Vlasov-Maxwell equilibrium solutions for Harris sheet magnetic field with Kappa velocity distribution

An exact solution of the steady-state, one-dimensional Vlasov-Maxwell equations for a plasma current sheet with oppositely directed magnetic field was found by Harris in 1962. The so-called Harris magnetic field model assumes Maxwellian velocity distributions for oppositely drifting ions and electrons and has been widely used for plasma stability studies. This paper extends Harris solutions by using more general κ distribution functions that incorporate Maxwellian distribution in the limit of κ→∞. A new functional form for the plasma pressure as a function of the magnetic vector potential p (A) is found and the magnetic field is a modified tanh z function. In the extended solutions the effective temperature is no longer spatially uniform like in the Harris model and the thickness of the current layer decreases with decreasing κ.