Maidana - Modification of particle accelerators for cargo inspection applications

Design, Modeling and Simulations of a

Cabinet Safe System for a Linear

Particle Accelerator of intermediate

low energy by optimization of the

beam optics.

Carlos O. Maidana, Ph.D.*

*Currently at Washington State University

and Idaho National Laboratory

9/4/2008 Carlos O. Maidana 2

Research foundations

Low energy accelerators systems (<1 MeV) have

established “cabinet safe” operation within several

meters of the accelerator.

Higher energy systems (1 – 25 MeV) needs the same

convenience and portability as low energy systems

For its use in cargo inspection applications

Which requires transportation and operation in harbors and borders.



To accomplish the portability and safety operation of particle

accelerators in cargo inspection applications

Beam Dynamics needs to be optimized and shielding minimized

Meaning reduction of the radiation field must be done by

other means such as Beam Optics.



As a first step towards our final goal

Modeling, Simulation and Optimization

of the IAC-Varian Accelerators had to be done.



As a second step towards our final goal

Radiation studies of the standard and optimized models

of the IAC-Varian Accelerators had to be done as well.


Microwave Linacs Concepts

Standing Wave oscillating in

amplitude vs. time.Source: Karzmark, Nunan, Tanabe; Medical

Electron Accelerators, McGraw Hill.

Biperiodic SW structures: a) On

axis coupling and b) side-cavity

coupling. --------------->>>>>>>

Klystron diagram

Transversal cut of a Clinac


A short story about RF Cavities, Fields

and Beams

Pillbox Cavity

Structure Mode

Basic SW def.: 2pi

divided by number

of cavities per

wavelength.

Cavity Mode

TE: Transversal Electric

TM: Transversal Magnetic



and Beams

Equivalent circuit for a biperiodic

cavity chain. K1 represent the

magnetic coupling constant

between on-axis and off-axis

cavities; K2 represents the one

between adjacent accelerating

cavities and K3 between adjacent

o f f - a x i s c a v i t i e s .

Dispersion relation

The accelerating cavities resonant frequency is w1 and the coupling cavity one is w2.

Always assuming n=0,2,…,2N accelerating cavities and n=1,3,…,2N-1 coupling

cavities. f is the mode number, which is given by f=pq/(2N) with q=0,1,…,2N.

Typical values are k1=0.03, k2=-0.002 and k3=0.



and Beams

Source: Wilson and Wolski academic lectures.

Vector Z of particle optical

coordinates:


Electron emission

•Thermal electron emission (heated material)

•Field emission (high gradient field)

•Photo-cathode emission (photoelectric effect)

•Secondary electron emission (induced by electron absorption)

Fermi-Dirac distribution.

T=0, Fermi level.

T>0, Higher Energy state

due to thermal energy.

Thermal emission: If T is high

enough the e are distributed up

to the vacuum level and e can

scape

Field emission: with a larger surface

field, the potential barrier to the outside

becomes thinner. When E>1E8 V/m the

tunnel current becomes important.


Electron emission

•Secondary Electron Emission

Main Phenomena to take care of

• Multipacting

Resonance multiplication of secondary

electrons

One electron impact with a surface

releasing more secondary electrons

Back scattered secondary: when the primary

electron is reflected off the surface

Rediffused secondary: the electron penetrates

the surface and scatters off one or more

atoms and is reflected back out

True secondary electrons: the electron

interacts inelastically with the material and

releases more electrons


Focusing Solenoids approach

and so the possibilities of secondary emission and/or highly dispersive radiation effects.

An important factor to take into consideration is the use of

focusing solenoids

Reduce the beam envelope Reduce the beam divergence


Solenoid Focusing

We are familiar with 3 kinds of solenoid focusing:

1. Focusing in one or more larmor rotation in a

uniform long solenoid (as in an image

intensifier).

2. The trapping of articles along field lines.

3. Focusing from point to point by a thin solenoid.


Solenoid Focusing: canonical

momentum derivation

Starting from the relativistic Lagrangian the canonical

momentum of a particle of charge q can be expressed as:AqpAqvm

q

LP

i

0

If E=0 in the region where the solenoid is placed, then the canonical momentum is conserved

d u e t o t h e p o s i t i o n i n d e p e n d e n c e o f t h e H a m i l t o n i a n .

If a particle goes from a region of magnetic field to a

region with zero magnetic field, it experiments a change in

momentum

)(2

10 zBqrqAp ff

The particles crossing the fringe fields experience a transverse force (kick in the azimuthal

momentum) causing the particles to follow a spiral path & a coupling between coordinates.


