Self-Consistent 3D modelling of electron beams: the code RETAR

1. Self-Consistent 3D modelling of electron beams: the code RETAR A.Bacci,C.Maroli,V.Petrillo,L.Serafini This Code is developed to study the dynamics of high-brightness electron beams The aim is to study the dynamics in photoinjectorsand inmagnetic compressors, where the interaction of the beam with its self-field is of crucial relevance to optimize the performances of these devices

2. The Retar model The EM self-fields are calculated directly in terms of the values of the charge density at time t and at all earlier times, through the following equations: (Obtained manipulating the usual retarded forms of the Lienard-Wiechert Potentials) Static terms Radiation terms

3. Problem about memory and speed of calculation • The algorithm of Retar needs the positions of all particles in all the previous temporal instants The Matrixes of variables become very quickly heavy to be handled. • The complexity of the calculation is quadratic • tn= number of loops (temporal istants) • n = number of macro particles The complexity increases with the following law: Comp.= tn x n2 t1 t2 t3

4. negligible part A solution to simplify the calculation (1) The contribution of “far time events” is very small and part of the “radiation doesn’t reach” the present time event • It’s necessary to omit part of the information So we adopted a description based on a matrix traveling with the particles, carrying only the necessary information

5. A solution to simplify the calculation (2) Shared information Bunch Shifted historical matrix Initial historical matrix This choice makes the code much quicker and we observed that the effectof neglecting the tail of the historical is negligible on the beam dynamics description

6. Features of the code The code has the following characteristics: • Fully 3D • Bunch that grows from the cathode, with the consideration of image particles, that travel specular to the real particles. • The possibility to insert external fields: • RF cavity (S –T Waves) • Solenoid fields • The output that we have evaluated to be more significant : • Envelope (σx,σy) —Emittance (x,y,z) —L.Bunch σz—Current Ez,Bzseen by particles—Bunch energy • To simulate one meter, in a configuration like Sparc, with 5000 particles, Retar needs about 60 minutes, running on PC-Intel-one cpu PIV 3GHz

7. Preliminary results

8. Comments to previous images The preliminary results indicate • Longitudinal beam dynamics is reproducible • A problem in emittance correction process (slice overlap). About these problems we are following these ways: >To find hidden numerical noises that have to be eliminated > The number of particles is not yet large enough the algorithm has to be further speeded up >To see how the code works switching-off the retarded potentials

9. Conclusions • The basilar structure of the code is completed • We are investigating the weightof the retarded terms. • Above all we must understand the source of the differences in the emittance minimum • We will study the synchrotron radiation as soon as possible (before the summer!)