The transport of test particles in a stochastic magnetic field with a
sheared component is studied. Two stages in the particle dynamics are
distinguished depending on whether the collisional effects perpendicul
ar to the main field are negligible or not. Whenever the perpendicular
collisions are unimportant, the particles show a subdiffusive behavio
r which is slower in the presence of shear. The particle dynamics is t
hen inhomogeneous and non-Markovian and no diffusion coefficient may b
e properly defined. When the perpendicular collision frequency is smal
l, this subdiffusive stage may be very long. In the truly asymptotic s
tage, however, the perpendicular collisions must be accounted for and
the particle motion eventually becomes diffusive. Here again, however,
the shear is shown to reduce the anomalous diffusion coefficient of t
he system. (C) 1997 American Institute of Physics.