Analysis of the scaling behavior of two-dimensional homogeneous MHD plasmas

Two-dimensional magnetohydrodynamic plasmas are believed to obey a power-la w behavior in terms of the size ilk of an eddy. The scaling law under a ran dom Gaussian stirring force is studied through the field-theoretical renorm alization-group (RG) method. In the process, a generating functional is con structed, and from power counting, the primitively divergent vertex functio ns are identified. These divergent functions are regularized by proper reno rmalizations of the viscosity, the resistivity, and the size of the fluctua tion and by invoking the Ward identities resulting from the Galilean invari ance. The fixed point of the RG equation is found, and the scaling solution s of the energy spectra are obtained in terms of the noise power spectrum.