Turbulent Equilibria for Charged Particles in Space

Abstract

It is well known that the solar wind electron distribution function is apparently composed of several components, but the energetic tail population is well fitted with kappa distribution function. It is also well established that the solar wind protons possess quasi power-law tail distribution function that is well fitted with an inverse power law model. In the recent past, the present author developed a theory that describes a system of electrons and Langmuir turbulence that are in dynamical steady-state. In such a model, the kappa distribution function for the electrons emerges as a unique solution of the steady-state weak turbulence plasma kinetic equation. For the proton inverse power-law tail problem, Fisk and Gloeckler’s theory of compressional turbulence received much attention in the literature. In the present paper, their model is revisited in the light of plasma kinetic theory that involves low-frequency kinetic Alfvén wave fluctuations. It is shown that the proton kappa distribution function satisfies the steady-state proton particle kinetic equation. The steady-state wave kinetic equation for the kinetic Alfvén wave is also solved. This shows that the proton suprathermal distribution with an inverse power law velocity dependence may indeed result from a steady-state wave-particle interaction of the compressional kinetic Alfvénic fluctuations in the solar wind, thus providing support for, and also providing an alternative view of Fisk and Gloeckler’s model. However, in the absence of additional constraint that may arise from the balance of nonlinear wave-particle interaction terms within the wave kinetic equations for kinetic Alfvénic waves, the index of inverse power-law velocity tail distribution is undetermined. This calls for further investigation of nonlinear kinetic Alfvénic turbulence.