design and simulation of the colorado state university linear

DESIGN AND SIMULATION OF THE
COLORADO STATE UNIVERSITY
LINEAR ACCELERATOR
Jonathan Edelen
M.S. Thesis Defense
18 June 2014
Pictures of the machine
The CSU Linear Accelerator System
RF Linear Accelerator
• 
• 
• 
• 
• 
Beam transport
system
Undulator
Photo injector uses photo-electric effect to generate electron beams
Accelerated by high power microwaves to 6 MeV
Quadrupole fields are used to match the beam into the undulator or wiggler
Wiggler uses sinusoidal magnetic fields to wiggle the beam and generate radiation
Beam is refocused and passed through a dipole (Spectrometer)
Spectrometer
Diagnostic
The CSU Photo-Injector
Solenoid(
RF(in(
Bucking(
Coil(
Cathode(Stalk(
Bucking(
Coil(
Solenoid(
RF Input: Provides 1.3 GHz
Microwaves to the LINAC
Bucking Coil: Cancels out
the field on the cathode to
minimize additional additive
components to the
Bucking
emittance
Solenoid
RF
in
Coil
Cathode Stalk
Bucking
Coil
Solenoid: Focuses the
beam, compensating for
space charge forces during
acceleration
Solenoid
Input Laser
Pulse: Excites
the electron
bunches off of
the cathode
Accelerator modeling
Schematic of coupling slot configuration [9]
Exploded view of
three cells modeled
in SUPERFISH
Coupling Slots
Cell Type 2
Exploded view
of coupling slots
and vacuum
ports
Coupling Cell
Half Cell (Cell Type 1)
Cell Type 3
Axial field map
(normalized)
Geometrical model with
field lines
Individual cell models and field maps
Type 1 Cell: Half cell is
optimized to achieve a high
field flatness (see bottom right)
which corresponds to a lower
cavity Q and a lower shunt
impedance
Type 2 Cell: Full cell is
optimized to have a high field
flatness, which corresponds to
a lower cavity Q and a lower
shunt impedance
Type 3 Cell: Full cell is optimized to
have a high shunt impedance and a
high Q. This maximizes the
acceleration efficiency at this end of
the accelerator
Normalized relative field strength
Axial field model comparison
Axial field map
produced by the
combination of
individual cell models
presented
Axial field map
measured by Los
Alamos National Lab
in 1989 [9]
Solenoid and bucking-coil model
Bucking Coil
Focusing Solenoid
Top Left: Schematic of the
solenoid and bucking coil.
Top Right: Electromagnetic model
of the solenoid and bucking coil
Bottom Right: Axial field map of
the solenoid (Bz) in Gauss
Magnetic Field [Gauss]
Ferrous Material
Position [cm]
Measurements of the CSU linear
accelerator
RF launcher: Interfaces
network analyzer and RF
window for measurement
Linear Accelerator
Reflection Coefficient [S11]
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.24
RF window: separates
vacuum of LINAC from
backfill in waveguides
1.26
1.28
1.3
1.32
1.34
1.36
Frequency [GHz]
S11 measurement of the CSU linear accelerator
from 1.24 GHz to 1.36 GHz
Student Version of MATLAB
2
Detailed view of the s11
measurements for each mode
18000
Quality Factor
16000
14000
12000
10000
8000
6000
4000
2000
0
0
2
4
6
8
10
12
Mode Quality
Number factor as a function of the mode
number.
Q=
fres
ff whm
Detailed view of individual resonances from previous slide,
mode number increases from left to right and top to bottom.
