D-dimensional developed MHD turbulence:: double expansion model

Developed magnetohydrodynamic turbulence near two dimensions d up to three dimensions has been investigated by means of a renormalization group approach and double expansion regularization. A modification of a standard minimal subtraction scheme has been used to analyse the stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. The exact analytical expressions have been obtained for the fixed points. The continuation of the universal value of the inverse Prandtl number u = 1.562 determined at d = 2 up to d = 3 restores the value of u = 1.393 which is known in the kinetic fixed point from the usual epsilon-expansion. The magnetic stable fixed point has been calculated and its stability region has also been examined. This point loses stability: (a) below a critical value of dimension d(c) = 2.36 (independently of the a-parameter of a magnetic forcing) and (b) below the value of a(c) = 0.146 (independently of the dimension).