Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

Abstract

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the "parasitic instabilities" that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in MHD). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

Shearing-box simulations of MRI-driven turbulence in weakly collisional accretion discs

“…Pm, box size), appears to be almost unaffected by even large Braginskii viscosities. Our systematic demonstration of MHD-like behavior in Braginskii MHD complements and clarifies some of the findings made by Sharma et al (2006), Kunz et al (2016), Squire et al (2017a) and Foucart et al (2017), who have seen strong similarities to MHD in their extended-MHD and kinetic simulations. Nevertheless, we do find that anisotropic viscosity leaves a clear imprint on the structure of the flow.…”

“…Because we find that the cascade continues almost unaffected to scales well below the Braginskii viscous scale, this could mean that the smallest-scale motions will be more strongly affected by ∆p forces than we assume here. It is unclear if and how these additional effects could be incorporated in a fluid model, and a kinetic description is likely necessary to fully capture all the underlying physics (see Schekochihin et al 2008, Kunz et al 2014, Squire et al 2017a for more discussion).…”

“…These are secondary instabilities that grow on the large field and flow gradients in the MRI mode, causing it to break up into turbulence. Squire et al (2017a) argued that the dominant parasitic modes are not too different in Braginskii MHD. This is broadly consistent with our numerical results summarized below, although we do often see somewhat larger α in the Braginskii case during a short initial transient phase.…”

Braginskii viscosity on an unstructured, moving mesh accelerated with super-time-stepping

“…Extensive modeling of this phenomenon, using both a collisionless Landau fluid closure and weakly-collisional Braginskii MHD, has been presented in Squire et al (2017a). The consequences for the magneto-rotational instability (MRI) have also been investigated (Squire et al 2018) and the interruption was studied using hybrid kinetic simulations in Squire et al (2017b).…”

Finite-Larmor-radius equilibrium and currents of the Earth’s flank magnetopause

“…In fact there are further shear-driven instabilities that may also get relevant feedback from anisotropy (and agyrotropy) developed (or sustained) by the underlying shear flow within a kinetic description such as, for instance, for the case of magneto-rotational instability (MRI) in accretion disks (e.g., Ferraro 2007;Riquelme et al 2012;Kunz et al 2016;Squire et al 2017b). Furthermore, ion-kinetic effects such as FLR and pressure-tensor dynamics can affect anisotropy-driven instabilities themselves (e.g., Schekochihin et al 2010;Rosin et al 2011;Sarrat et al 2016;Squire et al 2017a), which are relevant, e.g., in the evolution of the solar wind (e.g., Hellinger et al 2006;Tenerani et al 2017;Yoon 2017) and in magnetic reconnection (e.g.…”