Anomalous scaling of the magnetic field in the helical Kazantsev-Kraichnan model

The field-theoretic renormalization group and the operator product expansion are used to investigate the influence of spatial parity violation of the conductive turbulent environment on the anomalous scaling behavior of correlation functions of a weak magnetic field in the framework of the Kazantsev-Kraichnan rapid change model. Two-loop expressions for the critical dimensions of the leading composite operators, which drive the anomalous scaling of the two-point single-time correlation functions of the magnetic field in the presence of large-scale anisotropy, are found to be functions of the helicity parameter. It is shown that the presence of helicity in the system leads to a significantly stronger manifestation of anomalous scaling than in the nonhelical case. At the same time, it is also shown that helicity does not destroy the standard hierarchy of the anisotropic anomalous exponents in the framework of which the leading contribution to anomalous scaling is given by the isotropic shell.

Figure 1

Dependence of the leading two-loop anomalous dimensions for $N=2$, 3, 4, and 5 on the helicity parameter $\rho$ for $\varepsilon =1$.