A. M. Garofalo

Chapter 3: MHD stability, operational limits and disruptions

Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

Resistive wall mode stabilization with internal feedback coils in DIII-D

A set of twelve coils for stability control has recently been installed inside the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] vacuum vessel, offering faster time response and a wider range of applied mode spectra than the previous external coils. Stabilization of the n=1 ideal kink mode is crucial to many high beta, steady-state tokamak scenarios. A resistive wall converts the kink to a slowly growing resistive wall mode (RWM). With feedback-controlled error field correction, rotational stabilization of the RWM has been sustained for more than 2.5 s. Using the internal coils, the required correction field is smaller than with the external coils, consistent with a better match to the mode spectrum of the error field. Initial experiments in direct feedback control have stabilized the RWMs at higher beta and lower rotation than could be achieved by the external coils in similar plasmas, in qualitative agreement with numerical modeling. The new coils have also allowed wall stabilization in plasmas with...

ELM suppression in low edge collisionality H-mode discharges using n = 3 magnetic perturbations

Using resonant magnetic perturbations with toroidal mode number n = 3, we have produced H-mode discharges without edge localized modes (ELMs) which run with constant density and radiated power for periods up to about 2550 ms (17 energy confinement times). These ELM suppression results are achieved at pedestal collisionalities close to those desired for next step burning plasma experiments such as ITER and provide a means of eliminating the rapid erosion of divertor components in such machines which could be caused by giant ELMs. The ELM suppression is due to an enhancement in the edge particle transport which reduces the edge pressure gradient and pedestal current density below the threshold for peeling-ballooning modes. These n = 3 magnetic perturbations provide a means of active control of edge plasma transport.

Cross-machine comparison of resonant field amplification and resistive wall mode stabilization by plasma rotation

Dedicated experiments in the DIII-D tokamak [J. L. Luxon, Nucl. Fusion, 42, 614 (2002)], the Joint European Torus (JET) [P. H. Rebut, R. J. Bickerton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985)], and the National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)] reveal the commonalities of resistive wall mode (RWM) stabilization by sufficiently fast toroidal plasma rotation in devices of different size and aspect ratio. In each device the weakly damped n=1 RWM manifests itself by resonant field amplification (RFA) of externally applied n=1 magnetic fields, which increases with the plasma pressure. Probing DIII-D and JET plasmas with similar ideal magnetohydrodynamic (MHD) stability properties with externally applied magnetic n=1 fields, shows that the resulting RFA is independent of the machine size. In each device the drag resulting from RFA slows the toroidal plasma rotation and can lead to the onset of an unstable RWM. The critical plasma rotati...

Resistive wall mode dynamics and active feedback control in DIII-D

Recent DIII-D experiments have shown that the growth of the n = 1 resistive wall mode (RWM) can be influenced by an external magnetic field applied in closed loop feedback using a six element error field correction coil (C coil). The RWM constitutes the primary limitation to normalized beta in recent DIII-D advanced tokamak plasma experiments. The toroidal rotation of DIII-D plasmas does not seem sufficient to completely suppress the RWM: a very slowly growing (growth rate γ<<1/τw) or saturated RWM is often observed at normalized beta above the no wall limit and this small RWM slows the rotation. As the rotation decreases, there is a transition to more rapid growth (γ~1/τw, where τw is the resistive time constant of the wall). The application of magnetic feedback is able to hold the RWM to a very small amplitude, prolonging the plasma duration above the no wall limit for times much longer than τw. These initial experimental results are being used to compare control algorithms, to benchmark models of the feedback stabilization process and to guide the design of an upgraded coil sensor system for stabilization of the RWM at normalized beta values closer to the ideal wall limit.

Progress toward fully noninductive, high beta conditions in DIII-D

The DIII-D Advanced Tokamak (AT) program in the DIII-D tokamak [J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986, Vol. I (International Atomic Energy Agency, Vienna, 1987), p. 159] is aimed at developing a scientific basis for steady-state, high-performance operation in future devices. This requires simultaneously achieving 100% noninductive operation with high self-driven bootstrap current fraction and toroidal beta. Recent progress in this area includes demonstration of 100% noninductive conditions with toroidal beta, βT=3.6%, normalized beta, βN=3.5, and confinement factor, H89=2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive (ECCD). The equilibrium reconstructions indicate that the noninductive current profile is well aligned, with little inductively driven current remaining anywhere in the plasma. The current balance calculation improved with beam ion redistribution that was supported by recent fast ion diagno...

