On the equilibrium between proton distribution and compressible kinetic Alfvenic fluctuations

Protons with characteristic non-thermal velocity distribution functions are pervasively observed in the heliosphere. This paper investigates a class of proton velocity distribution functions that are in dynamical steady state with the low-frequency compressional fluctuations. The steady-state solution is obtained from the self-consistent quasi-linear kinetic equations for the protons and kinetic Alfvenic fluctuations. It is found that a class of velocity distribution functions for the protons exists under various models of the steady-state spectrum of kinetic Alfvenic fluctuation.