An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

O. Allanson; T. Neukirch; F. Wilson; S. Troscheit

doi:10.1063/1.4934611

An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

O. Allanson, T. Neukirch, F. Wilson, S. Troscheit

Electronic, Electrical and Systems Engineering

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Abstract

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
I. INTRODUCTION

Original language	English
Article number	102116
Journal	Physics of Plasmas
Volume	22
Issue number	10
DOIs	https://doi.org/10.1063/1.4934611
Publication status	Published - 1 Oct 2015

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N2 - We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.I. INTRODUCTION

AB - We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.I. INTRODUCTION

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An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

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