As part of an accelerator based Cargo Inspection System, studies were made to develop a Cabinet Safe System by Optimization of the Beam Optics of Microwave Linear Accelerators of the IAC-Varian series working on the S-band and standing wave pi/2 mode. Measurements, modeling and simulations of the main subsystems were done and a Multiple Solenoidal System was designed. This Cabinet Safe System based on a Multiple Solenoidal System minimizes the radiation field generated by the low efficiency of the microwave accelerators by optimizing the RF waveguide system and by also trapping secondaries generated in the accelerator head. These secondaries are generated mainly due to instabilities in the exit window region and particles backscattered from the target. The electron gun was also studied and software for its right mechanical design and for its optimization was developed as well. Besides the standard design method, an optimization of the injection process is accomplished by slightly modifying the gun configuration and by placing a solenoid on the waist position while avoiding threading the cathode with the magnetic flux generated. The Multiple Solenoidal System and the electron gun optimization are the backbone of a Cabinet Safe System that could be applied not only to the 25 MeV IAC-Varian microwave accelerators but, by extension, to machines of different manufacturers as well. Thus, they constitute the main topic of this paper.

1. 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

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.
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Carlos O. Maidana
2

3. Research foundations
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.
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Carlos O. Maidana
3

4. Research foundations
As a first step towards our final goal
Modeling, Simulation and Optimization
of the IAC-Varian Accelerators had to be done.
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4

5. Research foundations
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.
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Carlos O. Maidana
5

6. Microwave Linacs Concepts
Klystron diagram
Transversal cut of a Clinac
Biperiodic SW structures: a) On
axis coupling and b) side-cavity
coupling. --------------->>>>>>>
Standing Wave oscillating in
amplitude vs. time.
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Carlos O. Maidana
Source: Karzmark, Nunan, Tanabe; Medical
Electron Accelerators, McGraw Hill.
6

7. A short story about RF Cavities, Fields
and Beams
Pillbox Cavity
Structure Mode
Basic SW def.: 2pi
divided by number
of cavities per
wavelength.
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Cavity Mode
TE: Transversal Electric
TM: Transversal Magnetic
Carlos O. Maidana
7

8. A short story about RF Cavities, Fields
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 ff - axi s ca v iti 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.
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Carlos O. Maidana
8

9. A short story about RF Cavities, Fields
and Beams
Vector Z of particle optical
coordinates:
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Carlos O. Maidana
Source: Wilson and Wolski academic lectures.
9

10. 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.
9/4/2008
Thermal emission: If T is high
enough the e are distributed up
to the vacuum level and e can
scape
Carlos O. Maidana
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.
10

11. Electron emission
Main Phenomena to take care of
• Multipacting
•Secondary Electron Emission
Back scattered secondary: when the primary
electron is reflected off the surface
Resonance multiplication of secondary
electrons
Rediffused secondary: the electron penetrates
the surface and scatters off one or more
atoms and is reflected back out
One electron impact with a surface
releasing more secondary electrons
True secondary electrons: the electron
interacts inelastically with the material and
releases more electrons
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11

12. Focusing Solenoids approach
An important factor to take into consideration is the use of
focusing solenoids
Reduce the beam envelope
Reduce the beam divergence
and so the possibilities of secondary emission and/or highly dispersive radiation effects.
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12

13. 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.
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Carlos O. Maidana
13

14. Solenoid Focusing: canonical
momentum derivation
Starting from the relativistic Lagrangian the canonical
momentum of a particle of charge q can be expressed as:

 L
  
P    m0v  qA  p  qA
 qi
If E=0 in the region where the solenoid is placed, then the canonical momentum is conserved
due to the position independence of the Hamiltonian.
If a particle goes from a region of magnetic field to a
region with zero magnetic field, it experiments a change in
momentum
1
pf  qAf  qrB0 ( z )
2
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.
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14

15. 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.
M linear
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0
0
1
0
0
1
0  1/ f
0
0
0
qB
2p
1
0
0
1
0

0
0

1

0

0

0

1

 1

 0
M3  
 0
 qB
 2p


 1

0
M2  

 0

  sin f

p
sin f
qB
cos f
p

(1  cos f )
qB
0
 C

  CS
M 
  CS
 S 2

CS / 
C2
 S 2 /
 CS
2
f-1=[(qB)/(2p)]2L
 1

  1/ f

0

 0

 1

 0
M1  
 0
 qB
 2p

Carlos O. Maidana
CS
 S 2
C2
 CS
Taylor 1st order
0
0
qB
1 
2p
0
1
0
0
0

0

0

1

p

(1  cos f ) 
qB

sin f


p
sin f 
qB


cos f

0
0
1
0
S / 

CS 
CS /  

C2 

2
w h e r e
S=sin(q/2),
C=cos(q
/ 2 ) ,
a=qB/2p
and q =2La
if L is the
total length
of the
solenoid.
15

16. Solenoid Fields
Bz ( s) 
B0
tanh(s / R)  tanh((s  l ) / R)
2 tanh(l / 2 R)
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.
•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.
0 In 



