  A first analytic assessment of the role of anisotropic corrections to the
isotropic anomalous scaling exponents is given for the $d$-dimensional
kinematic magneto-hydrodynamics 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, $\zeta_j$, of second-order magnetic
correlations are associated to zero modes and have been calculated
non-perturbatively. For $d=3$, the limit $\xi\mapsto 0$ yields
$\protect{\zeta_j=j-2+ \xi (2j^3 +j^2 -5 j - 4)/[2(4 j^2 - 1)]} $ where $j$
($j\geq 2$) 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.
