An improved method to derive the kappa distribution in polytropic plasmas

Abstract

The paper presents an improved method to study the sufficient conditions deriving the kappa distribution in a non-uniform isotropic plasma. We find that the polytropic equation of state can lead to the kappa distribution without any other assumption only in one dimension. In higher dimensions, an extra assumption that the global distribution must only be the function of energy is needed. In addition, the restrictions on the potential are investigated. It is found that the potential cannot be arbitrary in one-component plasma. However, in two-component plasma, any arbitrary potential could exist if we construct the suitable ion density.