were optimized to minimizethe fitting error. In general Ef is less than 1% for profiles measuredat LW stations 1–4 and 12–15. The ion beam parameters: beamsize, beam center position, and amplitude (peak height), werecalculated from the fitted Gaussian function. The fitting accuracyof the parameters was estimated over multiple measurements.Overall, the fitting accuracy of the beam size and the beam centerposition was 0.1–0.2 mm and that of the peak height was about5%. Our measurement shows that the beam size is approximately3 mm at the beginning of the SCL, decreases along the accelerationpath, and eventually reduces to approximately 1 mm beforeexiting from the SCL, which agrees with the prediction from thephysics modeling of the SCL design.

Beam halos were observed in both horizontal and vertical H�

beam profiles at laser wire station 32. In this case, themeasured H� beam profiles were better fitted with a linearcombination of two Gaussian functions sharing the same beamcenter position, but with different beam sizes and amplitudes,e.g.

gðzÞ ¼ Az1 exp �ðz� Z0Þ

2

2s2z1

!þAz2 exp �

ðz� Z0Þ2

2s2z2

!: ð8Þ

Two examples are shown in Figs. 11(i) and (j) where both thesingle-Gaussian and double-Gaussian functions are plotted alongwith the measured data. The single-Gaussian function fitting givesAy=0.82, Y0=24.7 mm, sy=1.2 mm for the horizontal and Az=0.75,Z0=22.6 mm, sz=1.2 mm for the vertical profile, while the double-Gaussian function fitting results in Ay1=0.8, Ay2=0.16,Y0=24.7 mm, sy1=0.9 mm, sy2=4.5 mm for the horizontal andAz1=0.69, Az2=0.24, Z0=22.6 mm, sz1=0.8 mm, sz2=3.2 mm for thevertical profile. The fitting accuracy of the beam size and the beamcenter position was better than 0.1 mm and that of the amplitudewas within 1–2%. Compared with the single-Gaussian functionfitting, the fitting error of the double-Gaussian function fittingwas improved from 1.9% to 0.5% for the horizontal profile andfrom 2.9% to 0.5% for the vertical profile. Clearly, the profile at theend of the SCL is divided into two parts: a narrow Gaussian curveat the top and a wide Gaussian curve at the bottom, with the beamsize of the bottom part about five times larger than that of the toppart.

The overall accuracy of the laser wire system is determined byseveral factors including the accuracy of the linear translationstages that control the laser beam motion, the alignment of thelaser beam, and the laser–ion interaction configuration. Thecalibration of the laser wire measurement has been performedboth in the laboratory and on site. The laboratory calibrationindicates the laser beam motion is controlled by the linear stagewith an absolute accuracy of well within 0.1 mm. The on-sitecalibration was conducted by using a BPM installed next to thelaser wire station (Fig. 6). In the experiment, we adjusted a dipolemagnet in the SCL to shift the ion beam along the profile scandirection. The amount of the beam shift was monitored by theBPM. At the same time, the ion beam profiles before and after thebeam shift were measured by the laser wire. The change of theprofile center position was then compared with the BPM reading.

The two values matched each other within an accuracy ofo0.2 mm over a 5 mm beam shift range.

4.3. Longitudinal position dependence

Since the time delay (t1) between laser pulses and themacropulse of the H� beam is user adjustable, it is possible tomeasure beam profiles at different minipulses or even differentsegments within a single minipulse. This provides a unique profilestudy that is unavailable with the technology of conventional wirescanners.

A study on the minipulse dependence of the profile monitorhas been conducted at laser wire station 32. The macropulseconsists of 650 minipulses. Fig. 12 shows the measured (a) peakheight, (b) beam center position, and (c) beam size of bothhorizontal (Y) and vertical (Z) profiles measured for sevendifferent minipulses (minipulse #30 to #630) of onemacropulse. We found that the beam size measured at thecenter minipulses is slightly smaller than those at the endminipulses. Meanwhile, changes in the peak height and beamcenter position are only within a few percent, which means thebeam current and position changes very little along a macropulse.Similar measurements for twelve consecutive minipulses havebeen performed and the results are plotted in Fig. 13. It can beconcluded from the above measurements that there is nosignificant (mini-) pulse-to-pulse dependence in the profileparameters.

