The Parametric Instability of Alfvén Waves: Effects of Temperature Anisotropy

<jats:title>Abstract</jats:title> <jats:p>We study the stability of large-amplitude, circularly polarized Alfvén waves in an anisotropic plasma described by the double-adiabatic/CGL closure, and in particular the effect of a background thermal pressure anisotropy on the well-known properties of Alfvén wave parametric decay in magnetohydrodynamics (MHD). Anisotropy allows instability over a much wider range of values of parallel plasma beta (<jats:italic>β</jats:italic> <jats:sub>∥</jats:sub>) when <jats:italic>ξ</jats:italic> = <jats:italic>p</jats:italic> <jats:sub>0⊥</jats:sub>/<jats:italic>p</jats:italic> <jats:sub>0∥</jats:sub> > 1. When the pressure anisotropy exceeds a critical value, <jats:italic>ξ</jats:italic> ≥ <jats:italic>ξ</jats:italic>* with <jats:italic>ξ</jats:italic>* ≃ 2.7, there is a new regime in which the parametric instability is no longer quenched at high <jats:italic>β</jats:italic> <jats:sub>∥</jats:sub>, and in the limit <jats:italic>β</jats:italic> <jats:sub>∥</jats:sub> ≫ 1, the growth rate becomes independent of <jats:italic>β</jats:italic> <jats:sub>∥</jats:sub>. In the opposite case of <jats:italic>ξ</jats:italic> < <jats:italic>ξ</jats:italic>*, the instability is strongly suppressed with increasing parallel plasma beta, similarly to the MHD case. We analyze marginal stability conditions for parametric decay in the (<jats:italic>ξ</jats:italic>, <jats:italic>β</jats:italic> <jats:sub>∥</jats:sub>) parameter space and discuss possible implications for Alfvénic turbulence in the solar wind.</jats:p>