The challenge is that the kinetic dispersion analysis based on the bi-Kappa model is not straightforward. 2014, 2015 Eliasson & Lazar 2015 Shaaban et al. These observations call for a generalization of the standard instability analysis based upon the bi-Maxwellian models to the more general bi-Kappa models (Lazar 2012 dos Santos et al. 1998 Pierrard & Pieters 2014 Zirnstein & McComas 2015). 2019), which can be fitted with the (bi-)Kappa ( κ power-law) models (Collier et al. ![]() However, in many instances, the solar wind plasma particles, in particular, protons and heavier ions, are observed to possess nonthermal tail distributions (Gosling et al. In the literature, the temperature anisotropy instabilities are extensively examined within the framework of the bi-Maxwellian velocity distributions (Yoon & Seough 2012 Yoon 2017 Zhao et al. However, validating such a QL approach through numerical simulations and distinguishing these specific processes from other mechanisms of nonlinear saturation is recommended. Without requiring major computational resources, QL models are very handy in characterizing the QL growth of wave fluctuations and subsequent relaxation of anisotropic temperatures. ![]() The instability thresholds are commonly provided in plasma parameter space ( β ∥, T ⊥/ T ∥) (where is the proton parallel beta), by the wave dispersion and stability theories, which may require extended QL approaches to confirm the anisotropy relaxation to the thresholds derived from linear theory (Shaaban et al. There is, however, an unresolved dilemma in the case of protons with A > 1, which, contrary to expectations, appear to be better constrained by the mirror instability than electromagnetic ion cyclotron (EMIC) thresholds (Hellinger et al. Measurements of temperature anisotropy in the solar wind, A = T ⊥/ T ∥ (where ⊥, ∥ are directions defined with respect to the local magnetic field vector), reveal indeed quasi-stable states, upper-bounded by the thresholds of temperature anisotropy instabilities predicted by the linear and quasi-linear (QL) theories (Kasper et al. Therefore, their thermodynamic properties, including (kinetic) pressures and temperatures or their anisotropy, are expected to be regulated mainly by the interaction of particles with electromagnetic waves and fluctuations. Space plasmas in the heliosphere (e.g., solar wind and planetary magnetospheres), as well as in other astrophysical setups, are sufficiently hot and diluted to be considered collisionless. 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. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. ![]() Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi- κ power-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. 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. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropy T ⊥ > T ∥ (where ⊥, ∥ are directions defined with respect to the local magnetic field vector). These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. 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.
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