International School of Cosmic Ray Astrophysics <<Maurice M. Shapiro>>

21^st Course: Astroparticle Physics: Yesterday, Today, and Tomorrow
1-7 August, 2018

For linear MHD plasma waves the ordering B0  B  E, necessary for explaining the observed nearly isotropic cosmic ray momentum distribution functions, is the basis for a quasilinear perturbation scheme. This perturbation scheme leads to the small cosmic ray anisotropy and to the diusion-convection cosmic ray transport equation for the isotropic part of the cosmic ray distribution function. Augmented with the continuous and catastrophic momentum loss rates, the diusion-convection cosmic ray transport equation describes all electromagnetic acceleration and transport processes discussed today, including diusive shock acceleration and stochastic acceleration. The determination of the cosmic ray transport parameters (spatial and momentum diusion coecients, spatial and momentum convection rates) requires the knowledge of the second-order correlation functions of electromagnetic uctuations, either from observations in the interplanetary medium or from uctuation theory. By expanding in terms of the eigenfunctions of the spatial diusion operator the solu- tion of the diusion-convection transport equation can be expressed as an innite sum where the momentum dependent expansion coecients obey simpler leaky-box equa- tions. The conditions for generating power-law distribution functions are discussed.