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 , Massimo.Ferrario@lnf.infn.it

srsso

sscz AH

R

QE ,2

,2

srsso

sscr AG

LR

QE ,,

4

tss zz Position from tail

LRA sssr /, Slice aspect ratio in rest frame with Rs slice radius

Longitudinal equation

tzEtzEtzEm

ez image

zscz

accz

sos ,,,

3

..

Transverse equation : “envelope equation”

solenoid focusing space charge force thermal emittance pressure

3

22..2

.. 14*,,

2

srimagersc

ss

ps

rfs

solsssss

RcAsGAsG

R

kcRKKRR

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 : ylloyd@qwest.net , or jbillen@lanl.gov

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, 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.

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

LzrUzrUzr

UzaU

,,,0,0,0),(

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