1.3GHz mode highlighted in red
Student Version of MATLAB
Los Alamos Measurement
CSU Measurement
Quality Factor
16144
17551
Shunt Impedance
53 M-Ohm/m
(Not Measured)
LINAC SIMULATION STUDIES
LINAC Simulation Studies
•  For an accurate simulation PARMELA needs more than
1000 particles, and less than 0.1 degrees integration step
•  The space charge mesh in the longitudinal and transverse
direction should be greater than 200 and 50 respectively
•  Analysis of simulation parameters on the emittance
accuracy
•  Injection phase effects on emittance
•  Bunch charge and solenoid strength effects on emittance
•  Geometric beam size effects on emittance
•  Cathode spot size
•  Bunch length
•  Simulation parameters and settings used for beam-line
design
Emittance: a measure of beam quality/
disorder
High degree of disorder – high emittance
• 
• 
• 
• 
Beam ellipse in x-x’ phase space with important
parameters noted:
Beta – beam envelope function
Alpha – change in the beam envelope function
Epsilon – beam emittance
r
Low degree of disorder – low emittance
x’
✏
↵
p
✏
r
✏
x
RF Field Strength
RF effects on emittance: longitudinal emittance
Late
Early
RF Phase
1
0
1
RF Phase
Left to right: Particle
arriving early receives
slightly less energy, not
as early late particles
receive slightly more
energy making them
earlier, net compression
0
=1
cos( 0 )
2↵ sin2 ( 0 )
Asymptotic Bunch Compression Factor
Injection Phase
RF effects on emittance: transverse emittance
r
x’
A
B
z
x
⇣⇡
0)
A
The RF field imparts a kick
on the beam at the exit of the
gun, if the field is zero, there
is no additional kick. For
some nonzero field at the
exit the phase space evolves
as left to right.
B
0
f(
2
⌘
1
sin( 0 ) =
2↵
Minimum transverse emittance criteria
f(
Injection Phase
0)
=
⇣⇡
2
0
⌘
sin(
0)
1
2↵
Emittance as a function of injection
phase
Transverse and Longitudinal emittance as a function of injection phase
Injection Phase Constants
Bunch Charge: 2.3nC
Solenoid Strength: 1.4kG
Spot Size: 2mm
Bunch Length: 20 degrees
Beam space charge
r
A
C
D
B
z
=q
1
r̈ /
1
x’
v2
c2
I
3
A
B
C
D
x
Beam space charge
r
A
C
D
B
z
=q
1
r̈ /
1
x’
v2
c2
I
3
A
B
C
D
x
Beam space charge
r
A
C
D
B
z
=q
1
r̈ /
1
x’
v2
c2
I
3
A
B
C
D
x
Beam space charge
r
A
C
D
B
z
=q
1
r̈ /
1
x’
v2
c2
I
3
A
B
C
D
x
Beam space charge
r
A
C
D
B
z
=q
1
r̈ /
1
x’
v2
c2
I
3
A
B
C
D
x
Beam space charge
r
A
C
D
B
z
=q
1
r̈ /
1
x’
v2
c2
I
3
A
B
C
D
x
Increasing Bunch Charge [nC]
Emittance as a function of bunch
charge and solenoid field
Top Left: Transverse emittance vs. solenoid strength
normalized to 1.4 kGauss with bunch charge ranging
from 0.8 to 3.6 nC
Top Right: Longitudinal emittance vs. solenoid
strength normalized to 1.4 kGauss, with bunch
charge ranging from 0.8 to 3.6 nC
Beam Current Constants
Injection Phase: 40 degrees
Bunch Length: 20 degrees
Spot Size: 2mm
Emittance as a function of the
geometric beam size
Spot Size Constants
Beam Charge: 2.3nC
Solenoid Strength 1.4kG
Injection Phase: 40 degrees
Bunch Length: 20 degrees
Bunch Length Constants
Beam Charge: 2.3nC
Solenoid Strength 1.4kG
Injection Phase: 40 degrees
Spot Size: 2mm
Transverse and Longitudinal emittance as a
function of the injected beam radius. The beam
radius is determined by the laser pulse radius
Transverse and Longitudinal emittance as a function
of the injected beam length. The beam pulse length