Control of the resistive wall mode with internal coils in the DIII-D tokamak

Internal coils, I-Coils, were installed inside the vacuum vessel of the DIII-D device to generate non-axisymmetric magnetic fields to act directly on the plasma. These fields are predicted to stabilize the resistive wall mode (RWM) branch of the long-wavelength external kink mode with plasma beta close to the ideal wall limit. Feedback using these I-Coils was found to be more effective as compared to using external coils located outside the vacuum vessel. Locating the coils inside the vessel allows for a faster response and the coil geometry also allows for better coupling to the helical mode structure. Initial results were reported previously (Strait E.J. et al 2004 Phys. Plasmas 11 2505). This paper reports on results from extended feedback stabilization operations, achieving plasma parameters up to the regime of Cβ ≈ 1.0 and open loop growth rates of γopenτw ≳ 25 where the RWM was predicted to be unstable with only the rotational viscous stabilization mechanism. Here Cβ ≈ (β - βno-wall.limit)/(βideal.wall.limit - βno-wall.limit) is a measure of the beta relative to the stability limits without a wall and with a perfectly conducting wall, and τw is the resistive flux penetration time of the wall. These feedback experimental results clarified the processes of dynamic error field correction and direct RWM stabilization, both of which took place simultaneously during RWM feedback stabilization operation. MARS-F modelling provides a critical rotation velocity in reasonable agreement with the experiment and predicts that the growth rate increases rapidly as rotation decreases below the critical. The MARS-F code also predicted that for successful RWM magnetic feedback, the characteristic time of the power supply should be limited to a fraction of the growth time of the targeted RWM. The possibility of further improvements in the presently achievable range of operation of feedback gain values is also discussed.

Stabilization of the external kink and control of the resistive wall mode in tokamaks

One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low-n ideal magnetohydrodynamic instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Previous experiments have demonstrated that plasmas with a nearby conducting wall can remain stable to the n=1 ideal external kink above the beta limit predicted with the wall at infinity. Recently, extension of the wall stabilized lifetime τL to more than 30 times the resistive wall time constant τw and detailed, reproducible observation of the n=1 RWM have been possible in DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159] plasmas above the no-wall beta limit. The DIII-D measurements confirm characteristics common to several RWM theories. The mode is destabilized as the plasma rotation at the q=3 surfac...

Resistive wall stabilization of high-beta plasmas in DIII?D

Recent DIII?D experiments show that ideal kink-modes can be stabilized at high beta by a resistive wall, with sufficient plasma rotation. However, the resonant response to static magnetic field asymmetries by a marginally stable resistive wall mode can lead to strong damping of the rotation. Careful reduction of such asymmetries has allowed plasmas with beta well above the ideal MHD no-wall limit, and approaching the ideal-wall limit, to be sustained for durations exceeding 1?s. Feedback control can improve plasma stability by direct stabilization of the resistive wall mode or by reducing magnetic field asymmetry. Assisted by plasma rotation, direct feedback control of resistive wall modes with growth rates more than five times faster than the characteristic wall time has been observed. These results open a new regime of tokamak operation above the free-boundary stability limit, accessible by a combination of plasma rotation and feedback control.

Stability and control of resistive wall modes in high beta, low rotation DIII-D plasmas

Recent high-β DIII-D (Luxon J.L. 2002 Nucl. Fusion 42 64) experiments with the new capability of balanced neutral beam injection show that the resistive wall mode (RWM) remains stable when the plasma rotation is lowered to a fraction of a per cent of the Alfven frequency by reducing the injection of angular momentum in discharges with minimized magnetic field errors. Previous DIII-D experiments yielded a high plasma rotation threshold (of order a few per cent of the Alfven frequency) for RWM stabilization when resonant magnetic braking was applied to lower the plasma rotation. We propose that the previously observed rotation threshold can be explained as the entrance into a forbidden band of rotation that results from torque balance including the resonant field amplification by the stable RWM. Resonant braking can also occur naturally in a plasma subject to magnetic instabilities with a zero frequency component, such as edge localized modes. In DIII-D, robust RWM stabilization can be achieved using simultaneous feedback control of the two sets of non-axisymmetric coils. Slow feedback control of the external coils is used for dynamic error field correction; fast feedback control of the internal non-axisymmetric coils provides RWM stabilization during transient periods of low rotation. This method of active control of the n = 1 RWM has opened access to new regimes of high performance in DIII-D. Very high plasma pressure combined with elevated qmin for high bootstrap current fraction, and internal transport barriers for high energy confinement, are sustained for almost 2u2009s, or 10 energy confinement times, suggesting a possible path to high fusion performance, steady-state tokamak scenarios.