### Abstract

Language | English |
---|---|

Pages | 387-465 |

Number of pages | 79 |

Journal | Transport Theory and Statistical Physics |

Volume | 39 |

Issue number | 5-7 |

DOIs | |

Publication status | Published - 2010 |

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### Keywords

- simulations
- Vlasov-Maxwell system
- fourier method
- numerical simulations
- higher dimensions
- theory and applications
- wigner equations

### Cite this

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**Numerical simulations of the fourier-transformed Vlasov-Maxwell system in higher dimensions : theory and applications.** / Eliasson, Bengt.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical simulations of the fourier-transformed Vlasov-Maxwell system in higher dimensions

T2 - Transport Theory and Statistical Physics

AU - Eliasson, Bengt

PY - 2010

Y1 - 2010

N2 - We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier-transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier-transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier-transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.

AB - We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier-transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier-transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier-transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.

KW - simulations

KW - Vlasov-Maxwell system

KW - fourier method

KW - numerical simulations

KW - higher dimensions

KW - theory and applications

KW - wigner equations

UR - http://www.tandfonline.com/loi/ltty20

U2 - 10.1080/00411450.2011.563711

DO - 10.1080/00411450.2011.563711

M3 - Article

VL - 39

SP - 387

EP - 465

JO - Transport Theory and Statistical Physics

JF - Transport Theory and Statistical Physics

SN - 0041-1450

IS - 5-7

ER -