Solenoid Focusing: matrix formalism

The transfer matrix M of a solenoid

can be thought as the composition of

three different matrices corresponding to :

•M1: entrance fringe field,

•M2: constant axial magnetic field &

•M3: output fringe field.

1002

0100

02

10

0001

1

p

qB

p

qB

M

1002

0100

02

10

0001

3

p

qB

p

qB

M

ff

ff

ff

ff

cos00sin

sin1)cos1(0

sin0cos0

)cos1(0sin1

2

qB

p

qB

p

qB

p

qB

p

M

22

22

22

22

//

//

CCSCSS

CSCSCS

CSSCCS

SCSCSC

M

w h e r e

S=sin(q/2),

C = c o s ( q

/ 2 ) ,

a = q B / 2 p

and q =2La

if L is the

total length

o f t h e

s o l e n o i d .

1/100

0100

001/1

0001

f

fM linear

f-1=[(qB)/(2p)]2L

Taylor 1st order


Solenoid Fields

)/)tanh(()/tanh()2/tanh(2

)( 0 RlsRsRl

BsBz

2222

0

)(2)(

Rls

ls

Rs

sInsBz

22

11

22

22

22

11

22

22

12

0

)(

)(log)(log

)(2)(

lsRR

lsRRls

sRR

sRRs

RR

InsBz

Thin Solenoid – CMSI: this element is a thin

solenoid made of a single layer of thin wire

Thick Solenoid – CMST :

this element is a thick

solenoid extending

longitudinally & radially

•The tanh approximation is used because the on-axis field drops more quickly in the

fringe region compared to the pure theoretical fields. But, the discrepancy from the

actual field becomes large for sufficiently thick solenoids.

Thin solenoid - CMS: The hyperbolic tangents

are used as simple approximations for the rise

and fall-off of the field at s=0 and s=l.


ASTRA & COSY Infinity

ASTRA stands for A Space Charge Tracking Algorithm. The program ASTRA

tracks particles through user defined external fields taking into account the space

charge field of the particle cloud. The tracking is based on Runge-Kutta

integration of 4th order with fixed time step.

ASTRA was developed in DESY Hamburg by Dr. Klaus Floettmann.

COSY Infinity is a code for the study and design of beam physics systems. At

its core it is using Differential Algebraic (DA) methods and it allows the

calculation of arbitrary order effects of particle optical elements. COSY

Infinity is an object oriented language environment.

COSY was developed in Michigan State University by Dr. Martin Berz et al.


Front End Solenoids

COSY Infinity result for 18 MeV electrons under

the influence of multiple B fields (FE solenoids +

Linac’s thick solenoid).

•The particle was launched inside the Linac

solenoidal field.

•Each beam was set up to: 6 mm in size and

200mRad aperture.

•Symmetry between the x-a(=px/p0) and y-b(=py/p0)

planes can be observed

Bz field at the center of the solenoids: +/- 0.745 T

Drift Length: 0.1147 m

Drift between first solenoid and Linac: 0.05 m

Aperture (radius): 0.1015 m

The objec t ive of the f i t t ing

algorithm was to minimize (x,a),

( y, b ) and to k ee p s t ab i l i t y.

It’s clear that beam focusing and trapping of particles can be

accomplished by the used of thin solenoids.


Waveguide Modeling of IAC-Varian

Accelerator Series

RF Cavities:

•Analytical determination of main RF accelerating field: TM010

•Metrology of apertures using image processing software

•Generation of data files

Solenoids:

•Mapping of axial magnetic fields generated by the Linac integrated solenoids

•Generation of data files

Beam:

•Distribution characterization: Plateau for the bunch, Gaussian for the micro-bunch

•Efficiency from injection to exit

•Characterization of the beam emitted from the gun

Source: SLAC-PUB-8026


Waveguide Modeling of IAC-Varian

Accelerator Series

Confinement solenoids characteristics:

•Two long solenoids to confine the electrons to the waveguide and to avoid

multipacting

•External diameter: 25.5 cm; inner diameter: 21.5 cm.

•Length: 1.04 m and 0.33 m

•Operating points: 15.7 A at 137 V (long sol.) and 15.5 A at 42 V (short sol.)

