Numerical Study On High-order Harmonics Of MHD Instabilities In Cylindrical Plasmas

Macro magnetohydrodynamic (MHD) instability may cause a large disturbance of plasms and then bring a serious damage to plasma confinement. One of the most disruptive MHD instabilities is the current driven tearing mode on the low-mode-number resonant surface. For example, the instability of q= 1 kink-type tearing modes with poloidal and toroidal mode numbers m/n= 1/1 are closely related to sawtooth oscillations. The pressure driven interchange modes play a role in limiting the accessible beta (?) value in stellarators. The interchange modes are shown to be unstable in the central region of heliotron device, which seems consistent with the m / n-1/1,2/1,3/2 modes. In the thesis, we mainly study the high-order harmonic q=1 tearing mode during the sawtooth crashes, the influence of the microscopic effect on the tearing mode, and the interchange mode in heliotron plasmas. Furthermore, the effects of plasma poloidal rotation on the MHD instabilities are discussed detailedly.In Chapter 1, an introduction of the background, the fundamental characteritics of the tearing mode and interchange mode and the work progress are presented briefly.In Chapter 2, the effects of poloidal rotation profile on tearing and Kelvin-Helmholtz (KH) instabilities in a cylindrical plasma are investigated by using a reduced MHD model. Since the poloidal rotation has different effects on the tearing and KH modes in different rotation regimes, four unstable domains are numerically identified, i.e., the destabilized tearing mode domain, stabilized tearing mode domain, stable-window domain, and unstable KH mode domain. It is also found that when the rotation layer is in the outer region of the rational surface, the stabilizing role of the rotation can be enhanced so significantly that the stable window domain is enlarged. Moreover, Alfven resonances can be induced by the tearing and KH modes in such rotating plasmas. Radially wide profiles of current and vorticity perturbations can be formed when multiple current sheets on different resonance positions are coupled together.In Chapter 3, the effects of ion diamagnetic drift on the q= 1 high-order harmonic modes in rotating tokamak plasmas are numerically investigated by using a cylindrical reduced MHD model. It is found that the ion diamagnetic drift has a stabilizing effect on the q= 1 high-order tearing modes in the small ion diamagnetic drift regime and can excite the q= 1 high-order Kelvin-Helmholtz (KH) instability in the large ion diamagnetic drift regime. The effects of ion diamagnetic drift flow on affecting the tearing modes are different from those of the poloidal E×B shear flow. Moreover, the combined effect of the two flows on tearing modes and KH modes depends on their relative direction. Finally, the ion diamagnetic drift has an influence on the sawtooth reconnection time.In Chapter 4, the effects of initial perturbation on plasmoid formation and sawtooth reconnection in cylindrical plasmas are numerically studied. The different dynamics of plasmoid formation in different resistivity regimes are systematically analyzed, and then the relevant physical mechanisms are explained in terms of the profiles of the averaged energy spectra in each resistivity regime. It is found that the decrease in the resistivity value raises the spectrum profile of high-order harmonic modes in the large wave number regimes, easily giving rise to plasmoids and complicated flow structures. The initial random phase of the perturbations tends to result in asymmetrical reconnections among secondary islands (plasmoids), m/n-1/1 magnetic island, and original magnetic field near the magnetic axis. When a higher perturbation of m/n= 2/2 mode is initially included, two m/n= 2/2 islands appear and then merge into the m / n= 1/1 island in the early nonlinear phase, which is consistent qualitatively with the experimental observation of the magnetic structure on the HT-7 tokamak. Finally, the synergetic effects of the initial perturbation amplitude and random phase on the whole nonlinear evolution are discussed.In Chapter 5, the effects of poloidal rotation profile on the resistive tearing mode and ideal/resistive interchange mode are investigated by using a reduced MHD model in current carrying heliotron plasmas. The effects of pressure profile on the interchange mode in currentless heliotron plasmas are also studied. It is found that the poloidal shear rotation has a stabilizing effect on the m /n= 1/1 resistive tearing and resistive/ideal interchange mode. However, in moderate/high ? regime, the KH instability can be excited by the large flow shear. For the current-driven mode with double rational surfaces, the m/n=1/1 mode becomes more unstable when the pressure gradient is located on the inner rational surface. The t=1 high-order harmonic mode (like m/n= 3/3 mode) becomes more unstable with the increasing ? when the pressure gradient is located on the outer rational surface. The poloidal plasma rotation with the shear layer on the inner rational surface has the strongest stabilizing effect on the current-driven mode. For the interchange mode in currentless heliotron plasmas, the pressure profiles with local flattening have a stabilizing effect on the high-m modes.Finally, in Chapter 6, the conclusions are summarized and future work is presented.