Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system

The Time Splitting Scheme (TSS) has been examined within the context of the one-dimensional (1D) relativistic Vlasov-Maxwell model. In the strongly relativistic regime of the laser-plasma interaction, the TSS cannot be applied to solve the Vlasov equation. We propose a new semi-Lagrangian scheme based on a full 2D advection and study its advantages over the classical Splitting procedure. Details of the underlying integration of the Vlasov equation appear to be important in achieving accurate plasma simulations. Examples are given which are related to the relativistic modulational instability and the self-induced transparency of an ultra-intense electromagnetic pulse in the relativistic regime.

[1]  P. Mora,et al.  Modulational and Raman instabilities in the relativistic regime , 1995 .

[2]  M. R. Feix,et al.  A nonperiodic Euler–Vlasov code for the numerical simulation of laser–plasma beat wave acceleration and Raman scattering , 1990 .

[3]  E. Sonnendrücker,et al.  The Semi-Lagrangian Method for the Numerical Resolution of the Vlasov Equation , 1999 .

[4]  Alain Ghizzo,et al.  Two-Dimensional Vlasov Simulation of Raman Scattering and Plasma Beatwave Acceleration on Parallel Computers , 1999 .

[5]  M. Shoucri,et al.  Numerical Solution of the Two-Dimensional Vlasov Equation , 1979, IEEE Transactions on Plasma Science.

[6]  Eric Sonnendrücker,et al.  Two-dimensional semi-Lagrangian Vlasov simulations of laser–plasma interaction in the relativistic regime , 1999, Journal of Plasma Physics.

[7]  Rainer Salomaa,et al.  Two‐stage electron acceleration by simultaneous stimulated Raman backward and forward scattering , 1995 .

[8]  M. Shoucri,et al.  Simulations of wave–particle interactions in stimulated Raman forward scattering in a magnetized plasma , 1992 .

[9]  Chio Cheng,et al.  The integration of the Vlasov equation for a magnetized plasma , 1977 .

[10]  Eric Sonnendrücker,et al.  The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations , 1998 .

[11]  Alain Ghizzo,et al.  A Vlasov code for the numerical simulation of stimulated Raman scattering , 1990 .

[12]  Magdi Shoucri,et al.  A Hilbert-Vlasov code for the study of high-frequency plasma beatwave accelerator , 1996 .

[13]  G. Marchuk.  Methods of Numerical Mathematics , 1982 .

[14]  A. Staniforth,et al.  Semi-Lagrangian integration schemes for atmospheric models - A review , 1991 .

[15]  Réal R. J. Gagné,et al.  A Splitting Scheme for the Numerical Solution of a One-Dimensional Vlasov Equation , 1977 .

[16]  Thomas M. Antonsen,et al.  Kinetic modeling of intense, short laser pulses propagating in tenuous plasmas , 1997 .

[17]  G. Knorr,et al.  The integration of the vlasov equation in configuration space , 1976 .

[18]  R. Bermejo.  Analysis of an algorithm for the Galerkin-characteristic method , 1991 .