0.9

1

0.6

0.7

0.8

Az

Ay

0.5

25

26

Y0

21

22

23

24

Z0Bea

m C

ente

r (m

m)

11

1.2

1.321

0.8

0.9

1

1.1

100 200 300 400 500 600 7000

Bea

m S

ize

mm

)

Turn #

Am

plitu

de (

V)

�z

�y

Fig. 12. Minipulse dependence of profile parameters measured at the laser wire

station 32 across one macropulse. (a) Profile peak height, (b) beam center position,

and (c) beam size. Notations are the same as in Fig. 11.

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5. Conclusion

In this paper, we have described the design, numericalinvestigation, implementation, measurement results, and analysisof the laser wire profile monitor system installed in the SNSsuperconducting linac. The laser wire system has been designed tomeasure hydrogen ion beam profiles at all 23 cryomodule stations(32 in the upgrade project) of the superconducting linac. Presently9 laser wire stations have been commissioned which enable us tomeasure profiles of the beam at energy levels from 200 MeV to1 GeV. This is the largest laser-based nonintrusive beam diag-nostics system implemented in accelerator facilities.

The SNS laser wire system uses a single Q-switched pulsedlight source to measure profiles at multiple locations. A free-space, enclosed laser transport line was implemented to deliverthe laser beam to different laser wire stations distributed over250 m. The laser beam spatial instabilities caused by laser beamjitter and mechanical vibration in the laser transport line havebeen investigated by using a revised photoneutralization modelincluding realistic laser beam parameters and ion beam depletioneffect. The numerical results verify the robust performance of thelaser wire system and provide useful guidance for the opticalsystem design.

Measurements of horizontal and vertical profiles have beenparasitically conducted on the neutron production H� beam at apower level of 620 KW. The H� beam profiles have beensuccessfully obtained from all 9 laser wire stations. The depen-dence of the profile parameters measured by the laser wire on theminipulse position of the ion beam was experimentally investi-gated. Not only has the laser wire system minimized the potentialrisks to the superconducting cavity or the operational H� beam, italso offers a unique and useful tool for the ion beam diagnostics ina superconducting linac in general. With this setup, it becamepossible to separately measure the beam size of individualminipulses or even different segments within a single minipulse.In principle, it can measure the beam size of individualmicropulses with an improvement of laser pulse width/timingcontrol.

Acknowledgements

The authors thank members of the Beam Instrumentation,Accelerator Physics, and Operations Groups at the SNS ResearchAccelerator Division for their discussions and technical support.Ted Hunter is acknowledged for providing the information aboutthe magnet design. We are also grateful to Norbert Holtkamp andStuart Henderson for their support of this project. Oak RidgeNational Laboratory is managed by UT Battelle, LLC for the USDepartment of Energy under Contract no. DE-AC05-00OR22725.

Appendix A. Photon density distribution with realistic laserbeam parameters

With the assumptions made in Section 2, propagation of thelaser beam after the lens L1 in Fig. 2 results in beam tilting angles

yx ¼jx �Dx

fðA1Þ

yz ¼jz �Dz

f: ðA2Þ

At a given location y, the laser beam will have displacements inx and z directions which are determined, respectively, by

xs �Dxþðf þyþDyÞyx ¼ ðf þyþDyÞjx �yþDy

fDx ðA3Þ

zs �Dzþðf þyþDyÞyz ¼ ðf þyþDyÞjz �yþDy

fDz: ðA4Þ

Assuming the laser beam has a Gaussian profile, its size can beexpressed as [16]

s2lxðyÞ ¼ s

2lzðyÞ ¼

1

4½w2

0þðyþDyÞ2y20�: ðA5Þ

Here, w0 is the laser beam waist at the focal plane of lens L1,y0=l/pw0 is the laser beam divergence angle. Note that inGaussian optics the light intensity I is expressed asIpexp(�(2r2/w2)), while in accelerator physics, the photondensity distribution is denoted as ZlNexp(�(r2/2s2)). Hence sis related to w as s�w/2. Assuming a collimated Gaussian beamwith a beam waist wi is incident on the lens L1, we can express w0

as w0=(lf/pwi). Accordingly, one can rewrite Eq. (A5) as

s2lxðyÞ ¼ s

2lzðyÞ ¼

1

4

2lp f#

� �2

þyþDy

2f#

� �2" #

ðA6Þ

where f#= f/2wi is the f-number of the laser beam at the focusinglens. Taking Eqs. (A3)–(A6) into Eq. (4), one can revise the photonbeam distribution as Eq. (5).

