Quasilinear theory of anisotropy-beta relations for proton cyclotron and parallel firehose instabilities

Abstract

The solar wind and the Earth's magnetosheath frequently possess proton temperature anisotropies that violate the predictions of adiabatic fluid theory. In the literature, various threshold conditions expressed as inverse correlations between the proton anisotropy, T⊥/T ∥, and parallel beta, β∥, have been constructed on the basis of linear stability analysis for anisotropy-driven instabilities, hybrid simulations, or by simply fitting the observations. For T⊥/T∥ > 1, proton cyclotron and mirror instabilities are operative, while for T∥ > T ⊥, parallel and oblique firehose instabilities can be taken into account in the construction of the inverse correlation. In the present paper, quasilinear kinetic theory of parallel proton cyclotron and firehose instabilities are employed to self-consistently construct the T ⊥/T∥ vs β∥ threshold conditions. In principle, such an approach eliminates the necessity for empirical models of inverse correlations, since inverse correlations should naturally emerge as the time-asymptotic states of quasilinear processes. It is found that the self-consistent threshold conditions constructed on the basis of quasilinear formalism compare reasonably well with available models, thus confirming that quasilinear method is a reasonable approach. © 2012. American Geophysical Union. All Rights Reserved.