Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Abstract

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approximation are studied, using the 16-moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL-MHD fluid model (single fluid equations by Chew, Goldberger, and Low [9,5]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes -strongly modified compared to the CGL model -and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL-MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities -incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes -two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models.

The proton temperature anisotropy associated with bursty bulk flows in the magnetotail

“…One-dimensional (1-D) hybrid simulations show that the oblique firehose instability has density compressibility but no magnetic compressibility [Hellinger and Matsumoto, 2000]. Then again, Dzhalilov et al [2011] describe this new Alfvénic mode specifically as a compressible oblique firehose mode resulting from the resonant interaction of two thermal modes and a fast mirror mode. Our results in Figure 10 show that there is some magnetic compressibility (when T ⊥ <T || ) along the red oblique firehose mode curve.…”

“…Then again, Dzhalilov et al . [] describe this new Alfvénic mode specifically as a compressible oblique firehose mode resulting from the resonant interaction of two thermal modes and a fast mirror mode. Our results in Figure show that there is some magnetic compressibility (when T ⊥ < T || ) along the red oblique firehose mode curve.…”

“…In the MHD-CGL case, the firehose modes can be unstable when β || À β ⊥ > 2 [Gary et al, 1998;Wang and Hau, 2003], in which case the parallel firehose instability is noncompressional. Expanding on the MHD-CGL work, either by taking into account cyclotron kinetic effects [Hellinger and Matsumoto, 2000] or by modifying the MHD-CGL model with anisotropic heat flux equations [Dzhalilov et al, 2011], will lead to the appearance of the oblique firehose instability, which adheres to the same instability criteria as the original parallel firehose instability, but has its major growth rate under oblique propagation with respect to the magnetic field. One-dimensional (1-D) hybrid simulations show that the oblique firehose instability has density compressibility but no magnetic compressibility [Hellinger and Matsumoto, 2000].…”

An introductory guide to fluid models with anisotropic temperatures. Part 1. CGL description and collisionless fluid hierarchy

“…In § 9, a dispersion relation of a fluid model closed with the bi-Maxwellian 'normal' closure is provided for generally oblique propagation, and we call this model second-order CGL (CGL2). We specifically focus on the mirror instability, since this simple fluid model (without any Landau damping) corrects the erroneous 1/6 factor in the 'hard' mirror threshold found in the basic CGL description, a result also reported by Dzhalilov, Kuznetsov & Staude (2011). The mirror instability is not addressed to a higher level of sophistication in this guide.…”

On the Parallel and Oblique Firehose Instability in Fluid Models

“…The mirror instability is typically a highly oblique instability and the modern Landau fluid description (Passot & Sulem (2007); Passot et al (2012); Sulem & Passot (2015), and references therein) that incorporates Landau damping and sophisticated finite Larmor radius (FLR) corrections captures the entire mirror instability growth rate with excellent accuracy. Considering only the mirror threshold (and not the full wavenumber dependent growth rate), the erroneous mirror threshold in the CGL model can also be corrected by simpler fluid models that contain the fluctuating heat flux equations and do not contain Landau damping Dzhalilov et al 2011;Hunana et al 2016). The parallel and oblique firehose instabilities, even though present in the above cited modern Landau fluid description, are usually addressed only very briefly.…”