1. 0 APS-Sherwood Texas 2006-April 21-24 Study of nonlinear kinetic effects in Stimulated Raman Scattering using semi- Lagrangian Vlasov codes Alain Ghizzo 1, P. Bertrand 1, T.W. Johnston 2, M. Albrecht-Marc 1,T. Reveillé 1 1. LPMIA, CNRS-UMR7040, Université Henri Poincaré, Nancy, BP 239, F-54506 Vandoeuvre, France 2. I.N.R.S. Energie et Matériaux, Varennes, Québec Alain.Ghizzo@lpmi.uhp-nancy.fr

2. 1 APS-Sherwood Texas 2006-April 21-24 Topics 1.Vlasov plasmas 2.Vlasov codes and PIC codes 3.Application I: Resonant wave particle interaction 4.Application II: SRS-B in optical mixing 5.Conclusions

3. 2 APS-Sherwood Texas 2006-April 21-24 Topics 1.Vlasov plasmas 2.Vlasov codes and PIC codes 3.Application I: Resonant wave particle interaction 4.Application II: SRS-B in optical mixing 5.Conclusions

4. 3 APS-Sherwood Texas 2006-April 21-24 Introduction. Vlasov models have long been used to study collisionless plasmas. Vlasov codes: powerful tool for studying in details the particle dynamics due to very fine resolution in phase space. Questions for applications: Need for a kinetic model? PIC or Vlasov simulation?

5. 4 APS-Sherwood Texas 2006-April 21-24 Vlasov plasmas: collective effects A dichotomy experiment: (e,m) -> 2(e/2, m/2) -> 4(e/4, m/4) -> etc… = dimensionless parameter, - divided by 2 at each dichotomy - « graininess parameter »

6. 5 APS-Sherwood Texas 2006-April 21-24 Topics 1.Vlasov plasmas 2.Vlasov codes and PIC codes 3.Application I: Resonant wave particle interaction 4.Application II: SRS-B in optical mixing 5.Conclusions

7. 6 APS-Sherwood Texas 2006-April 21-24 Comparison PIC-Vlasov (1) Vlasov Codes : real space dimension is the graininess due to particules PIC Codes : momentum space dimension : sampling of momentum space in each direction Sampling the x-space needs Real space X momentum space

8. 7 APS-Sherwood Texas 2006-April 21-24 Comparison PIC-Vlasov (2) Assume the same CPU time to push a particle (PIC) to move a phase space mesh point (Vlasov) The ratio of the computationnal effort between Vlasov and PIC depends on PIC graininess (must be as low as possible) Sampling of momentum space (must be as high as possible)

9. 8 APS-Sherwood Texas 2006-April 21-24 Comparison PIC-Vlasov (3) D v =1D v =2D v =3 g PIC =10 -2 110010 000 g PIC =10 -4 0.011100 g PIC =10 -6 0.00010.011 Prefer PIC Prefer Vlasov

10. 9 APS-Sherwood Texas 2006-April 21-24 Topics 1.Vlasov plasmas 2.Vlasov codes and PIC codes 3.Application I: Resonant wave particle interaction 4.Application II: SRS-B in optical mixing 5.Conclusions

11. 10 APS-Sherwood Texas 2006-April 21-24 Stimulated Raman Scattering Using Coulomb gauge with Vacuum PLASMA Scattered wave (1) Plasma wave (2) LASER Pump wave (0) Vlasov equation for electrons1D momentum space

12. 11 APS-Sherwood Texas 2006-April 21-24 SRS : 3 mode coupling Vacuum PLASMA Scattered wave (1) Plasma wave (2) LASER Pump wave (0) Quasi particles (photons, plasmons) Energy conservation Momentum conservation Electron plasma in a fixed ion homogeneous background

13. 12 APS-Sherwood Texas 2006-April 21-24 Three mode coupling : a fluid description Scalar potential (Plasma mode) Multiple time-space scale expansion of fluid equations Vector potential (electromagnetic modes)

14. 13 APS-Sherwood Texas 2006-April 21-24 Three mode coupling : a fluid description Hydrodynamic equations for electrons Assume slowly varying envelopes: i.e. with

15. 14 APS-Sherwood Texas 2006-April 21-24 Three mode coupling : a fluid description Envelope equations + periodic conditions  Action conservation Energy density of mode i Action density of mode i photon (0)  photon (1)  plasmon (2)

16. 15 APS-Sherwood Texas 2006-April 21-24 Time evolution: pump + scattered Pump wave action Scattered wave action Good conservation Check the fluid predictions against a fully kinetic Vlasov simulation

17. 16 APS-Sherwood Texas 2006-April 21-24 Time evolution : pump + plasma pump plasma Poor Conservation !

18. 17 APS-Sherwood Texas 2006-April 21-24 Phase space portraits (1) Color scale

19. 18 APS-Sherwood Texas 2006-April 21-24 Phase space portraits (2) Color scale

20. 19 APS-Sherwood Texas 2006-April 21-24 Phase space portraits (3) Color scale

21. 20 APS-Sherwood Texas 2006-April 21-24 Accounting for « non fluid » particles Good conservation Compute: Kinetic energy density above the lower separatrix: Divide by plasma wave frequency:

22. 21 APS-Sherwood Texas 2006-April 21-24 Topics 1.Vlasov plasmas 2.Vlasov codes and PIC codes 3.Application I: Resonant wave particle interaction 4.Application II: SRS-B in optical mixing 5.Conclusions

23. 22 APS-Sherwood Texas 2006-April 21-24 SRS-B in the « kinetic » regime (1) SRS-B reflectivity presents a bursting behavior Nonlinear frequency shift - G.J. Morales and T.M. O’Neil, PRL 28, 417 (1972) -

24. 23 APS-Sherwood Texas 2006-April 21-24 SRS-B in the « kinetic » regime (2) Langmuir wave induced by SRS-B process Vortex-merging leading to weak turbulence BGK-like self- sustained structures (persisting over a long time)

25. 24 APS-Sherwood Texas 2006-April 21-24 Topics 1.Vlasov plasmas 2.Vlasov codes and PIC codes 3.Application I: Resonant wave particle interaction 4.Application II: SRS-B in optical mixing 5.Conclusions

26. 25 APS-Sherwood Texas 2006-April 21-24 Conclusions Vlasov codes as compared to PIC codes lack of numerical noise good resolution in phase space provided the dimension of velocity space is as low as possible. Kinetic effects in plasmas allow more phenomena than are found using only fluid theory with « ad hoc » kinetic damping.