Code Comparison for Simulations of Photo-Injectors
C.Limborg, Y.K.Batygin, SLAC, Stanford, CA 94309, USA
M.Boscolo, M.Ferrario, V.Fusco, LNF-INFN, 00044 Frascati, Italy
L.Giannessi, M.Quattromini, ENEA Research Center, 00044 Frascati, Italy
J.-P. Carneiro, K. Floettmann, DESY, 22603 Hamburg, Germany
TEST PROBLEM
1nC
10ps square pulse,
1 mm uniform transverse laser
pulse
No Thermal emittance
110MV/m
Solenoid 2.541 kG
DESCRIPTION OF CODES
HOMDYN
multi-envelope model based on the time dependent evolution of a uniform bunch.
basic approximation: bunch represented by a uniformly charged cylinder whose length and radius vary keeping anyway uniform the charge
distribution inside the bunch.
algorithm very efficient and despite some strong simplifying assumptions it allows the quick relaxation of the large number of parameters
involved in parameter studies, to quickly find a reasonably optimized configuration.
BEAMPATH
space charge potential calculated from the direct solution of Poisson's equation by cloud-in-cell method in a moving system of coordinates with
Dirichlet boundary conditions at the aperture and periodic conditions in z-direction.
Simulation of the beam with large energy spread is performed utilizing Green function method for interaction of particles with individual
energies.
PARMELA / ASTRA
space charge force by Lorentz-transforming the particles position and field maps into the average rest frame of the beam.
It then applies static forces to the various rings of the cylindrical map assuming a constant charge density inside a ring.
This algorithm requires to have at least 5 particles in each of the cell of the cylindrical grid.
PARMELA /SPCH3D
fast Fourier Transform set on a 3D grid over which the electric field is solved to verify Poisson’s equation.
time consuming : requires running at least 100k particles and small aspect ratios of the cell dimensions.
to be used when the AR horizontal to vertical of the beam is more than 2 and when the transverse profile does not have a cylindrical symmetry.
TREDI
fully 3D Monte Carlo code devoted to the simulation of beam dynamics.
Space charge fields computed with Lienard Wiechert formalism and taking into account the effects due to the finite propagation velocity of
signals. This is accomplished by storing the histories of macro-particles, and by tracking back in time the source coordinates until a retarded
condition is fulfilled. Short bunch injector simulations (as the test case) can be run also in a faster “Static” mode, where instantaneous signal
propagation is assumed. The “Retarded” mode allows the simulation of a wider class of problems such as CSR effects in bendings.
DESCRIPTION OF CODES
HOMDYN
multi-envelope model based on the time dependent evolution of a uniform bunch.
basic approximation: bunch represented by a uniformly charged cylinder whose length and radius vary keeping anyway uniform the charge
distribution inside the bunch.
algorithm very efficient and despite some strong simplifying assumptions it allows the quick exploration of a large number of parameters, to
quickly find a reasonably optimized configuration.
Contact : Massimo Ferrario , Massimo.Ferrario@lnf.infn.it
E zsc  s  
Ersc  s  
Q
2 o Rs2
Q
4 o Rs L
 s  zs  zt
Ar , s  Rs /  s L 




H  s , Ar , s
G  s , Ar , s
Position from tail
Slice aspect ratio in rest frame with Rs
slice radius
Transverse equation : “envelope equation”
Longitudinal equation
..
zs 

E acc z, t   E zsc z, t   E zimage z, t 
3 z
m
e
o s


2
..
. .
2c 2 k p
 4  1
2
sol
rf
Rs   s   s Rs  K s  K s Rs 
Gsc s, Ar   Gimage s*, Ar    c 
 s Rs
   Rs3
Damping
solenoid focusing

rf focusing
space charge force

image charge
thermal emittance pressure
DESCRIPTION OF CODES
PARMELA / ASTRA
Space charge force computation: Lorentz-transforming the particles position and field maps into the average rest frame of the beam.
It then applies static forces to the various rings of the cylindrical map assuming a constant charge density inside a ring.
This algorithm requires to have at least 5 particles in each of the cell of the cylindrical grid.
PARMELA : ylloyd@qwest.net , or jbillen@lanl.gov
ASTRA :
Also point-to-point option available but useless
In the rest frame of bunch,
sample particle
R
r
d
Cloud-in-cell
U 
Poisson Equation’s solver
Lorentz-transform to moving frame
Distribution of space charge of macroparticles among grid nodes
Solution of Poisson’s Equation on grid

