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Magnetohydrodynamic turbulence in a strongly magnetised plasma

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.