is determined by the laser pulse length
Summary of injector studies and point
design
Input Beam Parameters
Bunch Charge
2.3 nC
RF Phase
40 Degrees
Bunch Length
20 Degrees
Cathode Spot Size
2mm
Solenoid Field
1420 Gauss
Output Beam Parameters
Transverse Emittance
4 mm-mrad
Longitudinal Emittance
147.5 deg-keV
Alpha X
2.7
Beta X
2.20 [m/rad]
Alpha Y
2.7
Beta Y
2.26 [m/rad]
•  Injector point design provides
initial conditions for downstream
transport
Beam-line tuning for undulator
matching
Solenoid(
• 
RF(in(
Bucking(
Coil(
• 
Cathode(Stalk(
Bucking(
Coil(
Solenoid(
Input Beam
Inject to the undulator at a waist
Beam is round in the x-y plane
20 times compression from the
initial beam
Focusing Quads
Initial Beam
Target
Alpha X
2.66
0
Beta X
2.10 [m/rad]
0.106 [m/rad]
Alpha Y
2.62
0
Beta Y
2.17 [m/rad]
0.106 [m/rad]
Target Beam
Quadrupole Focusing
Diagram of quadrupole
forces on a beam: Grey
arrows indicate field
direction, red arrows
indicate forces. Note
this quad focuses in the
horizontal and
defocuses in the vertical
plane. Bottom shows
the linear variation in the
field with respect to
position
Left: End on picture of CSU
quadrupole and beam-pipe
N
S
S
N
Quadrupole doublet with drift:
Vertical beam envelope in green,
horizontal beam envelope in red
Right: Side view of CSU quadrupole
and beam-pipe
Alpha X [1/rad]
Beta X [m/rad]
Alpha Y [1/rad]
Beta X [m/rad]
Beam-line tuning in elegant
Blue: elegant simulation
Green: PARMELA simulation without space charge using settings from elegant
Red: PARMELA simulation with space charge using the settings from elegant.
Alpha X [1/rad]
Beta X [m/rad]
Alpha Y [1/rad]
Beta X [m/rad]
Beam-line tuning in TRACE
Blue: TRACE simulation without space charge
Green: PARMELA simulation without space charge using settings from TRACE
Red: PARMELA simulation with space charge using the settings from TRACE
Alpha X [1/rad]
Beta X [m/rad]
Alpha Y [1/rad]
Beta X [m/rad]
Beam-line tuning results in TRACE
(with space charge)
Magenta: TRACE simulation with space charge
Red: PARMELA simulation with space charge using settings from TRACE
Numerical results from TRACE without
space charge
Target
Alpha X
Beta X [m/rad]
Alpha Y
Beta Y [m/rad]
0
0.106
0
0.106
Results from TRACE settings matched without space charge
TRACE (W/O Space Charge)
-2.5e-6
0.106
8.8e-6
0.106
PARMELA (W/O Space Charge)
-4.8e-2
0.120
2.6e-3
0.104
0.37
1.527
2.29
0.634
PARMELA (W Space Charge)
Results from TRACE settings matched with space charge
TRACE (W Space Charge)
PARMELA (W Space Charge)
8.4e-6
0.106
1.2e-5
0.106
0.56
0.215
0.38
0.144
Results from TRACE settings iteratively increasing space charge
TRACE (W Space Charge)
5.0e-6
0.106
-4.8e-6
0.106
PARMELA (W Space Charge)
-0.13
0.118
-0.31
0.100
Results from PARMELA feedback optimization
PARMELA (W Space Charge)
-0.67
0.107
-0.044
0.108
Initial and final undulator values
Initial vs. Final values for the wiggler
Initial
Final
Alpha X
-0.6676
0.377
Beta X
0.1066 [m/rad]
0.112 [m/rad]
Alpha Y
-0.0443
-0.248
Beta Y
0.1078 [m/rad]
0.147 [m/rad]
Comparison of beam-line gradients for
feedback with trace and full PARMELA
optimization
Trace
Iteration
PARMELA
Optimization
Difference
Quad 1
-299.097
-299.190
-0.093
Quad 2
201.094
201.009
Quad 3
-225.389
Quad 4
Quad 5
Comparison of beam-line currents required with
trace and full PARMELA optimization