0.9

1

A

0.6

0.7

0.8Ay

Am

plitu

de (

V)

25

26

0.5

22

23

24

Bea

m C

ente

r (m

m)

1.2

1.3

21

0.9

1

1.1

Bea

m S

ize

(mm

)

0.8

Turn #

3028 32 34 36 38 40 42

�y

�z

Z0

Y0

Az

Fig. 13. Minipulse dependence of profile parameters measured at laser wire

station 32 on a consecutive 12 minipulses within one macropulse. (a) Profile peak

height, (b) beam center position, and (c) beam size. Notations are the same as in

Fig. 11.

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Appendix B. Calculation of photodetachment efficiency

Integration of Eq. (2) is conducted by using the followingformula:

nbðxþDx; y; z; tþtÞ ¼ nbðx; y; z; tÞ � ctS0nlðx; y; z; tÞnbðx; y; z; tÞ ðB1Þ

where t is the integration time step and Dx=bct. In the numericalcalculations, S0 is computed using

S0 ¼ 7:96� 10�17

� exp �0:514

l½mm�

� �1� exp 2:25�

3:72

l½mm�

� �� �¼ 3:51� 10�17 cm2

at l=1.064mm [14,4,5]. The ion beam will have an initial condition

nbðx; y; z; t0Þ ¼Nb

ð2pÞ3=2sbssbysbz

exp �ðx� bct0Þ

2

2s2bs

�y2

2s2by

�z2

2s2bz

" #:

ðB2Þ

Since the photon loss during the photodetachment process isnegligible, the photon density is assumed to have a stationarydistribution as defined in Eq. (B3).

The total photodetachment yield of an ion beam micropulseafter a complete interaction with a laser pulse can be calculatedby

Z¼ Ndet

Nb¼ 1�

RRRnbðx; y; z;1Þdx dy dz

Nb: ðB3Þ

Calculation steps Dx(=bct), Dy(=ct), Dz were chosen to betypically 10% of the focused laser beam waist w0. The integrationis carried out over a certain range [�Lk, Lk] (k=x, y, z) along each

axis. It is verified that the photodetachment yield Z approaches astable value for any LkZ5sbk.

References

[1] S. Henderson, et al., Spallation neutron source superconducting linaccommissioning algorithms, in: Proceedings of PAC 2005, Knoxville, USA, p.3423;S. Henderson, et al., Commissioning and initial operating experience with theSNS 1 GeV linac, in: Proceedings of LINAC 2006, Knoxville, USA, p. 1.

[2] R. Hardekopf, et al., Wire-scanner design for the SNS superconducting-RFlinac, in: Proceedings of PAC 2001, Chicago, USA, p. 1312.

[3] M.A. Plum, W. Christensen, R.E. Meyer, C.R. Rose, The SNS linac wire scannersystem, in: Proceedings of PAC 2003, Portland, USA, p. 2485.

[4] R. Connolly, et al., Laser beam-profile monitor development BNL for SNS, in:Proceedings of 2002 Beam Instrumentation Workshop (New York), BNL69258.

[5] R.E. Shafer, Laser diagnostic for high current H-beams, LA-UR 98-2643.[6] S. Assadi, et al, The SNS laser profile monitor design and implementation, in:

Proceedings of PAC 2003, Portland, USA, p. 2706.[7] S. Assadi, SNS transverse and longitudinal laser profile monitors design,

implementation and results, in: Proceedings of EPAC 2006, Edinburgh, UK, p.3161.

[8] C. Gabor, et al., Rev. Sci. Instrum. 73 (2002) 998.[9] Y. Honda, et al., Phys. Rev. ST Accel. Beams 6 (2003) 092802.

[10] Y. Honda, et al., Nucl. Instr. and Meth. A 538 (2005) 100.[11] R.C. Connolly, et al., Nucl. Instr. and Meth. A 312 (1992) 415.[12] V.W. Yuan, et al., Nucl. Instr. and Meth. A 329 (1993) 381.[13] W.H. Kuan, T.F. Jiang, K.T. Chung, Phys. Rev. A 60 (1999) 364.[14] A. Aleksandrov, Calculation of the neutralization degree in the H-beam due to

interaction with laser beam, SNS-Note-AP-44.[15] W. Blokland, A. Barker, W. Grice, Drift compensation for the SNS laser wire, in:

Proceedings of ICALEPCS 2007, Knoxville, USA, p. 576.[16] B.E.A. Saleh, M.C. Teich, Fundamental of Photonics, John Wiley & Sons, Inc.,

New York, 1991, pp. 92–100.

Y. Liu et al. / Nuclear Instruments and Methods in Physics Research A 612 (2010) 241–253 253