o
with boundary conditions
U (a, z )  0,
U
0, z   0,U r , z   U r , z  L 
r
Differentiation of potential grid function to determine components of
electrostatic field in moving system
Back to lab frame
BEAMPATH
space charge potential calculated from the direct solution of Poisson's equation by cloud-in-cell method in a moving system of coordinates
with Dirichlet boundary conditions at the aperture and periodic conditions in z-direction.
Simulation of the beam with large energy spread is performed utilizing Green function method for interaction of particles with individual
energies.
Contact: Yuri Batygin, batygin@slac.stanford.edu
PARMELA /SPCH3D
fast Fourier Transform set on a 3D grid over which the electric field is solved to verify Poisson’s equation.
time consuming : requires running at least 100k particles and small aspect ratios of the cell dimensions.
to be used when the AR horizontal to vertical of the beam is more than 2 and when the transverse profile does not have a cylindrical
symmetry.
Lienard Wiechert
TREDI
fully 3D Monte Carlo code devoted to the simulation of beam dynamics.
Space charge fields computed with Lienard Wiechert formalism and taking into account the effects due to the finite propagation velocity of
signals. This is accomplished by storing the histories of macro-particles, and by tracking back in time the source coordinates until a retarded
condition is fulfilled. Short bunch injector simulations (as the test case) can be run also in a faster “Static” mode, where instantaneous signal
propagation is assumed. The “Retarded” mode allows the simulation of a wider class of problems such as CSR effects in bendings.
http://www.tredi.enea.it/
• Powerful for image charge
problem space charge solver
• Point to grid evaluation
•Parallel processing
•The velocity of the source particle
doesn’t change on a time scale
comparable to the
retarded time; The contribution of
acceleration fields is negligible.
…
similar to Parmela, GPT, ASTRA
Matching initial parameters – without space charge
Injection phase, electric maps of fields, initial distribution
Define output quantities to compare
Inside the gun : comparison with space charge
Gun + solenoid + drift : comparison of codes with space charge
Code
Platform
CPU
Number
of
particles
Mesh
points
Nr x Nz
HOMDYN
PC Win
BEAMPATH
PC Win
1 GHz
104
256 x
2048
50x50
mm2
0.1o (Gun)
1o (Drift)
8000
PARMELA
PC Win
1 GHz
2.5 104
25 x 75
50x50
mm2
0.1o (Gun)
1o (Drift)
9846
PARMELA/
SPCH 3D
PC Win
1 GHz
105
32 x 32 x
1024
Autom
atic
0.1o (Gun)
1o (Drift)
1.4.104
ASTRA
PC Win
1.8 Ghz
1.5 104
20 x 60
Autom
atic
0.1o …5o
420
5 104
20 x 30
Auto
matic
Adaptive
7.5 103
5 104
20 x 30
75 slices
TREDI Static
PC
1.8 Ghz
Integration
step
CPU
time
(sec)
25
-
1.8 Ghz
TREDI
LienardWiechert
Mesh
size
hr x hz
Adaptive
7.4 104
PARMELA – Different meshing
Beam size, energy spread, bunch length unchanged, but
Transverse emittance varies
CPU time
SPACE
Meshing
Integration
Steps
Number
particles
9846 sec
50 x 50 mm2
1100, 0.1o then
1o
25 k
1286 sec
100 x 100 mm2
1100, 0.1o then
1o
12.5 k
445 sec
200 x 200 mm2
1100, 0.1o then
1o
6.25 k
345 sec
100 x 100 mm2
505, 0.2o then
1o
12.5 k
CONCLUSION
Good agreement between codes despite different treatment of the physics
Physics note represented:
Thermal emitance
Shottky effect (ASTRA is the only code including this effect)
Good approximation at initial acceleration ?
Other comparisons
MAFIA (P.Balleyguier CEA, R.Rimmer TJL)
IMPACT (Ji Qiang)
Future extension:
add S-Band accelerating structure
L-Band Gun for TTF
• Simulation Issues for RF PhotoInjectors [ICAPS 2002]
E.Colby, V.Ivanov, Z.Li, C.Limborg
• Extraction from cathode
First 40 ps after extraction when static field 100MV/m on cathode:
–
Image charge on cathode
Parmela includes image charge while PIC code solves Maxwell
equations
–
Sheer of velocities
Parmela computes in frame of reference particle at a stage where spread
in velocities is large;
• Parameters
- Ez=100 MV/m (peak on cathode) @ at 100 MHz.
- Q= 1nC, uniformly distributed in space and time in a 1 mm radius x
10 ps long cylinder.
- The beam is launched with 1 eV energy
Velocity sheer (max(z)-min(z)) ____
Mean bunch velocity <z> ____
versus mean bunch position <z>
• Good agreement for 4 codes
• Parmela overestimates emittance
• Need to include Shottky effect
High Charge –
Case of A0 experiment
• DUVFEL measurements
(W.Graves, D.Dowell, E.Loos, C.Limborg, P.Emma , P.Piot)
Slice emittance measurement
- quad scan combined with zero-crossing
Simulations for reconstituting the
- Slice emittance, Projected emittance
-Twiss parameters
1.6 cell gun
with copper
cathode
Bend
Linac tanks
5 MeV
75 MeV
Dump
Solenoid = 98 A
Solenoid = 108 A
To get good agreement, used experimental
- thermal emittance
- longitudinal profile
- non-uniformity of transverse profile
Solenoid = 104 A