Bz ( s) 

2
2 
2  s2  R2
(s  l )  R 

s
s l
 R  R2  s2
0 In 
2
 s log 2
Bz ( s) 
 R  R2  s2
2( R2  R1 ) 
1
 1

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Thin Solenoid – CMSI: this element is a thin
solenoid made of a single layer of thin wire
2
2


  ( s  l ) log R2  R2  ( s  l )

 R  R 2  (s  l )2
1

 1
Carlos O. Maidana




Thick Solenoid – CMST :
this element is a thick
solenoid extending
longitudinally & radially
16

17. 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.
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Carlos O. Maidana
17

18. 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
The objective of the fitting
algorithm was to minimize (x,a),
( y, b ) a n d t o k e e p s t a b i l i t y.
Aperture (radius): 0.1015 m
It’s clear that beam focusing and trapping of particles can be
accomplished by the used of thin solenoids.
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Carlos O. Maidana
18

19. 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
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Carlos O. Maidana
19

20. 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
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Carlos O. Maidana
20

21. 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.
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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
Carlos O. Maidana
21

22. Waveguide Simulation of IAC-Varian
Accelerator Series
Top, front and side view of the micro bunch. The
RMS Beam size is sx, y ~ 1.1 mm.
 E p    max 
Ep
E p ,max

s
 Ep
s 1 
E
 p ,max




s
Secondary electrons emission yield, defined as the ratio of
the number of emitted electrons to the number of incident
electrons to the solid.
Beam size evolution through the waveguide.
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22

23. Effect of Front End Solenoids on IACVarian Accelerator Series
Final characteristics:
•855 particles taken into account
•Secondaries: ~0.021% of the injected charge
•Micro bunch charge: -0.2138nC
•Beam size sx,y~0.63 mm
•Average energy: ~14 MeV
•Particle lost: ~90%
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23

24. Effect of Front End Solenoids on IACVarian Accelerator Series
The beam size and divergence are smaller and some
improvements can be seen at the exit of the Linac,
b u t n o t i m p o r t a n t o p t i mi z a t i o n s c a n b e
accomplished by the used of only FE solenoids
besides stronger focusing and trapping of secondary
particles generated in the exit port.
Very few improvements from the beam dynamics and linac
performance point of view respecting the original model.
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24

25. 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%)
•Beam size sx,y~2.4 mm
•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.
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25

26. Effect of Thin & Front End Solenoids on
IAC-Varian Accelerator Series
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Carlos O. Maidana
26

27. Effect of a Multiple Solenoidal System
on IAC-Varian Accelerator Series
F.E. solenoids with same characteristics than before
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
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27

28. Effect of a Multiple Solenoidal System
on IAC-Varian Accelerator Series
Final characteristics:
•Micro bunch charge: -1.99 nC (99%)
•Beam size sx,y~1.9 mm
•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.
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Carlos O. Maidana
28

29. Effect of a Multiple Solenoidal System
on IAC-Varian Accelerator Series
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
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29

30. 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).
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30

31. Gamma Shower results using Monte
Carlo methods for a generic Linac head.
Angular distribution of
electrons
Backscattered primary electrons: 0.346%
Angular distribution of
photons
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31

32. Electron Gun Characterization
One of the most used electron guns in microwave
accelerators
Pierce electron gun
Schematic of a thermo ionic e-source.
Electrons have a Boltzmann
distribution of energies.
Based on the Rodney-Vaughan
method an algorithm for the
complete characterization of
the gun was developed using
the VBasic language.
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Figure. Converging gun geometry for a beam with moderate perveance.
Courtesy Field Precision LLC.
Carlos O. Maidana
32

33. Electron Gun Characterization
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33

34. Electron Gun Characterization
Beams in general
Non uniform density profile
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.
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.
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34

35. Electron Gun Characterization
•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.
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35

36. Electron Gun Characterization
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.
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36

37. Electron Gun Modification
Specifications for a new e-gun
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)
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Carlos O. Maidana
37

38. 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.
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Carlos O. Maidana
38

39. 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).
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Carlos O. Maidana
39

40. Estimation of improvements using
the Multiple Solenoidal System.
Maximum estimated dose
transmitted by the cavities
0.005 rads/h
Minimum estimated dose
transmitted by the cavities
0.001 rads/h
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Carlos O. Maidana
40

41. Conclusion
Electron gun modification
Optimization
Multiple Solenoid System
Reduction of Radiation Emitted
is expected
Basis for a Cabinet Safe System Development Method
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Carlos O. Maidana
41

42. 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.
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42

43. T4 6 MeV Accelerator
Agreement with the
measurements done by
D. Wells and F. Harmon
in the IAC’s T4.
Last/exit cavity
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43

44. 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.
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44

45. GDR Neutron yield and differential
photon track length distributions
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
Source: Mao, Kase, Liu and Nelson,
Neutron sources in the Varian Clinac
2100C/2300C Medical Accelerator
Calculated by the EGS4 Code, SLACPUB-7077, June 1996.
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45

46. Neutron Sources in IAC-Varian
waveguides
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