G. Z. Hao

Stabilization of the resistive wall mode instability by trapped energetic particles

A theoretical model for investigating the effect of the trapped energetic particles (EPs) on the resistive wall mode (RWM) instability is proposed. The results demonstrate that the trapped EPs have a dramatic stabilizing effect on the RWM because of resonant interaction between the mode and the magnetic precession drift motion of the trapped EPs. The results also show that the effect of the trapped EPs depends on the wall position. In addition, the stabilizing effect becomes stronger when the plasma rotation is taken into account. For sufficiently fast plasma rotation, the trapped EPs can lead to the complete stabilization of the RWM. Furthermore, the trapped EPs can induce a finite real frequency of the RWM in the absence of plasma rotation.

Kinetic effects of trapped energetic particles on stability of external kink modes with a resistive wall

Kinetic effects of trapped energetic particles (EPs) on stability of the external kink mode with a resistive wall are investigated in detail, on the basis of the theory model developed in a previous paper [G. Z. Hao, A. K. Wang, Y. Q. Liu, and X. M. Qiu, Phys. Rev. Lett. 107, 015001 (2011)]. The results indicate that, when the perpendicular beta β* of the trapped EPs exceeds a critical value βc*, a bursting fishbone-like mode (FLM) instability, with external kink eigenstructure ,can be triggered, which rapidly grows with increasing β*(>βc*), and eventually becomes a dominant instability. Detailed physical analyses are carried out, comparing radial profiles of the EPs kinetic energy for both the FLM and the conventional resistive wall mode (RWM). On the other hand, a mode conversion between the FLM and RWM can directly occur. This work also presents a systematic investigation of effects of various physical parameters on the FLM instability. An interesting new finding is the existence of multiple critical p...

Modelling toroidal rotation damping in ITER due to external 3D fields

The linear and quasi-linear plasma response to the n = 3 and n = 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, produced by the in-vessel edge localized mode control coils, is numerically studied for an ITER 15MA H-mode baseline scenario. Both single fluid and fluid-kinetic hybrid models are used. The inclusion of drift kinetic effects does not strongly alter the plasma response compared to the fluid approximation for this ITER plasma. The full toroidal drift kinetic model is also used to compute the neoclassical toroidal viscous (NTV) torque, yielding results close to that of an analytic model based on geometric simplifications. The computed NTV torque from low-n RMP fields is generally smaller than the resonant electromagnetic torque for this ITER plasma. The linear response computations show a weak core kink response, contrary to a strong kink response often computed for plasmas from present day tokamak devices. Initial value quasi-linear simulations, including various torque models, show a localized damping of the plasma toroidal flow near the edge, as a result of the applied RMP fields. This localized rotation damping can be weak or strong depending on whether a weakly unstable edge localized peeling mode is present. No qualitative difference is found between the n = 3 and n = 4 RMP field configurations, in both the linear and non-linear response results.

Combined effects of trapped energetic ions and resistive layer damping on the stability of the resistive wall mode

A dispersion relation is derived for the stability of the resistive wall mode (RWM), which includes both the resistive layer damping physics and the toroidal precession drift resonance damping from energetic ions in tokamak plasmas. The dispersion relation is numerically solved for a model plasma, for the purpose of systematic investigation of the RWM stability in multi-dimensional plasma parameter space including the plasma resistivity, the radial location of the resistive wall, as well as the toroidal flow velocity. It is found that the toroidal favorable average curvature in the resistive layer contributes a significant stabilization of the RWM. This stabilization is further enhanced by adding the drift kinetic contribution from energetic ions. Furthermore, two traditionally assumed inner layer models are considered and compared in the dispersion relation, resulting in different predictions for the stability of the RWM.

Effects of Plasma shear flow on the RWM stability in ITER

Rotational stabilization of the resistive wall mode (RWM), with varying E × B flow shear and the radial location of peak shear, is systematically investigated using the MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503), following a non-perturbative magnetohydrodynamic–kinetic hybrid approach. The equilibrium is based on a 9 MA steady state target plasma from the ITER design, except for the plasma flow profile, which is significantly varied in this study. Generally two branches of unstable n = 1 kinetic RWMs are computed (n is the toroidal mode number), depending on the flow amplitude. The first unstable branch, which is normally the more unstable one, is sensitively affected by both the local flow shear as well as the radial location of the peak amplitude of the shear. On the contrary, the second unstable branch, which is often weakly unstable, is less affected by the flow shear. Consequently, stability domains are computationally mapped out in relevant two-dimensional parameter spaces.

