The Weakly Nonlinear Theory

Abstract

The nonlinear theories discussed in Chap. 4 have been developed to solve the 90ý- problem or the problem of perpendicular diffusion. As shown in Chap. 3, there is a third problem that occurs if the parallel mean free path is calculated linearly for nonslab models, namely the geometry problem. The test-particle simulations provide a much shorter parallel mean free path in comparison to the linear result. By combining the formulation of quasilinear theory with the six assumptions of the NLGC theory, a new transport theory can be derived that shows agreement with test-particle simulations for parallel as well as perpendicular diffusion. This new approach, which we refer to as weakly nonlinear theory, can solve the geometry problem and the problem of perpendicular transport by providing a coupled system of Fokker-Planck coefficients. Within the weakly nonlinear formulation, it can be demonstrated that pitch-angle and perpendicular diffusion cause resonance broad- ening. Mainly the resonance broadening due to the diffusive perpendicular motion makes the pitch-angle Fokker-Planck coefficient much larger and, thus, the parallel mean free path becomes smaller for most values of the rigidity.