Two-dimensional semi-Lagrangian Vlasov simulations of laser–plasma interaction in the relativistic regime

M. L. BÉGUÉ; A. GHIZZO; P. BERTRAND; E. SONNENDRÜCKER; O. COULAUD

doi:10.1017/S0022377899008065

Abstract

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A semi-Lagrangian two-dimensional fully relativistic Vlasov code for multicomputer environments is developed to study trapped-particle dynamics in phase space induced by relativistic modulational and Raman instabilities. Attention is focused on the efficiency properties of the numerical scheme, which allows a very fine description of particle dynamics in phase space. Vlasov simulations show the appearance of coherent vortex structures as a result of the nonlinear saturation mechanism of the relativistic modulational instability. Growth rates are computed and found to be in good agreement with theoretical values obtained from the dispersion relation by Quesnel et al, [Phys. Plasmas4, 3358–3368 (1997)] and Guérin et al. [Phys. Plasmas2, 2807–2814 (1995)]. In the case of coupling between the relativistic modulational instability and two-plasmon decay, stochastic behaviour can be observed due to the competition between different plasmas waves.

Crossref Citations

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Huot, F. Ghizzo, A. Bertrand, P. Sonnendrucker, E. and Coulaud, O. 2000. Study of propagation of ultraintense electromagnetic wave through plasma using semi-Lagrangian Vlasov codes. IEEE Transactions on Plasma Science, Vol. 28, Issue. 4, p. 1170.

Ghizzo, A. Huot, F. and Bertrand, P. 2003. A non-periodic 2D semi-Lagrangian Vlasov code for laser–plasma interaction on parallel computer. Journal of Computational Physics, Vol. 186, Issue. 1, p. 47.

Huot, F. Ghizzo, A. Bertrand, P. Sonnendrücker, E. and Coulaud, O. 2003. Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov–Maxwell system. Journal of Computational Physics, Vol. 185, Issue. 2, p. 512.

Malá, Z. 2006. Numerical search of optimal parameters for realistic measurements of change of electric field of quasimode. Czechoslovak Journal of Physics, Vol. 56, Issue. S2, p. B528.

Stepic, Milutin Wirth, Christian Rüter, Christian E. and Kip, Detlef 2006. Observation of modulational instability in discrete media with self-defocusing nonlinearity. Optics Letters, Vol. 31, Issue. 2, p. 247.

Besse, Nicolas Latu, Guillaume Ghizzo, Alain Sonnendrücker, Eric and Bertrand, Pierre 2008. A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov–Maxwell system. Journal of Computational Physics, Vol. 227, Issue. 16, p. 7889.

Bechouche, Philippe and Besse, Nicolas 2010. Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44, Issue. 3, p. 573.

Qiu, Jing-Mei and Shu, Chi-Wang 2011. Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow. Journal of Computational Physics, Vol. 230, Issue. 4, p. 863.

Qiu, Jing-Mei and Shu, Chi-Wang 2011. Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system. Journal of Computational Physics, Vol. 230, Issue. 23, p. 8386.

Guo, Wei and Qiu, Jing-Mei 2013. Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation. Journal of Computational Physics, Vol. 234, Issue. , p. 108.

Zhang, Qinghai 2013. Highly accurate Lagrangian flux calculation via algebraic quadratures on spline-approximated donating regions. Computer Methods in Applied Mechanics and Engineering, Vol. 264, Issue. , p. 191.

Christlieb, Andrew Guo, Wei Morton, Maureen and Qiu, Jing-Mei 2014. A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations. Journal of Computational Physics, Vol. 267, Issue. , p. 7.

Dovgiy, A A 2014. Modulation instability in a zigzag array of nonlinear waveguides with alternating positive and negative refractive indices. Quantum Electronics, Vol. 44, Issue. 12, p. 1119.

Lehmann, Götz 2016. Efficient Semi-Lagrangian Vlasov-Maxwell Simulations of High Order Harmonic Generation from Relativistic Laser-Plasma Interactions. Communications in Computational Physics, Vol. 20, Issue. 3, p. 583.

Qiu, Jing-Mei and Russo, Giovanni 2017. A High Order Multi-Dimensional Characteristic Tracing Strategy for the Vlasov–Poisson System. Journal of Scientific Computing, Vol. 71, Issue. 1, p. 414.

Sarrat, Mathieu Ghizzo, Alain Del Sarto, Daniele and Serrat, Laurent 2017. Parallel implementation of a relativistic semi-Lagrangian Vlasov–Maxwell solver. The European Physical Journal D, Vol. 71, Issue. 11,

Razavinia, S. N. and Ghorbanalilu, M. 2019. Effect of external magnetic field on wakefield generation in underdense plasma slab using backward semi-Lagrangian Vlasov code. Physical Review Accelerators and Beams, Vol. 22, Issue. 11,

Li, Yingzhe Sun, Yajuan and Crouseilles, Nicolas 2020. Numerical simulations of one laser-plasma model based on Poisson structure. Journal of Computational Physics, Vol. 405, Issue. , p. 109172.

Razavinia, S N and Ghorbanalilu, M 2020. Semi-Lagrangian Vlasov simulation of the interaction between femtosecond chirped and double laser pulses with a thin plasma slab. Plasma Physics and Controlled Fusion, Vol. 62, Issue. 4, p. 045007.

Chen, Leitao Succi, Sauro Cai, Xiaofeng and Schaefer, Laura 2020. Semi-Lagrangian implicit Bhatnagar-Gross-Krook collision model for the finite-volume discrete Boltzmann method. Physical Review E, Vol. 101, Issue. 6,

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Two-dimensional semi-Lagrangian Vlasov simulations of laser–plasma interaction in the relativistic regime

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