Linear theory of weakly amplified, parallel propagating, transverse temperature-anisotropy instabilities in magnetized thermal plasmas

Abstract

A rigorous analytical study of the dispersion relations of weakly amplified transverse fluctuations with wavevectors (̄→k ∥ ̄→B ) parallel to the uniform background magnetic field ̄→B in an anisotropic bi-Maxwellian magnetized electronproton plasma is presented. A general analytical instability condition is derived that holds for different values of the electron (Ae) and proton (Ap) temperature anisotropies. We determine the conditions for which the weakly amplified left-handed (LH) polarized Alfven proton cyclotron and right-handed (RH) polarized Alfven Whistler electron cyclotron branches can be excited. For different regimes of the electron plasma frequency phase speed w = ? p,e/(kc) these branches reduce to the RH- and LH-polarized Alfven waves, RH-polarized high and low phase speed Whistler, RH-polarized proton, and LH-polarized electron cyclotron modes. Analytic instability threshold conditions are derived in terms of the combined temperature anisotropy A = T⊥/T∥, the parallel plasma beta ?∥ = 8π nekBT∥/B 2 and the electron plasma frequency phase speed w = ? p,e/(kc) for each mode. The results of our instability study are applied to the observed solar wind magnetic turbulence at values of 90 ≤ w ≤ 330. According to the existence conditions of the different instabilities, only the LH- and RH-polarized Alfven wave instabilities can operate here. Besides the electronproton mass ratio μ = 1836, the Alfvenic instability threshold conditions are controlled by the single observed plasma parameter w. The Alfvenic instability diagram explains well the observed confinement limits at small parallel plasma beta values in the solar wind. © 2010. The American Astronomical Society. All rights reserved.