J. Bialek

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.

Principal physics developments evaluated in the ITER design review

As part of the ITER Design Review and in response to the issues identified by the Science and Technology Advisory Committee, the ITER physics requirements were reviewed and as appropriate updated. The focus of this paper will be on recent work affecting the ITER design with special emphasis on topics affecting near-term procurement arrangements. This paper will describe results on: design sensitivity studies, poloidal field coil requirements, vertical stability, effect of toroidal field ripple on thermal confinement, material choice and heat load requirements for plasma-facing components, edge localized modes control, resistive wall mode control, disruptions and disruption mitigation.

Equilibrium properties of spherical torus plasmas in NSTX

Research in NSTX has been conducted to establish spherical torus plasmas to be used for high ?, auxiliary heated experiments. This device has a major radius R0 = 0.86?m and a midplane halfwidth of 0.7?m. It has been operated with toroidal magnetic field B0 ? 0.3?T and Ip ? 1.0?MA. The evolution of the plasma equilibrium is analysed between discharges with an automated version of the EFIT code. Limiter, double null and lower single null diverted configurations have been sustained for several energy confinement times. The plasma stored energy reached 92?kJ (?t = 17.8%) with neutral beam heating. A plasma elongation in the range 1.6 ? ? ? 2.0 and a triangularity in the range 0.25 ? ? ? 0.45 have been sustained, with values of ? = 2.6 and ? = 0.6 being reached transiently. The reconstructed magnetic signals are fitted to the corresponding measured values with low errors. Aspects of the plasma boundary, pressure and safety factor profiles are supported by measurements from non-magnetic diagnostics. Plasma densities have reached 0.8 and 1.2 times the Greenwald limit in deuterium and helium plasmas, respectively, with no clear limit encountered. Instabilities including sawteeth and reconnection events, characterized by Mirnov oscillations, and a perturbation of the Ip, ? and li evolutions, have been observed. A low q limit was observed and is imposed by a low toroidal mode number kink instability.

Study of in-vessel nonaxisymmetric ELM suppression coil concepts for ITER

Large Type-I edge-localized mode (ELM) heat pulses may limit the life of divertor targets in a burning plasma. Recent experiments show that pitch-resonant nonaxisymmetric magnetic perturbations of the plasma edge of 0.0005 or less of the main magnetic field offer a useful solution, but there is little room in the presently designed ITER for even small perturbation coils. We present proposed coil requirements for ITER ELM suppression, derived primarily from DIII-D ELM suppression experiments. We show by calculated examples that large arrays of coils (e.g. four toroidal rows of nine coils each) on the outboard wall near the plasma (at the radius of the blanket-vacuum vessel interface R ~ 8 m) can meet the known requirements, expressed in terms of the toroidal helical Fourier harmonic spectrum, for both low- and high-q ITER plasmas, when coil currents are distributed to concentrate the magnetic perturbation into a single dominant Fourier spectral peak. Fields from arrays of less than four rows of nine coils (a) penetrate relatively more strongly into the core plasma, and (b) generate more and larger nonresonant spectral peaks. Both features are expected to brake desirable plasma rotation. We found that the Moire effect from approximating sinusoidal perturbations by a limited discrete coil set can be used to control nonfundamental harmonics in large arrays. We show that a judicious choice of current distribution among the coils ameliorates effects of an 80° toroidal gap where no coils are allowed in the ITER midplane.

Active feedback stabilization of the resistive wall mode on the DIII-D device

A proof of principle magnetic feedback stabilization experiment has been carried out to suppress the resistive wall mode (RWM), a branch of the ideal magnetohydrodynamic (MHD) kink mode under the influence of a stabilizing resistive wall, on the DIII-D tokamak device [Plasma Phys. and Contr. Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The RWM was successfully suppressed and the high beta duration above the no wall limit was extended to more than 50 times the resistive wall flux diffusion time. It was observed that the mode structure was well preserved during the time of the feedback application. Several lumped parameter formulations were used to study the feedback process. The observed feedback characteristics are in good qualitative agreement with the analysis. These results provide encouragement to future efforts towards optimizing the RWM feedback methodology in parallel to what has been successfully developed for the n = 0 vertical positional control. Newly developed MHD codes have been extremely useful in guiding the experiments and in providing possible paths for the next step.