Trace
Iteration (mA)
PARMELA
Optimization (mA)
Difference
(mA)
Quad 1
-446.28
-446.41
-0.14
-0.085
Quad 2
300.05
299.92
-0.13
-225.987
-0.598
Quad 3
-336.30
-337.19
-0.89
124.396
124.889
0.493
Quad 4
185.61
186.34
0.74
32.062
32.485
0.423
Quad 5
47.84
48.47
0.63
Beam-line robustness: verification that the beamline performs under many initial conditions
x vs. x’
y vs. y’
Initial
Final
Initial
Final
Alpha X
0
-3.7e-5
1
4.4e-5
Beta X
5
0.1060
5
0.1060
Alpha Y
0
-3.9e-6
1
-2.7e-6
Beta Y
5
0.1060
5
0.1060
Initial
Final
Initial
Final
Alpha X
-1
1.7e5
-3
-1.4e-5
Beta X
5
0.1060
5
0.1060
Alpha Y
1
-9.2e-6
3
1.4e-6
Beta Y
5
0.1060
5
0.1060
x vs. x’
y vs. y’
Beam-line robustness: verification that the beamline performs under many initial conditions
x vs. x’
y vs. y’
Initial
Final
Initial
Final
Alpha X
1
-2.8e-6
1
1.4e-6
Beta X
5
0.1060
5
0.1060
Alpha Y
1
-9.6e-6
1
1.9e-5
Beta Y
4
0.1060
2
0.1060
Initial
Final
Initial
Final
Alpha X
1
-1.1e5
1
4.4e-6
Beta X
5
0.1060
5
0.1060
Alpha Y
-1
-2.1e-5
-3
-3.8e-7
Beta Y
4
0.1060
2
0.1060
x vs. x’
y vs. y’
Beam-line Matching Spectrometer
Solenoid(
RF(in(
Bucking(
Coil(
Cathode(Stalk(
Bucking(
Coil(
Solenoid(
Focusing Quads
Bending Magnet
Screen/Beam Dump
The Spectrometer
• 
• 
The CSU spectrometer has an expected dispersion
of 0.78-m.
To resolve 3 significant figures in the energy, the
spot size must be smaller than 0.78mm.
S
N
Dipole schematic: Field
arrows in blue, force on
the particle in red.
Demonstration of dispersion:
Particles of different energy
passing through a dipole bend at
different radii
CSU Spectrometer dipole
Matching Results
Blue: Elegant simulation
Green: PARMELA simulation with space charge off using settings from elegant
Magenta: TRACE simulation with space charge
Red: PARMELA simulation with space charge using settings from TRACE
Particle Energy [MeV]
Dispersion Function [m]
Spectrometer dispersion and energyposition correlation
Vertical Position [cm]
Energy position correlation in the vertical
plane at the beam dump. The RMS size of
the beam due to emittance is 0.9 mm
Position [m]
Dispersion function computed by Elegant
and PARMELA: Blue (Elegant), Red
(PARMELA)
START TO END SIMULATIONS
Beam envelope
Transverse Alpha
Function
Background Colors:
Orange (injector)
Green (quadrupoles)
Blue (undulator)
Red (spectrometer)
Transverse Beta
Function [m/rad]
Line Colors:
Green: Y Plane
Blue: X Plane
Longitudinal Position [m]
Transverse and Longitudinal
Emittance
Transverse Emittance
[mm-mrad]
Background Colors:
Orange (injector)
Green (quadrupoles)
Blue (undulator)
Red (spectrometer)
Line Colors:
Green: Y Plane
Blue: X/Longitudinal
Plane
Longitudinal Emittance
[deg-keV]
Longitudinal Position [m]
Longitudinal Position [m]
Accelerator point design
Alpha X
2.66
Alpha X
0.377
Beta X
2.10 [m/rad]
Beta X
0.112 [m/rad]
Alpha Y
2.62
Alpha Y
-0.248
Beta Y
2.17 [m/rad]
Beta Y
0.147 [m/rad]
RF Linear Accelerator
Beam
transport
system
Undulator
Spectrometer
Diagnostic
Alpha X
-0.6676
Beta X
0.1066 [m/rad]
Alpha Y
-0.0443
Alpha X
-7.45
Beta Y
0.1078 [m/rad]
Beta X
4.50 [m/rad]
Alpha Y
-0.172
Beta Y
0.212 [m/rad]
Future work
•  Additional machine characterization steps
•  The first of these is to introduce alignment errors and offsets such that the position
of beam-position-monitors, corrector magnets, and other diagnostics can be
determined.
