The Second-Order QLT

Abstract

As shown in the previous chapter, the weakly nonlinear theory cannot solve the 90ý-problem of cosmic ray transport. Furthermore, previous theories that have been developed to describe pitch-angle diffusion at 90ý are not reliable or at least intractable. In this section, an alternative approach is described, which is based on quasilinear theory. By calculating corrections of the unperturbed orbit and by combining the improved particle trajectories with equations for the pitch-angle diffusion coefficient, a second-order theory can be formulated. As demonstrated here, the second-order QLT can describe pitch-angle diffusion for all values of μ in agreement with test-particle simulations. As an example, particle propagation in turbulent systems with steep wave spectra is considered.