Confinement and isotropization of Galactic cosmic rays by molecular-cloud magnetic mirrors when turbulent scattering is weak

Theoretical studies of magnetohydrodynamic (MHD) turbulence and observations of solar wind fluctuations suggest that MHD turbulence in the interstellar medium is anisotropic at small scales, with smooth variations along the background magnetic field and sharp variations perpendicular to the background field. Turbulence with this anisotropy is inefficient at scattering cosmic rays, and thus the scattering rate nu may be smaller than has been traditionally assumed in diffusion models of Galactic cosmic-ray propagation, at least for cosmic-ray energies E above 10(11)-10(12) eV at which self-confinement is not possible. In this paper, it is shown that Galactic cosmic rays can be effectively confined through magnetic reflection by molecular clouds, even when turbulent scattering is weak. Elmegreen's quasifractal model of molecular-cloud structure is used to argue that a typical magnetic field line passes through a molecular cloud complex once every similar to 300 pc. Once inside the complex, the held line will in most cases be focused into one or more dense clumps in which the magnetic field can be much stronger than the average held in the intercloud medium (ICM). Cosmic rays following field lines into cloud complexes are most often magnetically reflected back into the ICM, since strong-held regions act as magnetic mirrors. For a broad range of cosmic-ray energies, a cosmic ray initially following some particular held line separates from that held line sufficiently slowly that the cosmic ray can be trapped between neighboring cloud complexes for long periods of time. The suppression of cosmic-ray diffusion due to magnetic trapping is calculated in this paper with the use of phenomenological arguments, asymptotic analysis, and Monte Carlo particle simulations. Formulas for the coefficient of diffusion perpendicular to the Galactic disk are derived for several different parameter regimes within the E-v plane. In one of these parameter regimes in which scattering is weak, it is shown that molecular-cloud magnetic mirrors strongly reduce cosmic-ray anisotropy in the ICM, and analytic formulas for the angular harmonics are derived.