Synergetic Effects Of Plasma Rotation And Magnetic Feedback On Resistive Wall Modes In Tokamaks

The resistive wall mode (RWM) instability has been a major concern for advanced tokamaks, which aim at high pressure, large bootstrap current fraction, long pulse operation, such as ITER, since it limits the beta of fusion devices. The RWM can be viewed as a residual instability from the external ideal kink mode (XK), which is a global magnetohydrodynamic (MHD) instability driven by plasma current or pressure. The XK is one of the most dangerous MHD instabilities in advanced tokamaks. Luckily, the presence of a close-fitting perfectly conducting wall can stabilize the XK, while finite resistivity of the wall reduces the kink instability from the Alfvenic time scale down to the typical field penetration time through the wall. The resulting, slowly growing instability (the RWM) may be tolerable for a transient plasma pulse, but cannot be tolerated in a long-pulse (many times longer than the wall time) or a steady state pulse, because this mode, being of a global nature, usually does not reach a saturated state before causing the disruption of the discharge. The RWM can pose severe operational limits on the achievable beta values of tokamaks. In order to maximize the benefit of the concept of advanced tokamaks, stabilization of the RWM is a critical issue.It is now well established that either the plasma flow (mainly the toroidal rotation) or an active control scheme based on magnetic coils can potentially stabilize the RWM. A key theoretical question, which has so far not been well addressed, is the compatibility of the aforementioned stabilization methods, when applied for a realistic toroidal tokamak plasma. Very few, and moreover somewhat scattered study has been carried out on this issue, in both analytic theory and numerical simulations. We have carried out a systematic investigation of the synergetic effects between the plasma rotation and the magnetic feedback on the RWM stabilization by MARS code, based on a JET-like equilibrium.First, we find that feedback, combined with the plasma flow, helps to open two stability windows for the mode, as the wall moves away from the plasma. Secondly, it is found that negative phase of the feedback gain requires less critical gain amplitude when the drift kinetic effects combined with the magnetic feedback and plasma rotation. Finally, an analytic model is proposed to demonstrate the synergetic effects between the magnetic feedback and the drift kinetic damping. We find that the optimal choice of the toroidal phase of the feedback gain enhances the synergy effect, producing fully stable domain for the RWM.In chapter 1, we present a brief introduction about nuclear fusion and the MHD instabilities. It contains previous work on the resistive wall mode stability.Chapter 2 provides a short description of MARS code, combined with both toroidal flow and magnetic feedback. The core part of our formulation is the toroidal hybrid MHD-kinetic model, which combines the single-fluid MHD equations with a self-consistent drift kinetic closure for the perturbed pressure.In chapter 3, we discuss the synergetic effects of plasma rotation and magnetic feedback on resistive wall mode stability in tokamaks with fluid model. When the feedback is applied in addition to the rotational damping, we find a new stability window opens near the plasma. The width of the new stability window increases with the feedback gain. While the plasma rotation frequency affects both stability windows. The plasma resistivity can enhance the RWM stabilization in this synergetic scheme.Chapter 4 reports stabilization of resistive wall modes in tokamaks by drift kinetic effects combined with magnetic feedback. We find that the plasma resistivity significantly enlarges the stable domain, compared to that predicted by the ideal plasma model. And the negative gain phase leads to a better synergy, as the feedback enhances the mode rotation in the direction of the plasma flow.In chapter 5, we use a simple analytic model to explain the synergy between rotation and feedback. We find that the optimal choice of feedback gain phase of the upper and lower coils enhances the synergy effect, producing fully stable domain for the mode.Chapter 6 provides concluding remarks and suggests future work.