Modeling of feedback and rotation stabilization of the resistive wall mode in tokamaks

Abstract

Steady-state operation of the advanced tokamak reactor relies on maintaining plasma stability with respect to the resistive wall mode (RWM). Active magnetic feedback and plasma rotation are the two methods proposed and demonstrated for this purpose. A comprehensive modeling effort including both magnetic feedback and plasma rotation is needed for understanding the physical mechanisms of the stabilization and to project to future devices. For plasma with low rotation, a complete solution for the feedback issue is obtained by assuming the plasma obey ideal magnetohydrodynamics (MHDs) and utilizing a normal mode approach (NMA) [M.S. Chu, et al., Nucl. Fusion 43, 441 (2003)]. It is found that poloidal sensors are more effective than radial sensors and coils inside of the vacuum vessel more effective than outside. For plasmas with non-negligible rotation, a comprehensive linear non-ideal MHD code, the MARS-F has been found to be suitable. MARS-F [Y.Q. Liu, et al., Phys. Plasmas 7, 3681 (2000)] has been benchmarked in the ideal MHD limit against the NMA. Effect of rotation stabilization of the plasma depends on the plasma dissipation model. Broad qualitative features of the experiment are reproduced. Rotation reduces the feedback gain required for RWM stabilization. Reduction is significant when rotation is near the critical rotation speed needed for stabilization. International Thermonuclear Experimental Reactor (ITER) [R. Aymar, et al., Plasma Phys. Control. Fusion 44, 519 (2002)] (scenario IV for advanced tokamak operation) may be feedback stabilized with β above the no wall limit and up to an increment of ~50% towards the ideal limit. Rotation further improves the stability.

Chapter 3: MHD stability, operational limits and disruptions

“…Burning fusion plasmas, lacking the large neutral beam torque of present experiments, may not reach the critical rotation frequency for RWM stabilization. Modelling with the MARS code [132,133,195] indicates that in the regime of subcritical plasma rotation, both feedback control and rotation can contribute to stability [169,196]. As the rotation becomes small, stabilization must rely on feedback alone.…”

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

“…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. 3,15,[28][29][30][31][32][33][34][35][36][37] The latter means that the wall is described as resistive, but with utmost simplicity assuming that the induced electric field E is constant across the wall. This is a step ahead compared to the ideal-wall or no-wall approaches but can be justified for slow modes only with xs sk < 1, where s sk l 0 rd 2 w ;…”

Control of linear modes in cylindrical resistive magnetohydrodynamics with a resistive wall, plasma rotation, and complex gain

“…1,2,5, 7,8,[11][12][13]17,18,20,23,26,28 Studies have also been performed for reversed field pinches (RFPs). 4, 39,40 Earlier studies in tokamak geometry 3, 6,9,10,14,30,38 investigated sensing either the radial or the poloidal component of the magnetic field, concluding that it is better to sense the poloidal component, and that the latter measurement is of more use if it is inside the wall. 14,38 Results in Refs.…”