Quasi‐linear Theory of Cosmic Ray Transport and Acceleration: The Role of Oblique Magnetohydrodynamic Waves and Transit‐Time Damping

We calculate quasi-linear transport and acceleration parameters for cosmic ray particles interacting resonantly with undamped fast-mode waves propagating in a low-β plasma. For super-Alfvénic particles and a vanishing cross-helicity state of the fast-mode waves, we demonstrate that the rate of adiabatic deceleration vanishes, and that the momentum and spatial diffusion coefficients can be calculated from the Fokker-Planck coefficient D μμ . Adopting isotropic fast-mode turbulence with a Kolmogorov-like turbulence spectrum, we demonstrate that D μμ is the sum of contributions from transit-time damping and gyroresonant interactions. Gyroresonance refers to | n | ≠ 0 resonant particle-wave interactions. Transit-time damping refers to the n = 0 interaction of particles with the compressive magnetic field component of the fast-mode waves. We show that transit-time damping provides the dominant contribution to pitch-angle scattering in the interval ≤ | μ | ≤ 1, where is the ratio of Alfvén to particle speed. In the interval | μ | < , transit-time damping does not occur, and gyroresonance provides a small but finite contribution to particle scattering. As a consequence, the momentum diffusion coefficient is mainly determined by the transit-time damping contribution. On the other hand, since the spatial diffusion coefficient and the related mean free path are given by the average over μ of the inverse of D μμ , these spatial transport parameters are determined by the contribution from the interval | μ | < . We also calculate the cosmic ray transport parameters for plasma turbulence consisting of a mixture of isotropic fast-mode waves and slab Alfvén waves. Here, the momentum diffusion coefficient is determined by the transit-time damping of the fast-mode waves, and is a factor ln -1 larger than in the case of pure slab Alfvén wave turbulence. The mean free path and the spatial diffusion coefficient are modified significantly from the pure fast-mode case, since the crucial scattering at | μ | < is now provided by gyroresonances with slab Alfvén waves. The mean free path is a constant at nonrelativistic energies, and may account for the legendary λ fit -λ QLT discrepancy of solar energetic particles.