Theory And Simulation Of The Effects Of External Resonant Magnetic Perturbations On Resistive Tearing Mode And Plasma Response

In this thesis, effects of resonant magnetic perturbations on rotating tearing unsta-ble and static, tearing stable plasma are investigated from theory analysis and numerical simulations.First, we demonstrate in theory that both tearing mode locking and magnetic is-land suppression by resonant magnetic perturbations (RMPs) can be described using the well-known error-field model, which is governed by the torque balance and the nonlin-ear island evolution. Particularly, mode locking can be viewed as the exact steady state of this system. A new exact analytic solution has been obtained for such a steady state, which represents the relation between the island width (phase) of the locked mode and the RMP amplitude. Furthermore, we found that two different branches of the steady states exist in the analytical solution and the branch with suppressed island width is always unstable. On the other hand, the system also admits stable states of island sup-pression achieved via the RMP modulation of island frequency. In general, the island would be steadily suppressed by RMPs on time average until the RMP amplitude above a certain threshold. When the RMP amplitude is above such a threshold, the island suppression is transient and the tearing mode eventually gets locked.Second, the physics origin for the difference between mode locking and unlocking thresholds for tearing modes is illustrated from theory analysis and a numerical pro-cedure is developed to find both locking and unlocking thresholds. We derived a new scaling law for the unlocking threshold from the lowest amplitude of the RMP allowed for the locked mode solution. The criterion for phase-flip instability is extended to identify the entire locked-mode states above the unlocking threshold. When the RMP amplitude is above the unlocking threshold, the accessibility of the locked-mode states separates the RMP amplitude into two different regimes. The locked-mode state may or may not be accessible depending on the initial conditions of an evolving island in the first regime. In the second one, the locked-mode state can always be reached re-gardless of the initial conditions of the tearing mode and the lowest RMP amplitude for this regime is determined to be the mode locking threshold. Physics origin of the gap between the mode locking and unlocking thresholds, as well as the closely related and widely observed hysteresis phenomena in island evolution during the sweeping RMP amplitude, is revealed by the different characteristics of the two regimes above the un-locking threshold.At last, based on our previous analytical theory, nonlinear plasma response theory of the steady state is given in this thesis. The nonlinear effect demonstrates its impor- tance only in the large RMP amplitude regime due to the positive correlation between the island width and the RMP amplitude. Nonlinear simulation of the plasma response is used to validating our nonlinear response theory via the extended MHD code NIM-ROD. On the other hand, linear simulation results in single fluid model show that a seed magnetic island can be formed in a static plasma even when the RMP amplitude is very low.