Non-local MHD turbulence

We consider an example of strongly non-local interaction in incompressible magnetohydrodynamic (MHD) turbulence which corresponds to the case where th e Alfven waves travelling in the opposite directions have essentially diffe rent characteristic wavelengths. We use two approaches to the dynamics of t urbulent Alfvenic wavepackets: the first is a geometrical WKB theory [Phys. Lett. A 165 (1992) 330] and the second one is a three-wave kinetic equatio n derived for weakly turbulent waves [J. Plasma Phys., in press]. We show t hat these theories have a common limit of weak turbulence with scale separa tion in which they both predict the same Fokker-Planck equation for the wav e power spectrum. In both cases the packet wavenumbers (and therefore the L agrangian field-line separations) are allowed to experience order 1 changes . The WKB theory developed here formalises an intuitive geometrical argumen t of Goldreich and Sridhar [ApJ 485 (1997) 680] and allows one to see where such an intuition leads to a wrong conclusion about the inapplicability of the three-wave kinetic equation for order 1 wavepacket distortions. We sho w that the exponent of the constant flux non-local spectrum matches the val ue previously found for local turbulence at the boundary of the locality in terval. The relationship between the WKB theory and the weak turbulence the ory found in this paper for an ensemble of Alfven waves seems to be general for three-wave systems. (C) 2001 Elsevier Science B.V. All rights reserved .