Anisotropic Cosmic Ray Transport in strong MHD Turbulence due to Magnetic Mirroring and Resonant Curvature Scattering

TL;DR

This work tackles the problem of cosmic-ray transport in strong MHD turbulence by examining how magnetic mirroring and resonant curvature scattering drive pitch-angle reversals and shape both parallel and perpendicular diffusion. Using test-particle simulations in eight saturated MHD snapshots with $\delta B/B_0\approx1$, the authors identify two reversal mechanisms tied to local field-line structure and model parallel transport as a Lévy walk, with reversal times following a truncated power-law $p(\tau) \sim \tau^{-\alpha}$ and a diffusion coefficient $D^{\infty}_{\text{Lévy}} = \langle x^2\rangle/(2\langle\tau\rangle)$. They show that highly magnetized particles exhibit energy-independent parallel diffusion dominated by the largest time scales, while perpendicular transport is initially subdiffusive due to mirror confinement but enhanced by resonant curvature scattering in chaotic field regions. To connect to astrophysical observations, they propose a simplified intermittently inhomogeneous ISM model where patches of size $l$ with $p(l)\sim l^{-\alpha}$ yield an energy-dependent diffusion $D(r_g) \propto r_g^{\alpha}$, reconciling microphysical transport with large-scale CR propagation, and highlighting the role of magnetic-field-line geometry in diffusion processes.

Abstract

The transport of cosmic rays through turbulent astrophysical plasmas still constitutes an open problem. Building on recent progress, we study the combined effect of magnetic mirroring and resonant curvature scattering on parallel and perpendicular transport. We conduct test-particle simulations in snapshots of an anisotropic magnetohydrodynamics simulation with $δB/B_0\sim 1$ and record magnetic moment variation and field line curvature around pitch-angle reversals. We find for strongly magnetized particles that (i) pitch-angle reversals may occur either in coherent regions of the field with small variation of the magnetic moment via magnetic mirroring or in chaotic regions of the field with strong variation of the magnetic moment via resonant curvature scattering; (ii) parallel transport can be modeled as a Lévy walk with a truncated power-law distribution based on pitch-angle reversal times; and (iii) perpendicular transport is enhanced by resonant curvature scattering in synergy with chaotic field line separation and diminished by magnetic mirroring due to confinement in locally ordered field line bundles. While magnetic mirroring constitutes the bulk of reversal events, resonant curvature scattering additionally acts on trajectories that fall in the loss cones of typical mirroring structures and thus provides the cut-off for the reversal time distribution. Our results, which highlight the role of the magnetic field line geometry in cosmic-ray transport processes, are consistent with energy-independent diffusion coefficients. We conclude by considering how energy-dependent observations could arise from an intermittently inhomogeneous interstellar medium.

Figures (6)

• Figure 1: Example test-particle trajectories illustrating the two prevalent scattering mechanisms in our simulation: (a) resonant curvature scattering characterized by strong variations of the magnetic moment $M$ upon encountering sharply bent field lines, and (b) magnetic mirroring characterized by pitch-angle reversals with small variations of $M$ induced by particles traveling along field line configurations with slowly increasing magnetic field strengths. The structure of the magnetic field is illustrated by field line trajectories and slices of the out-of-plane current density $j_z$. Interactive versions of these figures are available online via sketchfab: (a) https://skfb.ly/pDwuD, (b) https://skfb.ly/pDwGD.
• Figure 2: Joint probability distribution $p(r_M,\kappa_\mathrm{max})$ of magnetic moment variation $r_M=M_\mathrm{max}/M_\mathrm{min}$ and maximum field line curvature $\kappa_\mathrm{max}$ experienced by test particles with $r_g=0.006\,L_x$ during $2\,T_g$-intervals centered around pitch-angle reversal events. The red line indicates the resonant curvature condition, above which unmagnetized scattering is expected to dominate.
• Figure 3: (a) Distributions $p_\mu(t)$ of durations $\tau$ between pitch-angle reversals, which exhibit a power-law scaling similar to the first-passage scaling $t^{-3/2}$ (indicated for reference) over about two orders of magnitude, as well as energy-dependent cut-off scales. (b) Average of the absolute value of the pitch-angle cosine $\mu$ conditional on segment duration $\tau$. Particles with large $\mu$ have a higher probability of falling into the loss cone of traversed structures and thus avoid mirroring, which leads to larger $\langle|\mu|\,|\,\tau\rangle$ at longer time scales.
• Figure 4: Diffusion coefficients as functions of the normalized gyro radius, parallel to the global direction of the background field $\hat{\boldsymbol{z}}$ and parallel to the local direction of the magnetic field $\hat{\boldsymbol{B}}$, as well as exact and approximate diffusion coefficients computed from the Lévy-walk model. The exact value takes the entire reversal time distribution $p_\mu(\tau)$ into account, while the approximate value is given by the cut-off time scale $\tau_\mathrm{max}$ and the effective Lévy speed $v_\mathrm{eff}$. Finally, the diffusion coefficients of the shuffled $\mu_t$--time-series ($\lozenge$) aid to resolve the discrepancy between $D^\infty_{\parallel\hat{\boldsymbol{B}}}$ and $D^\infty_\mathrm{L\acute{e}vy}$. Quantities in the frame of the local field direction $\hat{\boldsymbol{B}}$ are scaled by the field line speed $v_\mathrm{fl}$. The inset shows one minus the degree of magnetization $1-p_\mathrm{mag}=1-p(r_g\,\kappa<1)$.
• Figure 5: Running perpendicular diffusion coefficients of test particles and field lines. As indicated, convergence to diffusion occurs for displacements beyond the perpendicular box size. The inset relates the resulting perpendicular diffusion coefficients to the parallel diffusion coefficients.