[1] 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 k , and parallel beta, b k , 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 k > 1, proton cyclotron and mirror instabilities are operative, while for T k > 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 k vs b k 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.Citation: Seough, J., and P. H. Yoon (2012), Quasilinear theory of anisotropy-beta relations for proton cyclotron and parallel firehose instabilities,

[1] 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 k > 1, leads to the proton cyclotron and mirror instabilities. Marginal stability conditions for these instabilities may be expressed as inverse correlations between T ? /T k and parallel beta, b k . 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 b k regime, while for high b k values, the mirror instability dictates the inverse correlation.Citation: Yoon, P. H., and J. Seough (2012), Quasilinear theory of anisotropy-beta relation for combined mirror and proton cyclotron instabilities,

The present Letter puts forth a possible explanation for the outstanding problem of measured proton temperature anisotropy in the solar wind at 1 AU apparently being regulated by the mirror and oblique fire-hose instabilities. Making use of the fact that the local magnetic field intensity near 1 AU undergoes intermediate-scale temporal variations, the present Letter carries out the quasilinear analysis of the temperature anisotropy-driven instabilities with a time-varying local B field, assuming arbitrary initial temperature ratios and parallel betas. It is found that the saturated states in (β(∥), T(⊥)/T(∥)) space are bounded by the mirror and oblique fire-hose instabilities, which is superficially similar to the observation.

The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T∥ > T⊥ (or more precisely, parallel pressure anisotropy, P∥ > P⊥) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.