Anisotropic non-perturbative zero modes for passively advected magnetic fields

An analytic assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the d-dimensional kinematic magnetohydrodynamics problem in the presence of a mean magnetic field. The velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent \xi. Inertial-range anisotropic contributions to the scaling exponents, \xi_j , of second-order magnetic correlations are associated with zero modes and have been calculated nonperturbatively. For d=3, the limit \xi \to 0 yields ?j?j?2??(2j3?j2?5j?4)/?2(4j2?1)?, where j (j?2) is the order in the Legendre polyno- mial decomposition applied to correlation functions. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made.