Anisotropic nonperturbative 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, ii, of second-order magnetic correlations are associated with zero modes and have been calculated nonperturbatively. For d = 3, the limit xi --> 0 yields zeta(j) = j - 2 + xi(2j(3) +j(2) - 5J - 4)/ [2(4j(2) -1)], where j (j greater than or equal to 2) is the order in the Legendre polynomial decomposition applied to correlation functions. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made. [S1063-651X(99)51109-4].