•  Additionally a simulation of the RF cavity that captures the asymmetries not
modeled in this thesis can be performed utilizing a 3-D accelerator code. T.
•  Future simulation use
•  Novel electron gun designs can provide an input beam distribution to the accelerator
system, thus treating the 5.5 cell structure as a booster.
•  Diagnostics can be tested using the beam parameters and distributions at a
particular position along the beam line that would provide insight to how the
diagnostic would perform once implemented in the accelerator.
•  Beam-line elements, such as chicanes, novel magnets, kickers etc., can be
simulated using the models in this thesis to show how they might perform in the
system.
•  Control systems could also be developed with these simulations before
implementation on the accelerator. Virtually any experiment that utilizes the beamline as a workbench would begin by using these simulations to study performance
with the existing system
Conclusions
•  Useful electromagnetic model for beam simulations
•  Initial measurements of CSU accelerator
•  Characterizations of linear accelerator components
•  Beam transport system designed for undulator matching
•  Spectrometer diagnostic designed
•  Full start to end simulations constructed
References
[1] Kwang-Je Kim, “RF and Space Charge Effects in Laser Driven RF Electron Guns” Nuclear Instruments and
Methods in Physics Research A275 (1987) 201-208
[2] Klaus Wille, “The Physics of Particle Accelerators an Introduction” Oxford University Press 2000
[3] D. A. Edwards and M. J. Syphers “An Introduction to the Physics of High Energy Accelerators” Wiley Series
in Beam Physics and Accelerator Technology, 2004 Wiley-VHC
[4] Thomas Wangler “RF Linear Accelerators” Wiley Series in Beam Physics and Accelerator Technology,
1998 Wiley
[5] Carlsten, “New Photoelectric Injector Design for the Los Alamos National Laboratory XUV FEL Accelerator”
Nuclear Instruments and Methods in Physics Research A285 (1989) 313-319
[6] Martin Reiser, “Theory and Design of Charged Particle Beams” Wiley Series in Beam Physics and
Accelerator Technology, 1994 Wiley
[7] P. M. Lapostolle, IEEE Ttrans Nuclear Science NS-18 (1971) 1101-1104
[8] J. Billen “Poisson Superfish Codes”, Los Alamos National Laboratory, Copyright 1985-2005
[9] D.L. Schrage, L.M. Young, D.J. A&in, W.L. Clark, R.F. DePaula, C. Gladwell, F.A. Martinez, A.C. Naranjo,
P.L. Roybal and J.E. Stovall “University of Twente Photocathode Linac” Nuclear Instruments and Methods in
Physics Research B79 (1993) 721-725
[10] L. Young “PARMELA Codes” Los Alamos National Laboratory, Copyright 1985-205
[11] J.P. Edelen et. al “Electron Back-bombardment and mitigation in a short gap thermionic cathode RF Gun”
IEEE Transactions in Nuclear Science, Volume 61 Issue 2.
[12] M. Borland “ELEGANT (ELEctron Generation ANd Tracking) “ Argonne National Lab
[13] K. R. Crandall and D. P. Rusthoi “TRACE-3D” Los Alamos National Laboratory, May 1997
[14] J. B. Murphy “Synchrotron light source data book” AIP Conference Proceedings 249 , 1939 (1992); doi:
10.1063/1.41969