  The magnetic fields associated with young stellar objects are expected to
have an hour-glass geometry, i.e., the magnetic field lines are pinched as they
thread the equatorial plane surrounding the forming star but merge smoothly
onto a background field at large distances. With this field configuration,
incoming cosmic rays experience both a funneling effect that acts to enhance
the flux impinging on the circumstellar disk and a magnetic mirroring effect
that acts to reduce that flux. To leading order, these effects nearly cancel
out for simple underlying magnetic field structures. However, the environments
surrounding young stellar objects are expected to be highly turbulent. This
paper shows how the presence of magnetic field fluctuations affects the process
of magnetic mirroring, and thereby changes the flux of cosmic rays striking
circumstellar disks. Turbulence has two principle effects: 1) The (single)
location of the magnetic mirror point found in the absence of turbulence is
replaced with a wide distribution of values. 2) The median of the mirror point
distribution moves outward for sufficiently large fluctuation amplitudes
(roughly when $\delta B/B_0>0.2$ at the location of the turbulence-free mirror
point); the distribution becomes significantly non-gaussian in this regime as
well. These results may have significant consequences for the ionization
fraction of the disk, which in turn dictates the efficiency with which disk
material can accrete onto the central object. A similar reduction in cosmic ray
flux can occur during the earlier protostellar stages; the decrease in
ionization can help alleviate the magnetic braking problem that inhibits disk
formation.
