Force-free collisionless current sheet models with non-uniform temperature and density profiles

We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner (Phys. Plasmas 20, 102117, 2013) to allow for non-uniform density and temperature profiles. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al. (Phys. Plasmas 22, 112902, 2015). In one limit of the parameters, we recover the model of Kolotkov et al., while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk-flow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.