TY - JOUR
T1 - Multi-Scale Paraxial Models to Approximate Vlasov-Maxwell Equations
AU - Assous, Franck
AU - Furman, Yevgeni
N1 - Publisher Copyright:
© 2022 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - Even 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; 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.
AB - Even 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; 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.
KW - Asymptotic Methods
KW - Paraxial Model
KW - Vlasov-Maxwell Equations
UR - http://www.scopus.com/inward/record.url?scp=85124557358&partnerID=8YFLogxK
U2 - 10.1515/cmam-2021-0082
DO - 10.1515/cmam-2021-0082
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AN - SCOPUS:85124557358
SN - 1609-4840
VL - 22
SP - 277
EP - 295
JO - Computational Methods in Applied Mathematics
JF - Computational Methods in Applied Mathematics
IS - 2
ER -