Chapter 7 - Linear Kinetic Waves in Plasmas Described by Kappa Distributions

Abstract

In this chapter we present an overview of the excitation, propagation, and absorption of linear plasma waves in collisionless, spatially uniform, multicomponent, magnetized non-Maxwellian plasma characterized by a kappa velocity distribution based on a Vlasov kinetic description. Although traditional plasma physics texts are replete with examples of linear waves and instabilities in plasmas whose charged particles are modeled by the thermal Maxwellian velocity distribution, very few works exist that bring together in one place the analogous results for plasmas modeled by a kappa distribution—a more appropriate and versatile model for space and other collisionless plasmas. The treatment, which uses Vlasov kinetic theory coupled with Maxwell's equations, covers the range from low-frequency waves, where ion dynamics dominates the dispersion properties of the waves, up to frequencies in excess of the plasma frequency, where the electron physics plays the dominant role. For reasons of tractability, the primary focus is on waves and instabilities that propagate parallel to the ambient magnetic field, but both electrostatic as well as electromagnetic plasma waves are considered. The chapter begins with the fundamental concepts of nonequilibrium statistical mechanics and electrodynamics. The established kinetic theory of waves in a multispecies plasma with arbitrary velocity distribution is used to introduce the general dielectric tensor, which characterizes the plasma response to fluctuating electromagnetic fields. The general dielectric tensor is then derived using a drifting bi-kappa distribution for the special case of parallel propagation. Using this dielectric tensor in the Fourier-transformed wave equation, various fundamental parallel propagating longitudinal (electrostatic) and transverse (electromagnetic) plasma wave modes are discussed within the context of the bi-kappa velocity distribution. Both analytical and numerical results for the excitation (growth) and absorption (damping) of plasma waves in plasmas with a kappa velocity distribution will be discussed.