Article Contents

2024, Volume 17, Issue 6: 855-891. Doi: 10.3934/krm.2024004

This issue Previous Article Global well-posedness and stability of the inhomogeneous kinetic wave equation near vacuum Next Article On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework

Asymptotic study of an anisotropic Fokker-Planck collision operator in a strong magnetic field

1.
Université de Toulouse & CNRS, UPS, Institut de Mathématiques de Toulouse, UMR 5219, F-31062 Toulouse, France
2.
Max Planck Institute for Plasma Physics, Boltzmannstrasse 2, 85748 Garching, Germany

^*Corresponding author: Etienne Lehman
^*Corresponding author: Etienne Lehman

Received: July 2023

Revised: December 2023

Early access: February 2024

Published: December 2024

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Abstract

The present paper is concerned with the derivation, via asymptotic studies, of a reduced hybrid model describing the anisotropic fusion plasma dynamics. The parallel dynamics is governed by a kinetic equation, whereas the perpendicular dynamics is described by a Maxwellian distribution function, whose temperature $ T_\perp $ satisfies an evolution equation, exchanging information with the parallel direction via some coupling terms. The reduced model is obtained from the underlying fully kinetic model, under the assumption of a strong magnetic field and strong collisionality in the perpendicular direction. From a numerical point of view, reduced models are very advantageous, permitting significant savings in computational times and memory. To improve the precision of the reduced description, we propose in this paper also first order correction terms with respect to the parameter describing the anisotropy, and discuss these terms from a physical point of view. This first order truncated model is new to our knowledge, meets the desired requirements of precision and efficiency, and its derivation is clearly exposed in this work, based on formal asymptotic studies.

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Mathematics Subject Classification: Primary: 35Q84, 35C20, 35B40; Secondary: 82C40.

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