Weakly turbulent plasma processes in the presence of inverse power-law velocity tail population

Observations show that plasma particles in the solar wind frequently display power-law velocity distributions, which can be isotropic or anisotropic. Particularly, the velocity distribution functions of solar wind electrons are frequently modeled as a combination of a background Maxwellian distribution and a non-thermal distribution which is known as the “halo” distribution. For fast solar wind conditions, highly anisotropic field-aligned electrons, denominated as the “strahl” distribution, are also present. Motivated by these observations, the present paper considers a tenuous plasma with Maxwellian ions, and electrons described by a summation of an isotropic Maxwellian distribution and an isotropic Kappa distribution. The formalism of weak turbulence theory is utilized in order to discuss the spectra of electrostatic waves that must be present in such a plasma, satisfying the conditions of quasi-equilibrium between the processes of spontaneous fluctuations and of induced emission. The kappa index and relative density of the Kappa electron distribution are varied. By taking into account the effects due to electromagnetic waves into the weak turbulence formalism, we investigate the electromagnetic spectra that satisfy the conditions of “turbulent equilibrium,” and also the time evolution of the wave spectra and of the electron distribution, which occurs in the case of the presence of an electron beam in the electron distribution