Advances in global MHD mode stabilization research on NSTX

Stabilizing modes that limit plasma beta and reduce their deleterious effect on plasma rotation are key goals for the efficient operation of a fusion reactor. Passive stabilization and active control of global kink/ballooning modes and resistive wall modes (RWMs) have been demonstrated on NSTX and research is now advancing towards understanding the stabilization physics and reliably maintaining the high beta plasma for confident extrapolation to ITER and a fusion component test facility based on the spherical torus. Active n = 1 control experiments with an expanded sensor set, combined with low levels of n = 3 field phased to reduce error fields, reduced resonant field amplification and maintained plasma rotation, exceeded normalized beta = 6 and produced record discharge durations limited by magnet system constraints. Details of the observed RWM dynamics during active control show the mode being converted to a rotating kink that stabilizes or saturates and may lead to tearing modes. Discharges with rotation reduced by n = 3 magnetic braking suffer beta collapse at normalized beta = 4.2 approaching the no-wall limit, while normalized beta greater than 5.5 has been reached in these plasmas with n = 1 active control, in agreement with the single-mode RWM theory. Advanced state-space control algorithms proposed for RWM control in ITER theoretically yield significant stabilization improvements. Values of relative phase between the measured n = 1 mode and the applied correction field that experimentally produce stability/instability agree with RWM control modelling. Experimental mode destabilization occurs over a large range of plasma rotation, challenging the notion of a simple scalar critical rotation speed defining marginal stability. Stability calculations including kinetic modifications to the ideal MHD theory are applied to marginally stable experimental equilibria. Plasma rotation and collisionality variations are examined in the calculations. Intermediate rotation levels are less stable, consistent with experimental observations. Trapped ion resonances play a key role in this result. Recent experiments have demonstrated magnetic braking by non-resonant n = 2 fields. The observed rotation damping profile is broader than found for n = 3 fields. Increased ion temperature in the region of maximum braking torque increases the observed rate of rotation damping, consistent with the theory of neoclassical toroidal viscosity at low collisionality.

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...

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 stabilized operation in rotating high beta NSTX plasmas

The National Spherical Torus Experiment (NSTX) has demonstrated the advantages of low aspect ratio geometry in accessing high toroidal and normalized plasma beta, and βN ≡ 10 8〈βt〉 aB0/Ip. Experiments have reached βt = 39% and βN = 7.2 through boundary and profile optimization. High βN plasmas can exceed the ideal no-wall stability limit, βNno-wall, for periods much greater than the wall eddy current decay time. Resistive wall mode (RWM) physics is studied to understand mode stabilization in these plasmas. The toroidal mode spectrum of unstable RWMs has been measured with mode number n up to 3. The critical rotation frequency of Bondeson-Chu, Ωcrit = ωA/(4q2), describes well the RWM stability of NSTX plasmas when applied over the entire rotation profile and in conjunction with the ideal stability criterion. Rotation damping and global rotation collapse observed in plasmas exceeding βNno-wall differs from the damping observed during tearing mode activity and can be described qualitatively by drag due to neoclassical toroidal viscosity in the helically perturbed field of an ideal displacement. Resonant field amplification of an applied n = 1 field perturbation has been measured and increases with increasing βN. Equilibria are reconstructed including measured ion and electron pressure, toroidal rotation and flux isotherm constraint in plasmas with core rotation ω/ωA up to 0.48. Peak pressure shifts of 18% of the minor radius from the magnetic axis have been reconstructed.

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...