A family of one-dimensional Vlasov-Maxwell equilibria for the force-free Harris sheet

Abstract

A family of self-consistent collisionless distribution functions for the force-free Harris sheet is presented. This family includes the distribution function recently found by Harrison and Neukirch Phys. Rev. Lett. 102, 135003 (2009) as well as distribution functions with a different dependence on the particle energy, but with the same dependence on the canonical momenta. It is shown generally that the other distribution functions in the family give rise to the same pressure function and, thus, to the same current density and magnetic field as the known distribution function, provided certain conditions on the parameters are satisfied. A number of examples of distribution functions from the new family are given, which illustrate the use of the general method. © 2011 American Institute of Physics.