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-beta plasma. For super-Alfvenic 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-mu mu. Adopting isotropic fast-mode turbulence with a Kolmogorov-like turbulence spectrum, we demonstrate that D-mu mu is the sum of contributions from transit-time damping and gyroresonant interactions. Gyroresonance refers to \n\not equal 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 epsilon less than or equal to\mu\less than or equal to 1, where epsilon is the ratio of Alfven to particle speed. In the interval \mu\<epsilon, 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 mu of the inverse of D-mu mu), these spatial transport parameters are determined by the contribution from the interval \mu\<epsilon. Pie also calculate the cosmic ray transport parameters for plasma turbulence consisting of a mixture of isotropic fast-mode waves and slab Alfven waves. Here, the momentum diffusion coefficient is determined by the transit-time damping of the fast-mode waves, and is a factor 1n epsilon(-1) larger than in the case of pure slab Alfven 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 \mu\<epsilon is now provided by gyroresonances with slab Alfven waves. The mean free path is a constant at nonrelativistic energies, and may account for the legendary lambda(fit)-lambda(QLT) discrepancy of sellar energetic particles.