Understanding particle and energy transport problems is one of the most important tasks for the realization of a successful tokamak fusion reactor. In this thesis, among the various sources causing tokamak transport, nonlinear diffusion phenomena induced by the combined effects of weak nonaxisymmetric ripple fields and coulomb collisions between charged particles are studied. The principal motivation for the present study is from the fact that there has been no firm and rigorous theoretical framework for understanding these nonlinear diffusion processes.
To set the theoretical background, fundamental concepts concerning Hamiltonian dynamical systems are described. KAM (Kolmogorov-Arnol`d-Moser) theory, resonance and stochastic phenomena, transport process occurring in a stochastic region of a phase space, and anomalous transport theories are briefly reviewed and explained. We then launch a new theory: modification of phase space transport in the presence of extrinsic noise.
In the first part of the thesis, we investigate analytically the diffusion behaviors by extrinsic noise in two area preserving web mappings, i.e., the kicked Harper and Toggle mappings, where the phase space is divided into infinitely periodic two dimensional tiles.It has been found that significant enhancement of extrinsic diffusion rate is possible by the cross-interaction between the underlying Hamiltonian vortical flow and applied extrinsic noise.
In the second part of the thesis, we concentrate on the so-called ripple transport problem in tokamaks. Poincar$é$ mapping can be obtained by integrating the motions of banana trapped ions during one bounce period, to which extrinsic noise terms are added to model the effects of coulomb collisions.In the absence of extrinsic noise effects, the phase space of Poincar$é$ mapping is found to be characterized by the coexisting KAM and web structures. As expected, it has been observed that for the sufficiently large ripple strength,...