Cosmic-ray Perpendicular Superdiffusion and Parallel Mirror Diffusion in a Partially Ionized and Turbulent Medium

Understanding cosmic-ray (CR) diffusion in a partially ionized medium is both crucial and challenging. In this study, we investigate CR perpendicular superdiffusion and parallel transport in turbulent, partially ionized media using high-resolution 3D two-fluid simulations that treat ions and neutrals separately. We examine the influence of neutral-ion decoupling and the associated damping of turbulence on CR propagation in both transonic and supersonic conditions. Our simulations demonstrate that neutral-ion decoupling significantly damps velocity and magnetic field fluctuations at small scales, producing spectral slopes steeper than those of Kolmogorov and Burgers scaling. In supersonic turbulence, large-scale shock motion is not subject to damping and generates small-scale density enhancements. Moreover, the damping of magnetic field fluctuations substantially decreases pitch-angle scattering, which, however, only slightly affects the CR parallel mean free path λ_∥, due to the nonresonant mirror interactions of CRs. In the direction perpendicular to the mean magnetic field, we identify two regimes of the perpendicular superdiffusion of CRs: a diffusive regime (λ_∥ < L_inj, where L_inj is the turbulence injection scale) with perpendicular separation of CR proportional to t³/⁴ and a ballistic regime (λ_∥ > L_inj) with perpendicular separation scaling as t³/². At initially large pitch angles, the effects of magnetic mirroring—naturally arising in magnetohydrodynamic turbulence—become significant, enhancing the confinement of CRs and resulting in λ_∥ < L_inj, despite the damping effect. These results imply that large-pitch-angle CRs can be well confined in the cold interstellar medium, such as molecular clouds.