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

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Abstract

We calculate quasi-linear transport and acceleration parameters for cosmic ray particles interacting resonantly with undamped fast-mode waves propagating in a low-b plasma. For super-Alfve nic 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 di usion coefficients can be calculated from the Fokker-Planck coefficient Adopting isotropic fast-mode turbulence with a Kolmogorov-like D kk . turbulence spectrum, we demonstrate that is the sum of contributions from transit-time damping D kk and gyroresonant interactions. Gyroresonance refers to resonant particle-wave interactions. o n o D 0 Transit-time damping refers to the n \ 0 interaction of particles with the compressive magnetic eld component of the fast-mode waves. We show that transit-time damping provides the dominant contribution to pitch-angle scattering in the interval v o k o 1, where v is the ratio of Alfve n to particle speed. In the interval o k o \ v, transit-time damping does not occur, and gyroresonance provides a small but nite contribution to particle scattering. As a consequence, the momentum di usion coefficient is mainly determined by the transit-time damping contribution. On the other hand, since the spatial di usion coef-cient and the related mean free path are given by the average over k of the inverse of these spatial D kk , transport parameters are determined by the contribution from the interval o k o \ v. We also calculate the cosmic ray transport parameters for plasma turbulence consisting of a mixture of isotropic fast-mode waves and slab Alfve n waves. Here, the momentum di usion coefficient is determined by the transit-time damping of the fast-mode waves, and is a factor ln v~1 larger than in the case of pure slab Alfve n wave turbulence. The mean free path and the spatial di usion coefficient are modied signicantly from the pure fast-mode case, since the crucial scattering at o k o \ v is now provided by gyroresonances with slab Alfve n waves. The mean free path is a constant at nonrelativistic energies, and may account for the legendary discrepancy of solar energetic particles.

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