1nc 10ps square pulse, 1 mm uniform transverse laser pulse no thermal emittance 110mv/m solenoid...
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1nC10ps square pulse, 1 mm uniform transverse laser pulse No Thermal emittance110MV/mSolenoid 2.541 kG
1nC10ps square pulse, 1 mm uniform transverse laser pulse No Thermal emittance110MV/mSolenoid 2.541 kG
TEST PROBLEM
Code Comparison for Simulations of Photo-Injectors
C.Limborg, Y.K.Batygin, SLAC, Stanford, CA 94309, USAM.Boscolo, M.Ferrario, V.Fusco, LNF-INFN, 00044 Frascati, Italy
L.Giannessi, M.Quattromini, ENEA Research Center, 00044 Frascati, ItalyJ.-P. Carneiro, K. Floettmann, DESY, 22603 Hamburg, Germany
DESCRIPTION OF CODESHOMDYN
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 CODESHOMDYN
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 , [email protected]
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tss zz Position from tail
LRA sssr /, Slice aspect ratio in rest frame with Rs slice radius
Longitudinal equation
tzEtzEtzEm
ez image
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Transverse equation : “envelope equation”
solenoid focusing space charge force thermal emittance pressure
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Damping rf focusing image charge
DESCRIPTION OF CODESPARMELA / 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 : [email protected] , or [email protected]
ASTRA :
Also point-to-point option available but useless
In the rest frame of bunch,
d
rR
sample particle
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, [email protected]
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.
oU
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
Differentiation of potential grid function to determine components of electrostatic field in moving system
Back to lab frame
with boundary conditions
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Cloud-in-cell
Lienard WiechertTREDI
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 pointsNr x Nz
Mesh sizehr x hz
Integration step
CPU time (sec)
HOMDYN PC Win 75 slices - 25
BEAMPATH PC Win 1 GHz 104 256 x 2048
50x50m2
0.1o (Gun) 1o (Drift)
8000
PARMELA PC Win 1 GHz 2.5 104 25 x 75 50x50m2
0.1o (Gun) 1o (Drift)
9846
PARMELA/SPCH 3D
PC Win 1 GHz 105 32 x 32 x 1024
Automatic
0.1o (Gun) 1o (Drift)
1.4.104
ASTRA PC Win 1.8 Ghz 1.5 104 20 x 60 Automatic
0.1o …5o 420
TREDI Static 1.8 Ghz
5 104 20 x 30 Automatic
Adaptive 7.5 103
TREDI Lienard- Wiechert
PC 1.8 Ghz
5 104 20 x 30 Adaptive7.4 104
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 m2 1100, 0.1o then 1o
25 k
1286 sec 100 x 100 m2 1100, 0.1o then 1o
12.5 k
445 sec 200 x 200 m2 1100, 0.1o then 1o
6.25 k
345 sec 100 x 100 m2 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
• 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
• 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
• Simulation Issues for RF PhotoInjectors [ICAPS 2002]E.Colby, V.Ivanov, Z.Li, C.Limborg
• Simulation Issues for RF PhotoInjectors [ICAPS 2002]E.Colby, V.Ivanov, Z.Li, C.Limborg
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
• 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
75 MeV
Bend
Dump
5 MeV
Linac tanks
Solenoid = 98 A
Solenoid = 104 A
Solenoid = 108 A
To get good agreement, used experimental
- thermal emittance
- longitudinal profile
- non-uniformity of transverse profile