Numerical Studies On Resistive Wall Modes Driven By Plasma Flows

The stability of large-scale magnetohydrodynamic (MHD) modes is crucial to themagnetic confinement of toroidal plasmas. In advanced tokamaks, the maximum achievablevalue of the plasmaβ(the ratio of the plasma pressure to the magnetic field pressure) islimited by external kink modes with low toroidal mode numbers which can however bestabilized by a perfectly conducting wall of the plasma confinement device. Nevertheless thefinite resistivity of the real conducting wall can convert the external kind mode into a slowlygrowing MHD mode, called the resistive wall mode, which can partially brings the instabilityback and sets the limit for plasmaβvalue. Thus the resistive wall mode is important andhighly necessary to be studied for the advanced tokamak. In order to control the currentdriven resistive wall mode, a relative rotation between the plasma and the conducting wall isintroduced. The relative rotation and also high-speed plasma rotation induced by neutral beaminjection may generate a new flow-driven resistive wall mode. The investigation on the flowdriven resistive wall mode started in recent years in a slab geometry with an ideal MHDmodel assuming the plasma flow is uniform. In the long wavelength regime, the criticalvelocity for the resistive wall mode instability was derived. However, the evolution of modeunder various wavenumbers and effects of other parameters on the instability also needfurther studies. The effect of the plasma velocity shear on the resistive wall mode instability isalso a very realistic and need to be investigated in details. Furthermore, the effect of flowdriven resistive wall mode on the current driven kink modes and how the stbilities evolveshould be studied too.In this thesis, we first study the flow driven resistive wall mode in a slab geometry.Assuming that the plasma flow is uniform, we slove the linearized compressible MHD modelwith the viscosity and resistivity effects to study the linear growth of the resistive wallinstability and the effect of the different physical parameters on the instability numerically.Under the more realistic condition, the effect of the velocity shear on the resistive wallinstability is also further investigated. We then numerically discuss the stability of theresistive wall mode in the cylindrical plasma confined by a surface current.The contents of this thesis are arranged as follows:In Chapterâ… , the background of our research is introduced, and the methods of plasmainstability studies and other MHD instabilities are brieflydiscussed. The observation of thereisistive wall mode instability and the methods of stabilizing the resistive wall mode are alsointroduced. The previous researchs on the flow driven resistive wall mode are summerized. In Chapterâ…¡, with a uniform plasma flow in the slab geometry, the linearizedcompressible MHD model with the viscosity and resistivity effects is analyzed to discussnumerically the linear growth of the resistive wall mode instability with the different physicalparameters. We calculate the critical velocity for the instability with different wavelengths.The critical velocity in the long wavelength regime is found on the order of the ion soundspeed. It is also shown that the long wavelength mode is easily unstable, and the shortwavelength is more stable. It is on the other hand shown that the mode is more stable in theshort wavelength regime since only in a narrow region v_A＜v₀＜2^1/2v_A the criticalwavenumber is larger than kL/2π≈3.5 and less than 4.75. We obtain the critical curve in thelow velocity region and also a second critical curve for stability in the high velocity region. Itis found that the mode tends to be completely stable when the wavenumber kL/2π＞4.75. Bytaking the Laudau damping effect into account, in the low velocity region, it is found that theLaudau damping can suppress the instability. At the same time, we also find that the plasmaviscosity can suppress the resistive wall mode instability, and give the the power lawdependence of the critical velocity and mode growth rate on the viscosity. The effect of theplasmaβon the resistive wall mode is given as well.In Chapterâ…¢, the effect of a velocity shear on the flow driven resistive wall modeinstability is considered. In the uniform velocity case, the instability is generated if the flowvelocity is larger than a critical value. In comparison to the uniform case, in the low velocityregion, when there has a velocity shear, the resistive wall mode instability can still be stableeven if the peak velocity is higher than the critical velocity in the uniform case as long as thevelocity shear exceeds a threshold. In the higher velocity region, it is also found that thecritical velocity value for the nonuniform case is larger than the uniform case.In Chapterâ…£, a compressible MHD model is studied for the evolution of the resistivewall mode instability confined by a surface current. Bothδ-function and rectangulardistributions of the surface current are applied. Theδfunction distribution is studied incomparison with the reference of C. N. Lashmore-Davies [Phys. Plasmas, 8(1), 151, 2001]where the equation of state is not self-consistent. In the initial value problem, different kinkmodes are considered. It is found that there is no flow-driven resistive wall mode instabilityfor either m≥2 internal kink modes or external kink modes in this cylindrical geometry.The numerical results show that the perturbed magnetic field always oscilates evolving withtime, or damping, and the plasma flow has negligible effects on the instability. For therectangular current distribution, the thicker the surface current is, the more stable the resistivewall mode is.A brief summary then ends the thesis in the conclusion chapter.