Magnetohydrodynamic turbulence in a strongly magnetised plasma

TL;DR

This paper reviews the phenomenological theory of incompressible magnetohydrodynamic turbulence in strongly magnetized plasmas, focusing on inertial-range spectra and the effects of anisotropy and imbalance in turbulent cascades.

Contribution

It provides a comprehensive critique of existing theories and derives inertial-range spectra for four regimes of MHD turbulence, emphasizing anisotropic and imbalanced cases.

Findings

Derived spectra for balanced and imbalanced MHD turbulence regimes.

Highlighted the importance of anisotropy in turbulence spectra.

Discussed the role of wavepacket interactions in turbulent cascades.

Abstract

I present a review of incompressible magnetohydrodynamic (MHD) turbulence in a strongly magnetised plasma. The approach is phenomenological even where a more rigorous theory is available, so that a reader armed with paper, pencil and some determination may be able to work through most of the physics. The focus is on the inertial-range spectra for very large (fluid and magnetic) Reynolds numbers. These theories of the inertial-range are built on two important facts: (i) Kraichnan's insight that the turbulent cascades are a result of nonlinear interactions between oppositely directed wavepackets of Elsasser fields; (ii) these oppositely directed wavepackets do not exchange energy, but contribute only to changing each other's spatial structures. I begin with a description and critique of the Iroshnikov-Kraichnan theory, and explore the fundamental departures necessitated by the anisotropic nature of the turbulence. Derivations of the inertial-range spectra of four regimes of MHD turbulence -- the balanced weak, balanced strong, imbalanced weak and the imbalanced strong cascades -- are then presented. The need for studying the spectra of imbalanced turbulence when the waves on the outer scale have a short correlation time is briefly discussed.