American Institute of Mathematical Sciences

Advanced
June  2009, 2(2): 251-274. doi: 10.3934/krm.2009.2.251

Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel

Alexandre Mouton 1,

1. 

Institut de Recherche Mathématique Avancée (IRMA) - Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France

Received  July 2008 Revised  January 2009 Published  May 2009

This paper is devoted to numerical simulation of a charged particle beam submitted to a strong oscillating electric field. For that, we consider a two-scale numerical approach as follows: we first recall the two-scale model which is obtained by using two-scale convergence techniques; then, we numerically solve this limit model by using a backward semi-Lagrangian method and we propose a new mesh of the phase space which allows us to simplify the solution of Poisson's equation. Finally, we present some numerical results which have been obtained by the new method, and we verify its efficiency through long time simulations.
Keywords: semi-Lagrangian method, Vlasov-Poisson model., Two-scale convergence.
Mathematics Subject Classification: Primary: 35B27, 76X05, 65M25; Secondary: 65Y2.
Citation: Alexandre Mouton. Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel. Kinetic & Related Models, 2009, 2 (2) : 251-274. doi: 10.3934/krm.2009.2.251
[1]

Aurore Back, Emmanuel Frénod. Geometric two-scale convergence on manifold and applications to the Vlasov equation. Discrete & Continuous Dynamical Systems - S, 2015, 8 (1) : 223-241. doi: 10.3934/dcdss.2015.8.223
[2]

Gianluca Crippa, Silvia Ligabue, Chiara Saffirio. Lagrangian solutions to the Vlasov-Poisson system with a point charge. Kinetic & Related Models, 2018, 11 (6) : 1277-1299. doi: 10.3934/krm.2018050
[3]

Daniel Guo, John Drake. A global semi-Lagrangian spectral model for the reformulated shallow water equations. Conference Publications, 2003, 2003 (Special) : 375-385. doi: 10.3934/proc.2003.2003.375
[4]

Zili Chen, Xiuting Li, Xianwen Zhang. The two dimensional Vlasov-Poisson system with steady spatial asymptotics. Kinetic & Related Models, 2017, 10 (4) : 977-1009. doi: 10.3934/krm.2017039
[5]

Daniel Guo, John Drake. A global semi-Lagrangian spectral model of shallow water equations with time-dependent variable resolution. Conference Publications, 2005, 2005 (Special) : 355-364. doi: 10.3934/proc.2005.2005.355
[6]

Robert E. Miller. Homogenization of time-dependent systems with Kelvin-Voigt damping by two-scale convergence. Discrete & Continuous Dynamical Systems, 1995, 1 (4) : 485-502. doi: 10.3934/dcds.1995.1.485
[7]

Katherine Zhiyuan Zhang. Focusing solutions of the Vlasov-Poisson system. Kinetic & Related Models, 2019, 12 (6) : 1313-1327. doi: 10.3934/krm.2019051
[8]

Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a two-scale linear transport equation. Networks & Heterogeneous Media, 2006, 1 (1) : 143-166. doi: 10.3934/nhm.2006.1.143
[9]

Shi Jin, Xu Yang, Guangwei Yuan. A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface. Kinetic & Related Models, 2008, 1 (1) : 65-84. doi: 10.3934/krm.2008.1.65
[10]

Holger Heumann, Ralf Hiptmair. Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1471-1495. doi: 10.3934/dcds.2011.29.1471
[11]

Blanca Ayuso, José A. Carrillo, Chi-Wang Shu. Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system. Kinetic & Related Models, 2011, 4 (4) : 955-989. doi: 10.3934/krm.2011.4.955
[12]

Silvia Caprino, Guido Cavallaro, Carlo Marchioro. Time evolution of a Vlasov-Poisson plasma with magnetic confinement. Kinetic & Related Models, 2012, 5 (4) : 729-742. doi: 10.3934/krm.2012.5.729
[13]

Jack Schaeffer. Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior. Kinetic & Related Models, 2012, 5 (1) : 129-153. doi: 10.3934/krm.2012.5.129
[14]

Gang Li, Xianwen Zhang. A Vlasov-Poisson plasma of infinite mass with a point charge. Kinetic & Related Models, 2018, 11 (2) : 303-336. doi: 10.3934/krm.2018015
[15]

Meixia Xiao, Xianwen Zhang. On global solutions to the Vlasov-Poisson system with radiation damping. Kinetic & Related Models, 2018, 11 (5) : 1183-1209. doi: 10.3934/krm.2018046
[16]

Jean Dolbeault. An introduction to kinetic equations: the Vlasov-Poisson system and the Boltzmann equation. Discrete & Continuous Dynamical Systems, 2002, 8 (2) : 361-380. doi: 10.3934/dcds.2002.8.361
[17]

Yulia O. Belyaeva, Björn Gebhard, Alexander L. Skubachevskii. A general way to confined stationary Vlasov-Poisson plasma configurations. Kinetic & Related Models, 2021, 14 (2) : 257-282. doi: 10.3934/krm.2021004
[18]

Jack Schaeffer. On time decay for the spherically symmetric Vlasov-Poisson system. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021021
[19]

Fang Liu, Aihui Zhou. Localizations and parallelizations for two-scale finite element discretizations. Communications on Pure & Applied Analysis, 2007, 6 (3) : 757-773. doi: 10.3934/cpaa.2007.6.757
[20]

Alexandre Mouton. Expansion of a singularly perturbed equation with a two-scale converging convection term. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1447-1473. doi: 10.3934/dcdss.2016058

2020 Impact Factor: 1.432

Tools

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy