Quasilinear theory of anisotropy‐beta relation for combined mirror and proton cyclotron instabilities

The solar wind and the Earth's magnetosheath are often characterized by proton temperature anisotropies that cannot be discussed by adiabatic fluid theory. An excessive perpendicular temperature anisotropy may result when the plasma undergoes compression. The proton temperature anisotropy, T ⊥ / T ∥ > 1, leads to the proton cyclotron and mirror instabilities. Marginal stability conditions for these instabilities may be expressed as inverse correlations between T ⊥ / T ∥ and parallel beta, β ∥ . In the literature, these correlations are constructed on the basis of linear theory, hybrid simulations, or observational fitting. The present paper makes use of quasilinear theory for the proton cyclotron and mirror instabilities. In such an approach the inverse correlation naturally emerges as the time‐asymptotic states of self‐consistent evolution. The inverse correlation thus constructed shows the predominance of proton cyclotron instability for low β ∥ regime, while for high β ∥ values, the mirror instability dictates the inverse correlation.