Non-equilibrium Statistical Mechanics of Electron Kappa Distribution

Abstract

Among the theories and interpretations for the supra- or non-thermal electrons pervasively observed in space are those based upon collisional and/or collective effects, super-statistical principle, or non-standard entropic principle. In this chapter, the origin of non-thermal electrons is discussed within the framework of non-equilibrium statistical mechanics. In this theory, the non-Maxwellian electron velocity distribution function, known as the kappa distribution, is an end product of nonlinear wave-particle interaction processes. In the asymptotic state, the kappa-distributed electrons and high-frequency electrostatic fluctuations maintain a dynamical steady state, which may be called the turbulent quasi-equilibrium state. The non-equilibrium statistical mechanics, or kinetic theory, thus provides a physics-based explanation for the existence of kappa distribution. Theoretical prediction is tested against in-situ spacecraft measurements. This chapter also discusses some further extensions beyond the standard kappa model, which show that the non-equilibrium statistical mechanics allows for a broader class of solutions that depict the non-thermal electron velocity distribution function.