Some Physical Problems Of Tearing Modes In Tokamak Plasmas

Macro magnetohydrodynamic (MHD) instability may cause serious damage to plasma confinement. Tearing mode (TM) is one of dangerous MHD instabilities, which has been frequently observed in the Tokamak experiment. For instance, the instabilities of q=1kink-type tearing modes with poloidal and toroidal mode numbers m/n=1/1are closely related to sawtooth oscillations, and double tearing mode (DTM) can induce off-axis sawteeth in the reversed magnetic shear (RMS) configuration. In this thesis, we adopt the reduced MHD model to study the high-order harmonic q=1tearing mode generation during sawtooth crashes and the collisionless double tearing modes in the RMS configuration. Moreover, the effects of plasma rotation on the tearing instabilities are discussed in detail.In Chapter Ⅰ, a brief introduction of the magnetic field configuration of tokamak device, MHD equilibrium and instabilities are presented.In Chapter Ⅱ, the reduced collisionless MHD model including the electron inertia term in Ohm’s law is employed to investigate the effect of q-profiles on the excitation of high-order harmonic q=1tearing modes which has been observed during sawtooth crashes in HT-7tokamak. It is found that for a flat q-profile in the core region, the high-order harmonics, such as m/n=2/2and/or m/n=3/3modes that are comparable to or even stronger than the m/n=1/1component, can be excited during tokamak sawteeth. The basic feature of the magnetic island structures in the nonlinear evolution is consistent qualitatively with the experimentally reconstructed phenomenon.In Chapter III, within the framework of a reduced collisionless MHD model taking into account the collisionless effects including electron inertia, electron pressure gradient and electron viscosity, the broad linear spectra and the scaling power laws of the linear growth rate of DTM with various rational surface separations△rs and various mode numbers are numerically studied in the cylindrical geometry. It is found that, the high-order harmonics modes or the short wave length modes can be easily excited in the following case:(a) for the q-profile with small△r,(b)when the safety factor value between two rational surfaces is quite close to the mode’s helicity q(rs1≤r≤rs2)�'hs=m/n,(c) by taking into account the collisionless effects. The scaling laws of the fast growth of collisionless double tearing modes in the linear phase can be summarized as follows:As the rational surface separation△rsv or the mode number m increases, the scalings on resistivity SHp-1, electron inertial skin depth de and electron viscosity R-1change gradually from the large△’ non-constant-ψ tearing mode scalings～SHp-1/3,-de1and～R-1/5to small△’ constant-ψ tearing mode scalings～SHp-3/5,～de3and～R-1/3Furthermore, when the ion sound gyroradius is large ρs≥de, the scaling of the linear growth rate on de and ρs changes gradually from γ～de1/3ρs2/3to～de1ρs1,as Δrs or m number increases.In Chapter Ⅳ, the reduced resistive MHD model including poloidal plasma rotation is employed to investigate the error field penetration with tearing instability parameter Δ’<0and to study each-order harmonic q=1tearing mode during sawtooth reconnection. The results can be summarized as follows:(a) For the error field induced forced reconnection with tearing instability parameter Δ’<0, the penetration of the edge error field can be suppressed by the plasma rotation. When rotation frequency is large, two well separated current sheets will be excited on both sides of the rational surface where the Alfven resonance condition is satisfied. Thus, the penetrated error field on the rational surface is reduced and the forced reconnection is suppressed,(b) For the constant-ψ tearing mode with a△’～1. the growth rate varies non-monotonically with the rotation shear. The tearing mode will be destabilized in the small rotation shear regime and be stabilized in the large rotation shear regime. Moreover, the Kelvin-Helmholtz instability is easily excited when the rotation shear is large,(c) The m=1non-constant-Ψ tearing mode with large Δ’ can be stabilized by the large rotation shear. But the each-order harmonic q=1tearing mode could not be easily stabilized by the plasma rotation, since the m=1mode or the destabilized high-order harmonic q=1tearing mode will dominate if the rotation is small, while the Kelvin-Helmholtz instability can be excited in the large rotation regime.In Chapter Ⅴ, the effects of plasma rotation on the DTM instabilities are investigated by using the reduced resistive MHD model. We reveal a new mechanism of suppressing the DTM instability due to the self-induced Alfven resonance in rotating tokamak plasmas: tearing instability on the outer rational surface rs2will induce two Alfven resonances on both sides of the inner rational surface rs1which shields the tearing instability on rs1, then the linear growth rate is reduced from～SHp-1/3of the fast DTM regime to～SHp-3/5of the slow single tearing mode regime. When the rotation shear layer is located on the outer rational surface rs2the shear between two rational surfaces and the rotation shear on rs2have the synergetic effect on suppressing the DTM. It is found that the Alfven resonances on both sides of the inner rational surface rs1decouple the strongly coupled DTMs, and simultaneously the flow shear further stabilizes the tearing instability on the outer rational surface rs2. When the tearing instability on rs2is stabilized so significantly that it becomes less unstable than the original one on rs1, a mode transition occurs, in which the tearing instability excitation switches from rs2to rs1and meanwhile the Alfven resonances switch from both sides of rs1to both sides of rs2.Finally, a brief summary and conclusions end the thesis.