A relation between cosmic-ray fluctuations, gradient, and diffusion coefficient

The motion of charged particles in a stochastic magnetic field is considered via a generalized quasi-linear expansion of Liouville's equation. The result is an equation relating cosmic-ray scintillations to particle gradients and to magnetic-field fluctuations (or diffusion coefficient). The resulting theory may be regarded as an example of a fluctuation-dissipation phenomenon, in which the diffusion coefficient plays the role of the dissipative parameter. The resonant interaction between particles and the random interplanetary magnetic field is considered explicitly, and it is shown that observed scintillations of high-energy (about 1 GeV) cosmic rays may be reasonably explained by the model.