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Pré-Publication, Document De Travail Année : 2024

Fokker-Planck equation for energetic particles. The κ-distribution function

Résumé

The first concern of the present paper is the mathematical study of a specific Fokker-Planck equation describing the dynamics of energetic particles (runaway electrons for example) occurring in thermonuclear fusion plasmas or astrophysics. In the long-time limit, the velocity distribution function of these particles tends towards a (thermal) non-equilibrium distribution, namely a $\kappa$-distribution function which is a steady-state of the considered Fokker-Planck equation. Our aim is firstly to investigate the convergence rate of the velocity distributions towards these stationary states as $t \rightarrow \infty$, as well as in a second step to design an efficient spectral scheme, permitting to cope with this long-time asymptotics, without too much numerical costs. Non-equilibrium (or non-Maxwellian) distributions need to be considered properly enough in fusion or astrophysical plasmas in order to accurately reproduce the plasma dynamics and to understand the impact of the runaway electrons on the whole thermal plasma bulk as well as for issues like astronaut safety in astrophysics.
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Dates et versions

hal-04551722 , version 1 (18-04-2024)

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  • HAL Id : hal-04551722 , version 1

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Etienne Lehman, Claudia Negulescu. Fokker-Planck equation for energetic particles. The κ-distribution function. 2024. ⟨hal-04551722⟩
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