  Recent studies have suggested that low-energy cosmic rays (CRs) may be
accelerated inside molecular clouds by the shocks associated with star
formation. We use a Monte Carlo transport code to model the propagation of CRs
accelerated by protostellar accretion shocks through protostellar cores. We
calculate the CR attenuation and energy losses and compute the resulting flux
and ionization rate as a function of both radial distance from the protostar
and angular position. We show that protostellar cores have non-uniform CR
fluxes that produce a broad range of CR ionization rates, with the maximum
value being up to two orders of magnitude higher then the radial average at a
given distance. In particular, the CR flux is focused in the direction of the
outflow cavity, creating a 'flashlight' effect and allowing CRs to leak out of
the core. The radially averaged ionization rates are less than the measured
value for the Milky Way of $\zeta \approx 10^{-16} \rm s^{-1}$; however, within
$r \approx 0.03$ pc from the protostar, the maximum ionization rates exceed
this value. We show that variation in the protostellar parameters, particularly
in the accretion rate, may produce ionization rates that are a couple of orders
of magnitude higher or lower than our fiducial values. Finally, we use a
statistical method to model unresolved sub-grid magnetic turbulence in the
core. We show that turbulence modifies the CR spectrum and increases the
uniformity of the CR distribution but does not significantly affect the
resulting ionization rates.