Initial beam characteristics:

•8000 macro particles taken into account

•Gaussian distribution with sx,y=0.75 mm

•Quasi-randomly distribution using the Hammersley sequence to reduce statistical

fluctuations and to avoid artificial correlations

•Micro-bunch charge: -2nC ; Energy: 50 KeV


Waveguide Simulation of IAC-Varian

Accelerator Series

Final characteristics:

•871 macro particles reach the target position

•Secondaries: ~0.021% of the injected charge

•Beam size sx,y~1.1 mm

•Micro-bunch charge: 0.2178nC (10.89%)

•Energy: ~18 MeV (~14 MeV due to TM010)

•Active secondaries: 0.0025% of injected charge.

Longitudinal particle position showing the interaction

point of the electrons within the waveguide and with

the target. The stars at ~1.6 m represent the normal

macro-particles reaching the target; the dark circles

represent lost macro-particles and the gray ones are

macro-particles traveling backwards. Secondaries

generated at the exit window are not shown.

Cavity 0 1 2 3 22

Energy [MeV] 0.50 1.30 2.1 2.9 18

Charge lost [%] 56 22.5 10 2 < 0.1


Waveguide Simulation of IAC-Varian

Accelerator Series

Beam size evolution through the waveguide.

s

p

pp

p

p

E

Es

s

E

EE

max,

max,

max

1

Secondary electrons emission yield, defined as the ratio of

the number of emitted electrons to the number of incident

electrons to the solid.

Top, front and side view of the micro bunch. The

RMS Beam size is sx, y ~ 1.1 mm.


Effect of Front End Solenoids on IAC-

Varian Accelerator Series


•855 particles taken into account

•Secondaries: ~0.021% of the injected charge

•Micro bunch charge: -0.2138nC


•Average energy: ~14 MeV

•Particle lost: ~90%


Effect of Front End Solenoids on IAC-

Varian Accelerator Series

The beam size and divergence are smaller and some

improvements can be seen at the exit of the Linac,

bu t no t impor tan t op t imiza t ions can be

accomplished by the used of only FE solenoids

besides stronger focusing and trapping of secondary

p a r t i c l e s g e n e r a t e d i n t h e e x i t p o r t .

Very few improvements from the beam dynamics and linac

performance point of view respecting the original model.


Effect of Thin & Front End Solenoids on

IAC-Varian Accelerator Series

Final characteristics w/thin sol. @ 0.071 m:

•Micro bunch charge: -0.3965 nC (20%)


•Average energy: ~14 MeV

•Active secondary electrons: 2% total particles

•Particle lost: 80% of the injected one

Longitudinal particle distribution (interaction

points with matter) for IAC-Varian Accelerator

coupled to FE solenoids and a thin 0.087 T

solenoid over the first full cavity. The circles close

to the horizontal axis represents some few particles

lost traveling backwards.


Effect of Thin & Front End Solenoids on

IAC-Varian Accelerator Series


Effect of a Multiple Solenoidal System

on IAC-Varian Accelerator Series

Thin solenoids located at: 0.0005(0); 0.071(1); 0.228(4); 0.65(12) m (cavity)

Thin sol. characteristics: 0.08718 T on axis

0.025 m length; 0.14 m radius

F.E. solenoids with same characteristics than before





•Micro bunch charge: -1.99 nC (99%)


•Average energy: 18 MeV (14.2 MeV

TM010)

•Active secondary electrons: 0

•Macro particle loss: 0.1%

Longitudinal particle positions (interaction points) for the Multiple

Solenoidal System. Very few macro-particles lost at the beginning

of the waveguide (cavity 0) and more than 89% (±10%) of the

injected ones reaching the final tracking position at z=1.60 m. The

secondaries generated, and the particles lost, on the exit

port/window are not considered here and represent a source of

uncertainties to take into consideration.




Energy deposition due to particle

loss ~5.1 10-7 J/m

Huge improvements could be

accomplished by the used of a

Multiple Solenoidal System


Uncertainties due to Wakefields and

Accelerator Acceptance

The uncertainties in these models and simulations are given mainly by:

•Model and simulation of the bunching system is difficult without precise phase

information.

•Maximum acceptance for a bunching system is ~80% (being this last only

accomplished in RFQ systems).

•Wakefields modify the way that a cavity interacts with the beam and its calculations

are still a topic of research.

•Dipole mode could have some influence but it would be limited for this particular type

of accelerator. As we know, dipole modes are transverse fields deflecting the particles

if it is strong enough but it is my belief that the beam loading will avoid reaching the

point of instabilities (i.e. TM110 generates dipole modes).


Gamma Shower results using Monte

Carlo methods for a generic Linac head.

