  We investigate the ionization of the diffuse interstellar medium by cosmic
rays by modeling their propagation along the wandering magnetic fields using a
Monte Carlo method. We study how low-energy cosmic rays propagate in turbulent,
translucent molecular clouds, and how they regulate the ionization and both
lose and gain energy from the medium. As a test case, we use high spatial
resolution (0.03 pc) CO maps of a well-studied high latitude translucent cloud,
MBM 3, to model turbulence. The propagation problem is solved with a modified
Monte Carlo procedure that includes trapping, energization, and ionization
losses. In a homogeneous medium, trapping and re-energization do not produce a
significant effect. In a nonuniform medium, particles can be trapped for a long
time inside the cloud. This modifies the cosmic ray distribution due to
stochastic acceleration at the highest energies (about 100 MeV). At lower
energies, the re-energization is too weak to produce an appreciable effect. The
change in the energy distribution does not significantly affect the ionization
losses, so ionization changes are due to trapping effects.
