Numerical approximation of 3D particle beams by multi-scale paraxial Vlasov-Maxwell equations

F. Assous; Y. Furman

doi:10.1016/j.jcp.2023.112186

Numerical approximation of 3D particle beams by multi-scale paraxial Vlasov-Maxwell equations

F. Assous, Y. Furman

Ariel University

Research output: Contribution to journal › Article › peer-review

Abstract

Even now, solving numerically the 3D time-dependent Vlasov-Maxwell equations is a challenging problem. Hence, it is always interesting to develop simpler but accurate approximate models. By introducing a small parameter, we derived paraxial asymptotic models that approximate these equations, allowing us to treat relativistic cases, much slower beams or even non-relativistic cases. These models are static or quasi-static and with a n^th order accuracy that may be chosen as required. Here, we propose a 3D numerical approximation of this multi-scale model. It is based, for the paraxial Maxwell model, on a finite element method coupled with a Particle-In-Cell approximation of the paraxial Vlasov model. Numerical results illustrated the efficiency of the method.

Original language	English
Article number	112186
Journal	Journal of Computational Physics
Volume	488
DOIs	https://doi.org/10.1016/j.jcp.2023.112186
State	Published - 1 Sep 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Funding

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Franck Assous reports financial support was provided by Ariel University. Franck Assous reports a relationship with Ariel University that includes: employment.

Funders	Funder number
Ariel University

Keywords

Asymptotic methods
Paraxial approximation
Particle-in-cell numerical schemes
Vlasov-Maxwell equations

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10.1016/j.jcp.2023.112186

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abstract = "Even now, solving numerically the 3D time-dependent Vlasov-Maxwell equations is a challenging problem. Hence, it is always interesting to develop simpler but accurate approximate models. By introducing a small parameter, we derived paraxial asymptotic models that approximate these equations, allowing us to treat relativistic cases, much slower beams or even non-relativistic cases. These models are static or quasi-static and with a nth order accuracy that may be chosen as required. Here, we propose a 3D numerical approximation of this multi-scale model. It is based, for the paraxial Maxwell model, on a finite element method coupled with a Particle-In-Cell approximation of the paraxial Vlasov model. Numerical results illustrated the efficiency of the method.",

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Numerical approximation of 3D particle beams by multi-scale paraxial Vlasov-Maxwell equations

Abstract

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Keywords

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