Dec 12 – 16, 2022
Europe/Paris timezone

Vlasov-Poisson-Fokker-Planck equation in the adiabatic asymptotics

Dec 12, 2022, 3:30 PM
Amphithéâtre Schwartz (IMT)

Amphithéâtre Schwartz


Université Paul Sabatier, 118 Route de Narbonne, 31000 Toulouse France


Etienne LEHMAN


The main concern of this article is the study of a nonlinear Vlasov-Poisson-Fokker-
Planck equation describing the electron dynamics in a thermonuclear fusion plasma, in the regime of a small electron-to-ion mass ratio (ε ≪ 1). The first part of this work focuses on the rigorous ε → 0 asymptotic study, based on hypocoercive techniques, permitting to understand the transition from the kinetic level to the macroscopic, adiabatic electron level. The second part introduces a Hilbert-Fourier spectral method enabling to treat without too much numerical effort the above mentioned electron transition. This scheme has in particular the nice property of being Asymptotic
Preserving in the sense that ε-independent meshes can be chosen, without degrading the accuracy. Some numerical tests are finally performed validating on one hand the scheme and underscoring on the other hand the mathematical results.

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