Stabilization of resistive wall modes in tokamaks by drift kinetic effects combined with magnetic feedback

The synergetic effects of drift kinetic resonances, the resistive layer dissipation, the magnetic feedback, and the toroidal plasma flow on the stability of the resistive wall mode are numerically investigated using a full toroidal resistive magnetohydrodynamic-kinetic hybrid stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503). It is found that the plasma resistivity, coupled with the favourable average curvature effect, can enlarge the stable domain predicted by the drift kinetic model. A synergy between the precessional drift resonance damping, the magnetic feedback and the plasma flow helps open two stability windows. The width of the inner stability window increases with the feedback gain, but decreases with the flow speed. In addition, optimization of the toroidal phase difference of the feedback gains between the upper and lower active coils can lead to a full suppression of the mode.

Bifurcation of resistive wall mode dynamics predicted by magnetohydrodynamic-kinetic hybrid theory

The magnetohydrodynamic-kinetic hybrid theory has been extensively and successfully applied for interpreting experimental observations of macroscopic, low frequency instabilities, such as the resistive wall mode, in fusion plasmas. In this work, it is discovered that an analytic version of the hybrid formulation predicts a bifurcation of the mode dynamics while varying certain physical parameters of the plasma, such as the thermal particle collisionality or the ratio of the thermal ion to electron temperatures. This bifurcation can robustly occur under reasonably large parameter spaces as well as with different assumptions, for instance, on the particle collision model. Qualitatively similar bifurcation features are also observed in full toroidal computations presented in this work, based on a non-perturbative hybrid formulation.

Resistive wall tearing mode generated finite net electromagnetic torque in a static plasma

The MARS-F code [Y. Q. Liu et al., Phys. Plasmas 7, 3681 (2000)] is applied to numerically investigate the effect of the plasma pressure on the tearing mode stability as well as the tearing mode-induced electromagnetic torque, in the presence of a resistive wall. The tearing mode with a complex eigenvalue, resulted from the favorable averaged curvature effect [A. H. Glasser et al., Phys. Fluids 18, 875 (1975)], leads to a re-distribution of the electromagnetic torque with multiple peaking in the immediate vicinity of the resistive layer. The multiple peaking is often caused by the sound wave resonances. In the presence of a resistive wall surrounding the plasma, a rotating tearing mode can generate a finite net electromagnetic torque acting on the static plasma column. Meanwhile, an equal but opposite torque is generated in the resistive wall, thus conserving the total momentum of the whole plasma-wall system. The direction of the net torque on the plasma is always opposite to the real frequency of the mo...

Kinetic calculation of the resistive wall mode and fishbone-like mode instability in tokamak

Kinetic effects of both trapped thermal and energetic particles on the resistive wall mode (RWM) and on the fishbone-like mode (FLM) are investigated in theory. Here, the trapped thermal particles include both ions and electrons. The FLM is driven by trapped energetic particles. The results demonstrate that thermal particle collisions can either stabilize or destabilize the RWM, depending on the energetic particle pressure βh. Furthermore, the critical value of βh for triggering the FLM is increased when the thermal particle contribution is taken into account. The critical value sensitively depends on the plasma collision frequency. In addition, the plasma inertia is found to have a negligible influence on the FLM.

Finite toroidal flow generated by unstable tearing mode in a toroidal plasma

The neoclassical toroidal plasma viscosity torque and electromagnetic torque, generated by tearing mode (TM) in a toroidal plasma, are numerically investigated using the MARS-Q code [Liu et al., Phys. Plasmas 20, 042503 (2013)]. It is found that an initially unstable tearing mode can intrinsically drive a toroidal plasma flow resulting in a steady state solution, in the absence of the external momentum input and external magnetic field perturbation. The saturated flow is in the order of 0.5% ωA at the q=2 rational surface in the considered case, with q and ωA being the safety factor and the Alfven frequency at the magnetic axis, respectively. The generation of the toroidal flow is robust, being insensitive to the given amplitude of the perturbation at initial state. On the other hand, the flow amplitude increases with increasing the plasma resistivity. Furthermore, the initially unstable tearing mode is fully stabilized by non-linear interaction with the self-generated toroidal flow.