maidana - modification of particle accelerators for cargo inspection applications
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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.
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 4
Research foundations
As a first step towards our final goal
Modeling, Simulation and Optimization
of the IAC-Varian Accelerators had to be done.
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 6
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
9/4/2008 Carlos O. Maidana 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.
Cavity Mode
TE: Transversal Electric
TM: Transversal Magnetic
9/4/2008 Carlos O. Maidana 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 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.
9/4/2008 Carlos O. Maidana 9
A short story about RF Cavities, Fields
and Beams
Source: Wilson and Wolski academic lectures.
Vector Z of particle optical
coordinates:
9/4/2008 Carlos O. Maidana 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.
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.
9/4/2008 Carlos O. Maidana 11
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
9/4/2008 Carlos O. Maidana 12
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
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 14
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.
9/4/2008 Carlos O. Maidana 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.
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
9/4/2008 Carlos O. Maidana 16
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.
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 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
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.
9/4/2008 Carlos O. Maidana 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
9/4/2008 Carlos O. Maidana 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
9/4/2008 Carlos O. Maidana 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.
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
9/4/2008 Carlos O. Maidana 22
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.
9/4/2008 Carlos O. Maidana 23
Effect of Front End Solenoids on IAC-
Varian 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%
9/4/2008 Carlos O. Maidana 24
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.
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 26
Effect of Thin & Front End Solenoids on
IAC-Varian Accelerator Series
9/4/2008 Carlos O. Maidana 27
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
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 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
9/4/2008 Carlos O. Maidana 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).
9/4/2008 Carlos O. Maidana 31
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%
9/4/2008 Carlos O. Maidana 32
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 .
9/4/2008 Carlos O. Maidana 33
Electron Gun Characterization
9/4/2008 Carlos O. Maidana 34
Electron Gun Characterization
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
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 37
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
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 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).
9/4/2008 Carlos O. Maidana 40
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
9/4/2008 Carlos O. Maidana 41
Conclusion
Optimization
Electron gun modification
Multiple Solenoid System
Reduction of Radiation Emitted
is expected
Basis for a Cabinet Safe System Development Method
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 43
T4 6 MeV Accelerator
Agreement with the
measurements done by
D. Wells and F. Harmon
in the IAC’s T4.
Last/exit cavity
9/4/2008 Carlos O. Maidana 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.
9/4/2008 Carlos O. Maidana 45
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
9/4/2008 Carlos O. Maidana 46
Neutron Sources in IAC-Varian
waveguides
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