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The quasi-steady states of collisionless plasmas in space (e.g., in the solar wind and planetary environments) are governed by the interactions of charged particles with wave fluctuations. These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropyT_⊥>T_∥(where ⊥, ∥ are directions defined with respect to the local magnetic field vector). Theories relying on standard Maxwellian models fail to link these two instabilities (i.e., predicted thresholds) to the proton quasi-stable anisotropies measured in situ in a completely satisfactory manner. Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi-κpower-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. The reduced QL analysis based upon the assumption of a time-dependent bi-Kappa model thus becomes a valuable theoretical approach that can be incorporated into the present studies of solar wind dynamics.

The charged particles in the solar wind are often observed to possess a nonthermal tail in the velocity distribution function, a feature that can be fitted with the Kappa model. The anisotropic, or bi-Kappa, model of protons, electrons, and other charged particles is thus adopted in the literature for interpreting the data as well as in the context of the analysis of wave–particle interactions. The present paper develops an approximate but efficient theory of the mirror and cyclotron instabilities excited by the bi-Kappa protons in the solar wind. A velocity moment-based quasi-linear theory of these instabilities is also formulated in order to investigate the saturation behavior. Applications of the formalism are made for instabilities close to the marginally unstable state, which is typical of the solar wind near 1 au.

The solar wind plasma is characterized by unequal effective kinetic temperatures defined in perpendicular and parallel directions with respect to the ambient magnetic field. For electrons, the excessive perpendicular temperature anisotropy leads to quasi-parallel electromagnetic electron cyclotron (or whistler) instability and aperiodic electron-mirror instability with oblique wave vectors. The present paper carries out a direct side-by-side comparison of quasi-linear (QL) theory and particle-in-cell (PIC) simulation of combined mirror and cyclotron instabilities acting upon the initially anisotropic electron temperatures, and find that the QL theory satisfactorily encapsulates the non-linear aspect of the combined instability effects. However, a discrepancy between the present study and a previous PIC simulation result is also found, which points to the need for further investigation to resolve such an issue.