The Dispersion Relations for Dispersive Alfvén Waves in Superthermal Plasmas

Abstract:

The effects of velocity distribution functions (VDF) 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. One of the problems that
is being addressed on this new light is the temperature anisotropy
displayed by solar wind protons and electrons on the vicinity of Earth's
foreshock. The proton VDF show nonthermal features such as a very
anisotropic core, an extended high-energy tail and a beam population,
aligned to the local magnetic field and separated from the core by
speeds on the order of the Alfvén speed. The existence of these nonthermal
characteristics implies that the VDF contains a large amount of free
energy that can be used to excite the Alfvén waves present in the
solar wind. Conversely, the wave-particle interaction is important
to determine the shape of the VDF, as in the case of obliquely-propagating
dispersive Alfvén waves (DAW), which are relevant for the particle
acceleration processes in the Earth's magnetosphere. 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. The absence of a general treatment
prevents a complete analysis of the wave-particle interaction in superthermal
plasmas, since some instabilities, such as the firehose instability,
can operate simultaneously both in the parallel and oblique directions.
In this work we obtain expressions for the dielectric tensor components
and subsequent dispersion relations for oblique DAW 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 the obliquely-propagating
DAW is discussed.