Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

Abstract

This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action-the magnetic analog of the "shear-current" effect. In addition, consideration of α effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of α, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.

A new constraint on mean-field galactic dynamo theory

“…Likewise, a magnetic contribution to the Ω × J effect (Rädler 1969) was found by Squire & Bhattacharjee (2015b) to play a role. Their results were supported with analytical calculations using quasilinear theory (Squire & Bhattacharjee 2015a). However, it is not clear what the implications are for the large R m and fluid Reynolds number R e (along with Strouhal number ∼ 1) regime relevant for galaxies.…”

A drift of Langmuir waves in a magnetized inhomogeneous plasma

“…Ensemble plasma averaging is also implied by any hydrodynamic modelling of plasma phenomena, and recent examples of such modelling were reported by Araki (2015), Bhattacharjee et al. (2015), Stawarz & Pouquet (2015), Squire & Bhattacharjee (2015), Andrés & Sahraoui (2017) and Viciconte, Gréa & Godeferd (2018). Implicitly, plasma ensemble substitutions are present in many numerical plasma simulations (see, e.g.…”

Dynamo theories

“…At this point, things become tricky. Indeed, FOSA calculations (Krause & Rädler 1980; Moffatt & Proctor 1982) show that the Rädler effect alone can promote a dynamo ( ) when the rotation is anticyclonic (corresponding to positive with our convention), but not the shear-current effect ( , Rädler & Stepanov 2006; Rüdiger & Kitchatinov 2006; Sridhar & Subramanian 2009; Sridhar & Singh 2010; Squire & Bhattacharjee 2015 a ). Calculations based on the MTA closure agree with FOSA calculations as far as the Rädler effect is concerned, but find dynamo growth ( ) for the shear-current effect (Rogachevskii & Kleeorin 2003, 2004)!…”

“…To understand how the Rädler and shear-current effects may affect large-scale dynamos in rotating shear flows, let us have a look at the mean-field dynamo problem for small-scale homogeneous turbulence forced isotropically and non-helically in the simplest possible unstratified, rotating shearing sheet configuration, , , for which and the only non-zero components of the deformation tensor are . Under these assumptions, there are no mean and effects and the kinematic evolution equations for the and components of a -dependent mean magnetic field (defined as the average over and of the total magnetic field) can be cast in the simple form where we have introduced a contracted generalised anisotropic turbulent diffusion tensor appropriate to the configuration of the problem, namely Using (4.8)–(4.10), it can be shown that where is the usual isotropic turbulent diffusion coefficient, is an anisotropic contribution to the tensor arising from the presence of the large-scale strain associated with the shear flow, and , and are contributions to the mean-field tensor arising (similarly to and ) from the presence of rotation, large-scale vorticity, and strain associated with the shear flow (for a detailed derivation, see Rädler & Stepanov 2006; Squire & Bhattacharjee 2015 a ).…”

“…An interesting recent twist on this problem has been the realisation that the presence of dynamical small-scale magnetic fluctuations (characterised by ), driven either by the self-consistent saturation of a small-scale dynamo or by an independent magnetic-forcing process (such as an antenna-driving or MHD instability), may actually promote rather than quench the growth of the large-scale field in a large-scale turbulent shear flow (Squire & Bhattacharjee 2015 a , b , c , 2016). This effect can be interpreted within the mean-field framework as a magnetic version of the shear-current effect discussed in § 4.4.3, in the sense that the interaction between the shear and dynamical small-scale MHD fluctuations appears to generate an off-diagonal turbulent diffusivity on its own (a tentative physical explanation of how this effect originates can be found in Squire & Bhattacharjee 2016).…”