Simulation Studies Of Tearing Mode And Sawtooth Oscillation In Tokamaks

In tokamak plasma,the MHD instabilities such as tearing mode,double tearing mode,sawtooth oscillation are the most urgent problems,they can destroy seriously the magnetic surface structure and result in degradation of the plasma confinement or even disruption.Therefore,it is important to study the physical mechanisms and the controlling methods of MHD instabilities in order to achieve the controlled thermal fusion.In the thesis,the effects of RMPs(Resonant Magnetic Perturbations)on tearing mode and sawtooth and the nonlinear evolution of double tearing mode are studied by CLT code,which solves a full set of MHD equations in cylindrical coordinate system(R,φ,Z)and can automatically include the toroidal effect.It can study the MHD instabilities more comprehensively.For the effect of the RMPs on the tearing mode,it is found that the magnetic islands entered into an oscillated state with a low amplitude of RMP.However,for a higher amplitude,it brakes the rotation of magnetic islands and results in locked mode.With applied single m/n=2/1RMP,the mode locking threshold increases with the increasing of the toroidal rotation frequency and the ramp-up time of the RMPs.It can contribute to the locked mode with multiple harmonics of RMPs applied.The results show that the m/n=3/1(m is the poloidal toroidal number)and m/n=4/2 RMPs along with the m/n=2/1 RMPs can increase both the m/n=2/1 perturbation and its higher-harmonics through the mode coupling due to both the toroidal and nonlinear effects,but it becomes more effective if the m/n=4/2 RMPs is imposed directly.The m/n=3/1 RMPs in-phase(anti-phase)with the m/n=2/1 RMPs leads to a positive(negative)contribution to intensification of the m/n=2/1 tearing mode and the mode locking.For the nonlinear evolution of the m/n=2/1 double tearing mode,firstly,it is found that for both medium and large separations between the two rational surfaces,the double tearing mode can exhibit a rapid growth in the nonlinear stage with the increasing magnetic shear strength at the outer rational surface.Then,the effects of the radial locations and the magnetic shear strength of the inner and outer rational surface as well as the safety factor at the magnetic axis on the double tearing mode are investigated systematically.It is found that for a large separation or a weak shear strength of the two rational surfaces or the low q value at the magnetic axis,the inner and outer magnetic islands grow independently and then saturate in the end,and the half of the sum of the inner and outer magnetic island width is always below the separation between the two rational surfaces.On the contrary,the inner and outer magnetic islands exhibit an explosive burst growth in the early nonlinear period following falls off rapidly due to strong interaction with each other,and the half of the sum of the inner and outer magnetic island width is always larger than the separation between the two rational surfaces.For the influence of RMPs on sawtooth oscillation in an ITER configuration,the results shows that the sawtooth can be controlled by applied either the n=1 RMPs or the n=2RMPs.The occurrence of the m/n=2/1 magnetic islands can contribute to the sawtooth suppression.With the equilibrium toroidal flow,the period and amplitude of sawtooth decreases obviously when both the m/n=2/1 and m/n=1/1 modes are locked.The locked m/n=2/1 magnetic islands interact with the m/n=2/2 mode to contribute to the sawtooth suppression.It is also suggests the m/n=2/1magnetic islands have a significant role for the sawtooth suppression.Moreover,the plasma shielding effect caused by equilibrium toroidal flow can weaken the sawtooth reduction.At last,through the investigation of the effects of different applied RMPs on the sawtooth oscillation,it is found that with simultaneously applied n=1 and n=2 RMPs is the best,since multiple harmonics of RMPs can weak the shielding effect due to the toroidal effect.