1. Collisional Model in LSP. Simulation of Collisional Slowing Down of Relativistic Electrons in Plasma. A. Solodov, J. Myatt University of Rochester Laboratory for Laser Energetics 3d Meeting of the Fusion Science Center for Extreme States of Matter and Fast Ignition Physics University of Rochester 26–27 January 2006

2. Summary The LSP collisional model has been modified to include relativistic effects and tested to reproduce correctly the collisional slowing down of electrons in plasma predicted by the theory The non-relativistic LSP collisional model has been found correct (except for the value of Coulomb logarithm which we modified) and consistent with other theoretical models suggested for multi-fluid and hybrid PIC simulations Relativistic electron scatter and drag rates have been calculated and implemented in the LSP code The slowing-down of relativistic electron beams have been simulated and compared with the theory With the improved collision model, the LSP code is capable of reproducing the blooming, straggling and penetration predicted by the theory

3. LSP 1 can model larger, more dense plasmas for longer simulation times than explicit PIC codes 1 D. R. Welch, D. V. Rose, B. V. Oliver, R. E. Clark, Nucl. Instrum. Methods Phys. Res. A 464, 134 (2001). LSP uses: an implicit solution of the electromagnetic fields; an implicit particle push; hybrid fluid-kinetic descriptions for electrons; inter- and intra-species collisions based on Spitzer collision rate: - kinetic particle scattering off its own distribution and a pressure gradient force for fluid species to model intra-species collisions, - a frictional momentum push, dissipative heating and temperature equilibration in collisions between species (both kinetic and fluid).

4. The inter-species collisions are based on the model of Rambo & Procassini 2 suggested, originally, for multi-fluid simulations 2 P. W. Rambo and R. J. Procassini, Phys. Plasmas 2, 3130 (1995). 3 Unpublished, referred by others as private communication with A. Decoster.

5. Kinetic particle velocities are rotated in the weighted scattering reference frame and the random velocity components are advanced according to the temperature change

6. We modify the scattering rates in the equations of Rambo & Procassini to account for the relativistic effects

7. The new scattering rates are obtained using the relativistic Rutherford electron scattering cross-section 4 4 E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics, Pergamon Pres, Oxford (1981).

8. With the improved collisional model, the LSP code reproduces the blooming, straggling and penetration of monoenergetic relativistic electron beams predicted by the theory 5 5 C. K. Li and R. D. Petrasso, Phys. Rev. E 73, 016402 (2006) Simulation Theory 5

9. With the improved collisional model, the LSP code reproduces the blooming, straggling and penetration of monoenergetic relativistic electron beams predicted by the theory 5 5 C. K. Li and R. D. Petrasso, Phys. Rev. E 73, 016402 (2006) Simulation Theory 5

10. Conclusion The LSP collisional model has been modified to include relativistic effects and tested to reproduce correctly the collisional slowing down of electrons predicted by the theory The non-relativistic LSP collisional model has been found correct (except for the value of Coulomb logarithm which we modified) and consistent with other theoretical models suggested for multi-fluid and hybrid PIC simulations Relativistic electron scatter and drag rates have been calculated and implemented in the LSP code The slowing-down of relativistic electron beams have been simulated and compared with the theory With the improved collision model, the LSP code is capable of reproducing the blooming, straggling and penetration predicted by the theory