Cosmic rays in a random magnetic field: Breakdown of the quasilinear derivation of the kinetic equation
The problem of deriving a kinetic equation for the cosmic ray distribution function in a random magnetic field is considered. A model is adopted which is mathematically simple but which contains the essential physics. The perturbation expansion upon which the quasi-linear treatment is based is investigated. The existence of resonant particles causes the breakdown of the adiabatic approximation frequently used in this theory. Resonant particles cause a general secular growth of higher order terms in the expansion which invalidates the entire perturbative approach.