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.
Highlights
Equilibria are a suitable starting point for investigations of plasma instabilities and waves
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
This paper contains a first analysis of a distribution function (DF) capable of describing low plasma beta, nonlinear force-free collisionless equilibria
Summary
Equilibria are a suitable starting point for investigations of plasma instabilities and waves. Force-free equilibria, with fields defined by r Á B 1⁄4 0;. Equation (1) implies that the current density is everywhereparallel to the magnetic field l0j 1⁄4 aðrÞB;. Extensive discussions of force-free fields are given in Refs. For a macroscopic equilibrium to be described, the DF must solve Maxwell’s equations and describe force balance, via the coupling to the charge and current densities, as well as to the pressure. Three families of exact nonlinear force-free Vlasov-Maxwell (VM) equilibria are known, all of which describe 1D current sheets. The first family uses the force-free Harris sheet (FFHS) as their magnetic field profile.. With L being the width of the current sheet, and B0 being the constant magnitude of the magnetic field. Examples of linear force-free VM equilibria are discussed in Ref. 18.
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