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arXiv · 2508.12231

Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field

Anh-Tuan Vu
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Abstract

The subject matter of this paper concerns the magnetic confinement of plasma. We investigate the long time behavior of the Vlasov-Maxwell-Fokker-Planck system under the effect of a strong external magnetic field. We first formally derive an asymptotically reduced model. In three space dimensions, a constraint occurs along the parallel direction to the magnetic field. To eliminate the corresponding Lagrange multiplier, we then study the Vlasov-Maxwell-Fokker-Planck system in two spatial dimensions and three velocity dimensions. In this setting, we show that the obtained asymptotic model defines a well-posed dynamical system, and we provide a rigorous mathematical justification of the formally derived system. Our proofs rely on the modulated energy method.

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Anh-Tuan Vu. 2025-08-17. Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field. https://arxiv.org/abs/2508.12231

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