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.
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