  External cosmic rays impinging upon circumstellar disks associated with young
stellar objects provide an important source of ionization, and as such, play an
important role in disk evolution and planet formation. However, these incoming
cosmic rays are affected by a variety of physical processes internal to
stellar/disk systems, including modulation by turbulent magnetic fields.
Globally, these fields naturally provide both a funneling effect, where cosmic
rays from larger volumes are focused into the disk region, and a magnetic
mirroring effect, where cosmic rays are repelled due to the increasing field
strength. This paper considers cosmic ray propagation in the presence of a
turbulent spiral magnetic field, analogous to that produced by the Solar wind.
The interaction of this wind with the interstellar medium defines a transition
radius, analogous to the Heliopause, which provides the outer boundary to this
problem. We construct a new coordinate system where one coordinate follows the
spiral magnetic field lines and consider magnetic perturbations to the field in
the perpendicular directions. The presence of magnetic turbulence replaces the
mirroring points with a distribution of values and moves the mean location
outward. Our results thus help quantify the degree to which cosmic ray fluxes
are reduced in circumstellar disks by the presence of magnetic field structures
that are shaped by stellar winds. The new coordinate system constructed herein
should also be useful in other astronomical applications.
