External kink instabilities are suppressed in a tokamak experiment by either ͑1͒ energizing a distributed array of independently controlled active feedback coils mounted outside a segmented resistive wall or ͑2͒ inserting a second segmented wall having much higher electrical conductivity. When the active feedback coils are off and the highly conducting wall is withdrawn, kink instabilities excited by plasma current gradients grow at a rate comparable to the magnetic diffusion rate of the resistive wall.

The plasma response to external resonant magnetic perturbations is measured as a function of stability of the resistive wall mode ͑RWM͒. The magnetic perturbations are produced with a flexible, high-speed waveform generator that is preprogrammed to drive an in-vessel array of 30 independent control coils and to produce an m/nϭ3/1 helical field. Both quasi-static and ''phase-flip'' magnetic perturbations are applied to time-evolving discharges in order to observe the dynamical response of the plasma as a function of RWM stability. The evolving stability of the RWM is estimated using equilibrium reconstructions and ideal stability computations, facilitating comparison with theory. The plasma resonant response depends upon the evolution of the edge safety factor, q*, and the plasma rotation. For discharges adjusted to maintain relatively constant edge safety factor, q* Ͻ3, the amplitude of the plasma response to a quasistatic field perturbation does not vary strongly near marginal stability and is consistent with the Fitzpatrick-Aydemir equations with high viscous dissipation. Applying ''phase-flip'' magnetic perturbations that rapidly change toroidal phase by 180°allows observation of the time scale for the plasma response to realign with the applied perturbation. This phase realignment time increases at marginal stability, as predicted by theory. This effect is easily measured and suggests that the response to time-varying external field perturbations may be used to detect the approach to RWM instability.

A new sawtooth control mechanism relying on toroidally propagating ion cyclotron resonance frequency waves: Theory and Joint European Torus tokamak experimental evidencea) Phys. Plasmas 17, 056118 (2010); 10.1063/1.3363201 Sawtooth control using beam ions accelerated by fast waves in the DIII-D tokamakClosed and open loop control techniques were applied to growing m/nϭ2/1 rotating islands in wall-stabilized plasmas in the High Beta Tokamak-Extended Pulse ͑HBT-EP͒ ͓J. Fusion Energy 12, 303 ͑1993͔͒. HBT-EP combines an adjustable, segmented conducting wall ͑which slows the growth or stabilizes ideal external kinks͒ with a number of small ͑6°wide toroidally͒ driven saddle coils located between the gaps of the conducting wall. Two-phase driven magnetic island rotation control from 5 to 15 kHz has been demonstrated powered by two 10 MW linear amplifiers. The phase instability has been observed and is well modeled by the single-helicity predictions of nonlinear Rutherford island dynamics for 2/1 tearing modes including important effects of ion inertia and finite Larmor radius, which appear as a damping term in the model equations. The closed loop response of active feedback control of the 2/1 mode at moderate gain was observed to be in good agreement with the theory. Suppression of the 2/1 island growth has been demonstrated using an asynchronous frequency modulation drive which maintains the inertial flow damping of the island by application of rotating control fields with frequencies alternating above and below the natural mode frequency. This frequency modulation control technique was also able to prevent disruptions normally observed to follow giant sawtooth crashes in the plasma core.

Fundamental theory, experimental observations, and modeling of resistive wall mode (RWM) dynamics and active feedback control are reported. In the RWM, the plasma responds to and interacts with external current-carrying conductors. Although this response is complex, it is still possible to construct simple but accurate models for kink dynamics by combining separate determinations for the external currents, using the VALEN code, and for the plasma's inductance matrix, using an MHD code such as DCON. These computations have been performed for wall-stabilized kink modes in the HBT-EP device, and they illustrate a remarkable feature of the theory: when the plasma's inductance matrix is dominated by a single eigenmode and when the surrounding current-carrying structures are properly characterized, then the resonant kink response is represented by a small number of parameters. In HBT-EP, RWM dynamics are studied by programming quasi-static and rapid "phase-flip" changes of the external magnetic perturbation and directly measuring the plasma response as a function of kink stability and plasma rotation. The response evolves in time, is easily measured, and involves excitation of both the wall-stabilized kink and the RWM. High-speed, active feedback control of the RWM using VALEN-optimized mode control techniques and high-throughput digital processors is also reported. Using newly-installed control coils that directly couple to the plasma surface, experiments demonstrate feedback mode suppression in rapidly rotating plasmas near the ideal wall stability limit.

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Experiments on the HBT-EP (High Beta Tokamak-Extended Pulse) tokamak provided local measurements of the pressure and ion velocity perturbations from rotating magnetic island using Mach probes. The presence of magnetic islands created two distinct features in ion fluid velocity measurements. First, the toroidal velocity profile was sharply peaked near the center of the 2/1 magnetic island. Second, the ion velocity near this island was only ~30% of the magnetic island velocity. Measurements of the perturbations from rotating magnetic islands with stationary detectors prompted the development of a new data analysis technique using the Hilbert transform. This method generated plots of the pressure profile co-rotating with the magnetic island, allowing the analysis of the pressure profile behavior at the O and X-points of the magnetic island. Experiments with active rotation control demonstrated that the pressure perturbations followed the magnetic island motion, while simultaneously measuring that the ion velocity and acceleration were less that those of the magnetic island. These observations agreed with predictions from a two-fluid plasma model that included the effect of magnetic islands on the diamagnetic velocity as well as neutral damping effects. Understanding the effect of magnetic islands on the pressure and ion velocity profiles is crucial for both fundamental plasma studies and the development of more efficient tokamaks using advanced tokamak (AT) concepts.

Observations of a performance limiting feedback phase instability in the HBT-EP tokamak are reported. The phase instability consists of a rapid growth of the phase difference between an m/n = 2/1 tearing mode and an external resonant magnetic perturbation. Observations of mode angular dynamics during phase instability test discharges show good agreement with theoretical estimates of the phase instability timescale. The phase instability limits feedback performance in HBT-EP by decreasing the feedback loop's phase accuracy as gain increases.

A high-speed, non-invasive velocity diagnostic has been developed for measuring plasma rotation. The Doppler shift is determined by employing two detectors that view line emission from the identical volume of plasma. Each detector views through an interference filter having a passband that varies linearly with wavelength. One detector views the plasma through a filter whose passband has a negative slope and the second detector views through one with a positive slope. Because each channel views the same volume of plasma, the ratio of the amplitudes is not sensitive to variations in plasma emission. With suitable knowledge of the filter characteristics and the relative gain, the Doppler shift is readily obtained in realtime from the ratio of two channels without needing a low throughput spectrometer. The systematic errors -arising from temperature drifts, stability, and frequency response of the detectors and amplifiers, interference filter linearity, and ability to thoroughly homogenize the light from the fiber bundle -can be characterized well enough to obtain velocity data with ±1 km/sec with a time resolution of 0.3 msec.-2 -