## Abstract

Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus imposes to use a much smaller time step, we perform in this paper a homogenization of the Vlasov equation and the Vlasov-Poisson system which yield approximate equations describing the mean behavior of the particles. The convergence proof is based on the two-scale convergence tools introduced by N'Guetseng and Allaire. We also consider the case where, in addition to the magnetic field, a large external electric field orthogonal to the magnetic field and of the same magnitude is applied.

Original language | English |
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Pages (from-to) | 193-213 |

Number of pages | 21 |

Journal | Asymptotic Analysis |

Volume | 18 |

Issue number | 3-4 |

State | Published - Dec 1998 |

Externally published | Yes |

## Keywords

- Gyrokinetic approximation
- Homogenization
- Kinetic equations
- Multiple time scales
- Two-scale convergence
- Vlasov-Poisson equations