0 APS-Sherwood Texas 2006-April 21-24 Study of nonlinear kinetic effects in Stimulated Raman Scattering using semi- Lagrangian Vlasov codes Alain Ghizzo.

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Presentation transcript:

0 APS-Sherwood Texas 2006-April 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 Vandoeuvre, France 2. I.N.R.S. Energie et Matériaux, Varennes, Québec

1 APS-Sherwood Texas 2006-April 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

2 APS-Sherwood Texas 2006-April 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 APS-Sherwood Texas 2006-April 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?

4 APS-Sherwood Texas 2006-April 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 »

5 APS-Sherwood Texas 2006-April 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

6 APS-Sherwood Texas 2006-April 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

7 APS-Sherwood Texas 2006-April 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)

8 APS-Sherwood Texas 2006-April Comparison PIC-Vlasov (3) D v =1D v =2D v =3 g PIC = g PIC = g PIC = Prefer PIC Prefer Vlasov

9 APS-Sherwood Texas 2006-April 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

10 APS-Sherwood Texas 2006-April 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

11 APS-Sherwood Texas 2006-April 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

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

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

14 APS-Sherwood Texas 2006-April 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)

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

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

17 APS-Sherwood Texas 2006-April Phase space portraits (1) Color scale

18 APS-Sherwood Texas 2006-April Phase space portraits (2) Color scale

19 APS-Sherwood Texas 2006-April Phase space portraits (3) Color scale

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

21 APS-Sherwood Texas 2006-April 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

22 APS-Sherwood Texas 2006-April 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) -

23 APS-Sherwood Texas 2006-April 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)

24 APS-Sherwood Texas 2006-April 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

25 APS-Sherwood Texas 2006-April 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.