Angular distribution of

electrons

Angular distribution of

photons

Backscattered primary electrons: 0.346%


Electron Gun Characterization

Schematic of a thermo ionic e-source.

Electrons have a Boltzmann

distribution of energies.

One of the most used electron guns in microwave

accelerators

Pierce electron gun

Figure. Converging gun geometry for a beam with moderate perveance.

Courtesy Field Precision LLC.

Based on the Rodney-Vaughan

method an algorithm for the

complete characterization of

the gun was developed using

t h e V B a s i c l a n g u a g e .





Beam profile for electrons created in a Pierce gun with 25 mA current at 10 keV voltage. It is clear that they

don’t follow a Gaussian distribution because of the presence of strong space charge forces in their center. Picture

created by Matt Hodek (MSU) with experimental data taken with Carlos O. Maidana (WSU) and Adam Lichtl

(BNL) on a diode Pierce gun at the University of Maryland, College Park.

When the beam currents are high enough that self fields (space charge effects) can no longer be

neglected in comparison to the applied fields, then the analysis becomes more difficult and

complex.

Non uniform density profileBeams in general



•A way to optimize the injection of electrons emitted from the gun is the

placing of a thin solenoid on the waist position.

•Calculation of the solenoid parameters is done using COSY Infinity. The

objective imposed is stability of the transfer map and the corresponding

conditions for focusing or parallel movement.



Time resolved images of a low current electron beam generated in a Pierce gun after transport through a thin

focusing solenoid. A higher density of electrons can be appreciated in the front center of the beam while a higher

electron density distribution is located at the edges in the middle of the beam pulse. Images taken by Tiago Da Silva

(University of Sao Paulo) and Carlos O. Maidana (WSU) at the University of Maryland, College Park.


Electron Gun Modification

Pulses of ~200 s length and ~ 5nC charge

Bunches of ~1 ns (macro-inner pulse)

Bunch separation of ~1 s

Micro-bunch structure: S band (2.586 GHz)

Specifications for a new e-gun


Electron Gun Modification

Effect of adjusting the control grid bias in a triode electron gun for optimal beam output. The disadvantage for high

currents is the higher erosion rate that such a grid can suffer. Courtesy of Dr. Santiago Bernal, UMER – University

of Maryland, College Park.


Estimation of photons and dose

transmitted by the RF cavities.

Photons transmitted by the main

radiated cavities in the IAC-Varian

Linacs

Dose rate transmitted by the main radiated

cavities in the IAC-Varian Linacs (water

phantom: 94.01 rads/h; empty phantom:

115.57 rads/h).


Estimation of improvements using

the Multiple Solenoidal System.

Maximum estimated dose

transmitted by the cavities

Minimum estimated dose

transmitted by the cavities

0.005 rads/h

0.001 rads/h


Conclusion

Optimization

Electron gun modification

Multiple Solenoid System

Reduction of Radiation Emitted

is expected

Basis for a Cabinet Safe System Development Method


Acknowledgement

Dr. Alan W. Hunt (IAC-ISU)

Dr. Klaus Floettmann (DESY)

Dr. Shashikant Manikonda (ANL)

Dr. Alberto Rodriguez (CERN)

Mr. Mike Smith (IAC-ISU)

This research is being developed thanks to

the U.S. Department of Defense.


T4 6 MeV Accelerator

Agreement with the

measurements done by

D. Wells and F. Harmon

in the IAC’s T4.

Last/exit cavity


Emittance and Liouville’s theorem

Liouville's theorem tells us that under symplectic transport, particle densities in

phase space must be conserved.

The symplectic condition for Liouville's theorem to be satisfied is that the dynamics

of individual particles must be governed by Hamilton's equations. This is the case

for particles moving along an accelerator beam line if:

– we neglect dissipative effects like radiation;

– we keep a constant reference momentum, P0.

Assuming that Liouville's theorem holds, the emittance of a bunch must be

conserved as the bunch moves along an accelerator beam line.


GDR Neutron yield and differential

photon track length distributions

Source: Mao, Kase, Liu and Nelson,

Neutron sources in the Varian Clinac

2100C/2300C Medical Accelerator

Calculated by the EGS4 Code, SLAC-

PUB-7077, June 1996.

Total photoneutron yield

cross sections for W & Cu.

Differential photon track

length distributions

produced in 1-radiation

length-thick W targets

struck by 10, 15 and 20

MeV electrons


Neutron Sources in IAC-Varian

waveguides

Maidana - Modification of particle accelerators for cargo inspection applications

Technology

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s2 r2 s

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