Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Inertial-range scaling behavior of high-order (up to order N=51) structure functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. It has been shown that in inertial range the leading terms of the structure functions are coordinate independent, but powerlike corrections appear with the same anomalous scaling exponents as for the passively advected scalar field. These exponents depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to structure functions have not been found.