The acceleration of fast particles by Alfvén and magnetic sound waves of small amplitude is considered. The waves exist against the background of a strong, uniform magnetic field. We take into accunnt the contributions to acceleration from a large scale random field (harmonics withk<R −1, whereR is the Larmor radius), as well as from a small scale field (k>R −1). The small scale field was considered by perturbation theory, while large scale random field-in an adiabatic approximation. The energy dependence of the diffusion coefficient in momentum space, and the time of acceleration are estimated. The possible anisotropy of angular distribution is taken into account.
If the Alfvén waves have spectral power index ν>2 and wave amplitude is small enough, then the energy dependance of the diffusion coefficient is stronger than in the case of the Fermi acceleration. For magnetic sound waves with ν≥2 the energy dependance of the diffusion coefficient is the same as for the Fermi acceleration, but for ν<2 this dependance is less.
The space diffusion coefficient of particles across the regular magnetic field is estimated. It is shown that this diffusion is due mainly to the large scale random field.
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Toptygin, I.N. Interaction of fast particles with magneto-hydrodynamical turbulence. Astrophys Space Sci 20, 351–371 (1973). https://doi.org/10.1007/BF00642208
- Magnetic Field
- Diffusion Coefficient
- Perturbation Theory
- Angular Distribution