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

Abstract

[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,

Quasilinear analysis of saturation properties of broadband whistler mode waves

“…The main advantage of PIC simulations is that all nonlinear wave-particle and wave-wave interactions are included. In a companion paper, Seough and Yoon [2012] reported the quasilinear analysis for parallel proton cyclotron instability for T ⟂ ∕T ‖ > 1 and parallel firehose instabilities for T ⟂ ∕T ‖ < 1. Saturation properties of broadband waves can also be analyzed using quasilinear theory [Kennel and Engelmann, 1966].…”

Formation of electron kappa distributions due to interactions with parallel propagating whistler waves

“…This causes the slow decrease in the wave intensity dB 2 ¼ dB 2 x þ dB 2 y after saturation, as noted by Ossakow et al 21 A similar slow decrease in wave magnetic field energy density has been observed for electromagnetic ion cyclotron waves (EMIC) waves and explained in a similar way by Seough and Yoon. 22 Figure 1 also shows that jdB 2…”

Solar wind proton temperature anisotropy versus beta inverse correlation

“…Hellinger et al [7] recently expressed all the results available to date in a unifying empirical relation It has been suggested that one may use the inverse correlations (1) as a closure relation for macroscopic models of the solar wind [12,13]. In a recent pair of papers [14,15], the present authors put forth a physics-based scheme to derive these inverse correlations instead of empirically modeling them. Our method was based on quasi-linear kinetic theory based on the simplifying assumption of bi-Maxwellian proton distribution function.…”

“…Of course, this is an approximation which is not expected to be strictly valid in the nonlinear regime [18]. However, such a simplifying assumption was proven to be quite adequate [14,15]. Despite this development, however, there is a major discrepancy between the theory and observations.…”