  Diffusive shock acceleration at collisionless shocks is thought to be the
source of many of the energetic particles observed in space. Large-scale
spatial variations of the magnetic field has been shown to be important in
understanding observations. The effects are complex, so here we consider a
simple, illustrative model. Here, we solve numerically the Parker transport
equation for a shock in the presence of large-scale sinusoidal magnetic-field
variations. We demonstrate that the familiar planar-shock results can be
significantly altered as a consequence of large-scale, meandering magnetic
lines of force. Because perpendicular diffusion coefficient $\kappa_\perp$ is
generally much smaller than parallel diffusion coefficient $\kappa_\parallel$,
the energetic charged particles are trapped and preferentially accelerated
along the shock front in the regions where the connection points of magnetic
field lines intersecting the shock surface converge, and thus create the "hot
spots" of the accelerated particles. For the regions where the connection
points separate from each other, the acceleration to high energies will be
suppressed. Further, the particles diffuse away from the "hot spot" regions and
modify the spectra of downstream particle distribution. These features are
qualitatively similar to the recent Voyager's observation in the Heliosheath.
These results are potentially important for particle acceleration at shocks
propagating in turbulent magnetized plasmas as well as those which contain
large-scale nonplanar structures. Examples include anomalous cosmic rays
accelerated by the solar wind termination shock, energetic particles observed
in propagating heliospheric shocks, and galactic cosmic rays accelerated by
supernova blast waves, etc.
