Anisotropic MHD Turbulence Near Two Spatial Dimensions: General Field Theoretic Renormalization Group Analysis

Using the so-called double-expansion approach we perform a general field theoretic renormalization group analysis of the MHD turbulence with the presence of the weak small-scale uniaxial anisotropy valid for all spatial dimensions \(d\ge 2\). The ultraviolet divergent Green’s functions are identified and the renormalization of the model is performed in the first order of the corresponding perturbation theory. The explicit form of all renormalization constants is found and the corresponding anomalous dimensions are determined. The explicit form of the system of all renormalization group \(\beta \) functions is found, which can be directly used for the analysis of all possible scaling regimes of the model deep inside of the inertial range.