The dispersion relations of dispersive Alfvén waves in superthermal plasmas

Abstract

The effects of velocity distribution functions (VDFs) that exhibit a power law dependence on the high-energy tail have been the subject of intense research by the space plasma community. Such functions, known as superthermal or kappa distributions, have been found to provide a better fitting to the VDF measured by several spacecraft in the plasma environment of the solar wind. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well established. However, for kappa distributions, either isotropic or anisotropic, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation. Contributions for the general case of obliquely propagating waves have been scarcely reported so far. In this work we introduce a mathematical formalism that provides expressions for the dielectric tensor components and subsequent dispersion relations for oblique propagating dispersive Alfvén waves (DAWs) resulting from a kappa VDF. We employ an isotropic distribution, but the methods used here can be easily applied to more general anisotropic distributions, such as the bi-kappa or product-bi-kappa. The effect of the kappa index and thermal corrections on the dispersion relations of DAW is discussed.

The oblique firehose instability in a bi-kappa magnetized plasma

“…The particular form of the κVDF in (1) is the model more frequently employed in the literature for reasons that have been discussed at length in Ref. 26 and in Papers I and II.…”

“…Among the several low-frequency wave modes observed in the solar wind and Earth's magnetosphere, of particular importance are the dispersive Alfvén waves (DAW). 26,31 In regions where the plasma thermal effects on the wave dispersion can not be ignored, the DAW are known as the kinetic Alfvén waves (KAW). Measuring the thermal effect with the parallel/perpendicular plasma beta parameter β (⊥)s = 8πn s T (⊥)s /B 2 0 , the dispersion relation of KAW propagating in an isotropic Maxwellian plasma with moderate values of the electron beta (m e /m i β e 1) is 31…”

“…A first contribution considered the effect of the κVDF on the propagation and damping of highly-oblique dispersive Alfvén waves in the Earth's magnetosphere. 26 Further contributions provided the closed-form expressions for the dielectric tensor of an isotropic kappa plasma in Ref. 27 and a bi-kappa plasma in Ref.…”

The general dielectric tensor for bi-kappa magnetized plasmas

“…Rather than giving here a long list of references, we suggest that the Reader consults the cited literature in our previous works. 5,6 In the present work, we continue the development of a mathematical formulation destined to the study of electromagnetic/electrostatic waves (and their instabilities) propagating at arbitrary angles in a warm magnetized plasma, in which the particles are described by asymmetric superthermal, or bi-kappa, VDFs. The formulation presented here employs the linear kinetic theory of plasmas and is an extension and generalization of the treatment developed in Refs.…”

DSHARK: A dispersion relation solver for obliquely propagating waves in bi‐kappa‐distributed plasmas

“…However, as was noticed by Gaelzer and Ziebell [2014], the investigations were largely restricted to purely parallel or perpendicular propagation, whereas general oblique propagation has rarely been considered so far. To the authors' knowledge, only Xue et al [1996] properly applied kappa distributions to a case of obliquely propagating modes, namely, ion cyclotron waves in the Earth's magnetosphere.…”