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Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations

Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations AbstractEven today, solving numerically the time-dependent Vlasov–Maxwell equations is a challenging issue, and developing simpler but accurate approximate models is still worthwhile.Here, we propose a new family of paraxial asymptotic models that approximates the Vlasov–Maxwell system of equations.We introduce parameters in our models that allow us to handle relativistic cases, much slower beams or even non-relativistic cases.These models are derived by introducing a small parameter and provide static or quasi-static approximate equations that are 𝑛-th order accurate; 𝑛 may be chosen as required.Practically, one can select a model by determining the regime one is interested in and choosing the degree of accuracy needed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods in Applied Mathematics de Gruyter

Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations

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References (17)

Publisher
de Gruyter
Copyright
© 2022 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1609-9389
eISSN
1609-9389
DOI
10.1515/cmam-2021-0082
Publisher site
See Article on Publisher Site

Abstract

AbstractEven today, solving numerically the time-dependent Vlasov–Maxwell equations is a challenging issue, and developing simpler but accurate approximate models is still worthwhile.Here, we propose a new family of paraxial asymptotic models that approximates the Vlasov–Maxwell system of equations.We introduce parameters in our models that allow us to handle relativistic cases, much slower beams or even non-relativistic cases.These models are derived by introducing a small parameter and provide static or quasi-static approximate equations that are 𝑛-th order accurate; 𝑛 may be chosen as required.Practically, one can select a model by determining the regime one is interested in and choosing the degree of accuracy needed.

Journal

Computational Methods in Applied Mathematicsde Gruyter

Published: Apr 1, 2022

Keywords: Vlasov–Maxwell Equations; Paraxial Model; Asymptotic Methods; 41A60; 78A25; 78A30; 78A35; 34E05; 35A15

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