Hall Effect On Tearing Mode Instabilities In Tokamak

It is widely accepted that tearing mode instabilities play an important role in both space and laboratory plasmas. Tearing mode instability leads to topological change of magnetic fields. During this process,magnetic energy is converted into kinetic energy and thermal energy. Tearing mode instability is considered to be the primary cause for the degradation of the plasma confinement in the magnetic confined fusion device such as Tokamak. Investigations of tearing mode instability are crucial to realize controlled nuclear fusion.A three-dimensional toroidal geometry tokamak MHD simulation code (CLT) was developed to study tearing mode instabilities in Tokamak. CLT is further upgraded from second-order to fourth-order accuracy in space and the edge region is optimized. The new version of CLT is largely improved in both accuracy and numerical stability. CLT can be used to handle strong nonlinear MHD instabilities such as sawtooth and to study influences of Hall effect, current driven, and RMP on tearing mode instabilities.We have studied influences of Hall effect on tearing mode instabilities. It is indicated that electron diamagnetic effect is self-consistently contained in Hall-MHD equations. The mangetic perturbation resulted from tearing mode instability rotates in the direction of electron diamagnetic velocity and its frequency is slightly smaller than electron diamagnetic frequency. It is also found that the linear growth rate increases with increase of ion skin depth. Since magnetic perturbation rotates due to Hall effect, Hall effect on double tearing mode instability should be considered. Due to different pressure gradients on the two resonant surfaces, the magnetic perturbations on two resonant surfaces will rotate with different velocities, which lead to the failure of mutual excitation. Therefore, the growth rate is much smaller than that without Hall effect.The sawtooth oscillation is a common signature for tokamak devices with q<1. The m/n=1/1 resistive kink mode instability is considered to be the major driven source. The sawtooth oscillation has been studied for several decades, however, there is no model that can successfully explain all phenomena of sawtooth oscillations. Without Hall effect, magnetic perturbation remains relative symmetry during sawtooth oscillations. It is found that there exists a magnetic axis that acts as a damping role, which leads to decay of sawtooth oscillation to small oscillation after a few of periods. With Hall effects, the magnetic perturbation rotates due to electron diamagnetic drifting effect, which weakens the damping of sawtooth. Thus, the periodicity of the sawtooth is significantly improved by Hall effect.Resonant magnetic perturbations (RMP) can be used to control tearing mode instability and suppress edge localized mode. The error fields are unavoidable in Tokamaks. Its Fourier component will induce finite size magnetic islands on the resonant surfaces, which may cause neo-classical tearing mode instability.Therefore, it is worthwhile to study RMP on tearing mode instabilities in Tokamak. During the simulations,the phenomenon of 'mode locking' is observed. It is found that the amplitude and the frequency of RMP determine whether the 'mode locking' takes place. The amplitude of RMP plays a positive role while the frequency shows a negative effect on mode-locking, which is in good agreement with previous results.