Yueqiang Liu

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.

Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model

Active feedback stabilization of pressure-driven modes in tokamaks is studied computationally in toroidal geometry. The stability problem is formulated in terms of open-loop transfer functions for fluxes in sensor coils resulting from currents in feedback coils. The transfer functions are computed by an extended version of the MARS stability code [A. Bondeson et al., Phys. Fluids B 4, 1889 (1992)] and can be accurately modeled by low order rational functions. In the present paper stability is analyzed for a system with an ideal amplifier (current control). It is shown that feedback with modest gain, and a single coil array poloidally, gives substantial stabilization for a range of coil shapes. Optimum design uses sensors for the poloidal field, located inside the resistive wall, in combination with rather wide feedback coils outside the wall. Typically, the feedback does not strongly modify the plasma-generated magnetic field perturbation. A future companion paper [C. M. Fransson et al., Phys. Plasmas (ac...

Resonant magnetic perturbation experiments on MAST using external and internal coils for ELM control

Experiments have been performed on MAST using both external (n = 1, 2) and internal (n = 3) resonant magnetic perturbation (RMP) coils. ELM suppression has not been achieved even though vacuum modelling shows that either set of coils can produce a region (ΔΨpol > 0.17), for which the Chirikov parameter is greater than 1, wider than that correlated with ELM suppression in DIII-D. Although complete ELM suppression has not been achieved, application of RMPs has triggered ELMs in ELM free H-mode periods (n = 3) and increased the ELM frequency in regularly ELM-ing discharges (n = 2, 3). In addition, the application of RMPs in an n = 3 configuration has produced large changes to the edge turbulence in L-mode discharges.

Toroidal self-consistent modeling of drift kinetic effects on the resistive wall mode

A self-consistent kinetic model is developed to study the stability of the resistive wall mode in toroidal plasmas. This model is compared with other models based on perturbative approaches. The degree of the kinetic modification to the stability of the mode depends on the plasma configurations. Both stabilizing and destabilizing kinetic effects are observed. The nonperturbative approach, with a self-consistent inclusion of the eigenfunctions and the eigenvalues of the resistive wall mode, normally finds less stabilization than the perturbative approach.

Full toroidal plasma response to externally applied nonaxisymmetric magnetic fields

The plasma response to resonant magnetic perturbation (RMP) and nonresonant perturbation fields is computed within a linear, full toroidal, single-fluid resistive magnetohydrodynamic framework. The response of resonant harmonics depends sensitively on the plasma resistivity and on the toroidal rotation. The response of nonresonant harmonics is not sensitive to most of the plasma parameters, except the equilibrium pressure. Both midplane and the off midplane odd parity RMP coils trigger a similar field response from the plasma. The RMP fields with different toroidal mode numbers trigger qualitatively similar plasma response. A simple model of the electron diamagnetic flow suggests significant effects both in the pedestal region and beyond.

Modelling of plasma response to resonant magnetic perturbation fields in MAST and ITER

The resonant magnetic perturbation (RMP) fields, including the plasma response, are computed within a linear, full toroidal, single-fluid resistive magnetohydrodynamic (MHD) model, and under realistic plasma conditions for MAST and ITER. The response field is found to be considerably reduced, compared with the vacuum field produced by the magnetic perturbation coils. This field reduction relies strongly on the screening effect from the toroidal plasma rotation. Computations also quantify three-dimensional (3D) distortions of the plasma surface, caused by RMP fields. A correlation is found between the computed mode structures, the plasma surface displacement and the observed density pump-out effect in MAST experiments. Generally, the density pump-out tends to occur when the surface displacement peaks near the X-points.

Observation of Lobes near the X Point in Resonant Magnetic Perturbation Experiments on MAST

The application of nonaxisymmetric resonant magnetic perturbations (RMPs) with a toroidal mode number n = 6 in the MAST tokamak produces a significant reduction in plasma energy loss associated with type-I edge localized modes (ELMs), the first such observation with n > 3. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. These lobes or manifold structures, that were predicted previously, have been observed for the first time in a range of discharges and their appearance is correlated with the effect of RMPs on the plasma; i.e., they only appear above a threshold when a density pump out is observed or when the ELM frequency is increased. They appear to be correlated with the RMPs penetrating the plasma and may be important in explaining why the ELM frequency increases. The number and location of the structures observed can be well described using vacuum modeling. Differences in radial extent and poloidal width from vacuum modeling are likely to be due to a combination of transport effects and plasma screening.

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...

Stabilization of resistive wall modes in ITER by active feedback and toroidal rotation

Two approaches are examined for stabilization of the resistive wall mode (RWM) of toroidal mode number n = 1 in an advanced ITER scenario. Active feedback control, with the present coil design and poloidal sensors placed just inside the inner wall, can be very efficient in stabilizing the RWM. Within the voltage limit of the present design for the feedback coils and conservative constraints on performance, the plasma pressure can be increased up to at least 70% between the no-wall and ideal-wall beta limits. Stabilization of the RWM by toroidal plasma rotation depends on the rotation profile as well as on the model for ion Landau damping. Feedback control of rotating plasmas for the advanced scenario is considered. The effect of the blanket is also studied using a simplified model.

Magnetic perturbation experiments on MAST L- and H-mode plasmas using internal coils

Experiments have been performed on MAST using internal (n = 3) resonant magnetic perturbation (RMP) coils. The application of the RMPs to L-mode discharges has shown a clear density pump-out when the field line pitch angle at the low-field side of the plasma is sufficiently well aligned with the applied field. The application of the RMPs before the L–H transition increases the power required to achieve H-mode by at least 30%. In type I ELMing H-mode discharges, at a particular value of q95, the ELM frequency can be increased by a factor of 5 by the application of the RMPs. This effect on the ELMs and the L-mode density pump-out is not correlated with the width of the region for which the Chirikov parameter, calculated using the vacuum field, is greater than 1 but may be correlated with the size of the resonant component of the applied field in the pedestal region or with the location of the peak plasma displacement when the plasma response is taken into account.