The Effects of Nonlinear Terms in Cosmic-Ray Diffusion Theory

A heuristic method of including the effects of nonlinear terms in the derivation of the interaction between cosmic rays and stochastic magnetic fields is presented. The nonlinear terms in the Liouville equation are subsumed into a quasi-phenomenological stochastic scattering term. The resulting theory is similar to quasilinear theory except for the replacement of delta functions in wavenumber with broadened resonance functions. The model indicates that nonlinear terms damp out the initial-value terms, broaden cyclotron resonances, provide scattering for particles with pitch angles near 90 , and set limits on the region of validity of the commonly adopted quasi-linear approximation. An important result is that the ratio K1/K11 of the perpendicular to parallel spatial diffusion coefficient for particles with scattering length much larger than the correlation scale of the magnetic irregularities is equal to the relative mean-squared field fluctuation, \ B2AIB02 0.2. Subject headings: cosmic rays - hydromagnetics - interplanetary medium