Physics of resistive wall modes

Abstract

The advanced tokamak regime is a promising candidate for steady state tokamak operation which is desirable for a fusion reactor. This regime is characterized by a high bootstrap current fraction and a flat or reversed safety factor profile, which leads to operation close to the pressure limit. At this limit, an external kink mode becomes unstable. This external kink is converted into the slowly growing Resistive Wall Mode (RWM) by the presence of a conducting wall. Reduction of the growth rate allows one to act on the mode and to stabilize it. There are two main factors which determine the stability of the RWM. The first factor comes from external magnetic perturbations (error fields, resistive wall, feedback coils, etc). This part of RWM physics is the same for tokamaks and reverse field pinch (RFP)configurations. The physics of this interaction is relatively well understood and based on classical electrodynamics. The second ingredient of RWM physics is the interaction of the mode with plasma flow and fast particles. These interactions are particularly important for tokamaks, which have higher plasma flow and stronger trapped particle effects. The influence of the fast particles will also be increasingly more important in ITER and DEMO which will have a large fraction of fusion born alpha particles. These interactions have kinetic origins which make the computations challenging since not only particles influence the mode, but also the mode acts on the particles. Correct prediction of the "plasma-RWM" interaction is an important ingredient which has to be combined with external fields influence (resistive wall, error fields and feedback) to make reliable predictions for RWM behavior in tokamaks. All these issues are reviewed in this paper.2

Controlling sawtooth oscillations in tokamak plasmas

“…The ICRH fast ions lead to long sawtooth periods, but despite the presence of these highly energetic ions, the ECCD is able to drop the sawtooth period back to a level approaching that observed in Ohmically heated plasmas when the deposition is optimally located just inside the q = 1 surface. Similarly, ECCD destabilisation has also been achieved in the presence of ICRH accelerated NBI ions in ASDEX Upgrade [144] as well as with normal NBI fast ions in ASDEX Upgrade [119], JT-60U [129] and HL-2A [145]. Despite these promising results, destabilisation of monster sawteeth in the presence of a significant population of highly energetic particles at high β h has yet to be demonstrated and remains a key goal of ongoing sawtooth control activity.…”

Rotational stabilization of the resistive wall modes in tokamaks with a ferritic wall

“…[1][2][3][6][7][8][9][10][11][12][13][14][15][19][20][21] Sometimes, an explanation is offered that at large enough angular rotation frequency x of the mode the wall would behave as a perfect conductor. 12,13,[22][23][24][25][26][27] However, with this simple picture, one cannot explain why the ideal wall stability limit is not recovered in experiments. In a search of more plausible reasons aside from ideal plasmas or walls, several theories for the rotational stabilization have been proposed that rely on some dissipation in the plasma and incorporate a magnetically thin wall.…”

On Lyapunov boundary control of unstable magnetohydrodynamic plasmas

“…σ is the conductivity of the wall. The last volume integral in (13) can be transformed in a surface integral…”