E. A. Lazarus

Control of the Vertical Instability in Tokamaks

The problem of control of the vertical instability is studied for a massless filamentary plasma with finite resistivity included for the shell and active control coil. Stability boundaries are determined. The system can be stabilized up to a critical decay index, which is predominantly a function of the geometry of the passive stabilizing shell. A second, smaller, critical index, which is a function of the geometry of the control coils, determines the limit of stability in the absence of derivative gain in the control circuit. The system is also studied numerically in order to incorporate the non-linear effects of power supply dynamics. The power supply bandwidth requirement is determined by the open-loop growth rate of the instability. The system is studied for a number of control coil options which are available on the DIII-D tokamak. It is found that many of the coils will not provide adequate stabilization and that the use of inboard coils is advantageous in stabilizing the system up to the critical index. A hybrid control system which utilizes such inboard coils on a time-scale which is faster than the vessel L/R time is proposed. Experiments carried out on DIII-D confirm the appropriateness of the model. Using the results of the model study, DIII-D plasmas with decay indices exceeding 90% of the critical index have been stabilized. Measurement of the plasma vertical position is also discussed.

Low voltage Ohmic and electron cyclotron heating assisted startup in DIII-D

There is considerable interest in the development of low voltage startup scenarios for large tokamaks since it is proposed that in ITER the electric field which will be applied for ionization and plasma current ramp-up will be limited to values of E ≤ 0.3 V/m. Studies of low voltage startup have been carried out in DIII-D with and without electron cyclotron preionization and preheating. Successful Ohmic startup has been achieved with E ~ 0.25 V/m by paying careful attention to error fields and prefill pressure, while electron cyclotron heating (ECH) assisted startup with E ~ 0.15 V/m has been demonstrated. ECH assisted startup gives improved reliability at such low electric fields and permits operation over an extended range of prefill pressures and error magnetic fields. Using ECH, startup at E = 0.3 V/m with |B⊥| > 50 G over most of the vessel cross-section has been demonstrated. Such an error field represents an increase by more than a factor of two over the highest value for which Ohmic startup was achieved at the same electric field. During low voltage Ohmic startup with extreme values of prefill pressure and/or error magnetic fields, excessive breakdown delays are observed. The experimental data agree well with theoretical predictions based on the Townsend avalanche theory. ECH assisted startup is always prompt. The primary effect of ECH during the plasma current ramp-up is a decrease of the resistive component of the loop voltage Vrcs. A significant reduction (~30%) in Vres is achieved for low ECH powers (PRF ~ 300-400 kW), but a further large increase in PRF results in only a modest additional decrease in Vres. ECH was not applied over the whole ramp-up phase in these experiments and produced a reduction in volt-second consumption up to the current flat-top (Ip ~ 1 MA) of 10%. These experiments confirm that the low electric fields specified in the ITER design are acceptable and demonstrate the substantial benefits which accrue from the use of ECH assisted startup.

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.

V3FIT: a code for three-dimensional equilibrium reconstruction

The V3FIT code for performing equilibrium reconstruction in three-dimensional plasmas is described. It is a modular code that has the potential to be coupled with a variety of equilibrium solvers to compute the externally measured response to an arbitrary internal state of the plasma. Singular-value decomposition is used to identify the dominant components of the plasma state that can be accurately determined by the reconstruction process and to guide the minimization of the χ2 variance-normalized mismatch between the measured and computed signals. Comparison of a tokamak plasma equilibrium computed by V3FIT and by the axisymmetric equilibrium reconstruction code EFIT is presented. V3FIT is used to reconstruct an axisymmetric DIII-D equilibrium using experimentally observed magnetic diagnostic signals. Three-dimensional reconstructions of stellarator plasma equilibria in the CTH device show the code behaves as expected in the presence of experimental noise, appropriately ignores near-singular directions in parameter space and robustly reconstructs equilibria starting from substantially different initial parameter values.

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...

Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbationsa)

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10−3 relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated non...

Impurity transport and plasma rotation in the ISX-B tokamak

Recent calculations have shown that when external momentum sources and plasma rotation are included in the neoclassical theory, the standard results for impurity transport can be strongly altered. Under appropriate conditions, inward convection is reduced by co-injection and enhanced by counter-injection. In order to examine the theoretical predictions, several observations of impurity transport have been made in the ISX-B tokamak during neutral-beam injection for comparison with the transport seen with Ohmic heating alone. Both intrinsic contaminants and deliberately introduced test impurities display a behaviour that is in qualitative agreement with the predicted beam-driven effects. These correlations are particularly noticeable when the comparisons are made for deuterium where the impurity transport in the Ohmically heated discharges exhibits neoclassical-like characteristics, i.e. accumulation and long confinement times. Similar but smaller effects are observed in beam-heated hydrogen discharges; neoclassical-like behaviour is not seen in Ohmically heated hydrogen sequences. Emphasis has been placed on measuring toroidal plasma rotation, and semi-quantitative comparisons with the theories of beam-induced impurity transport have been made. It is possible that radial electric fields other than those associated with momentum transfer and increased anomalous processes during injection could also play a role.

CONTROL OF THE RESISTIVE WALL MODE IN ADVANCED TOKAMAK PLASMAS ON DIII-D

Resistive wall mode (RWM) instabilities are found to be a limiting factor in advanced tokamak regimes with low internal inductance. Even small amplitude modes can affect the rotation profile and the performance of these ELMing H mode discharges. Although complete stabilization of the RWM by plasma rotation has not yet been observed, several discharges with increased beam momentum and power injection sustained good steady state performance for record durations. The first investigation of active feedback control of the RWM has shown promising results: the leakage of radial magnetic flux through the resistive wall can be successfully controlled and the duration of the high beta phase can be prolonged. The results provide a comparative test of several approaches to active feedback control, and are being used to benchmark the analysis and computational models of active control.

The beryllium limiter experiment in ISX-B

An experiment to test beryllium as a limiter material has been performed in the ISX-B tokamak. The effect of the plasma on the limiter and the effect of the limiter on the plasma were studied in detail. Heat and particle fluxes to the limiter were measured, and limiter damage by melting was documented as a function of power flux. Strong melting and evaporation of the limiter caused beryllium gettering of the vacuum vessel. Postmortem analysis of the limiter was performed to document the amount of retained hydrogen and the erosion and impurity deposition on the limiter. The effect of the limiter on the plasma performance was studied in terms of parameter space, impurity content, and confinement for the ungettered and gettered cases. Operational experience with beryllium in a fusion experiment is discussed.

Confinement in beam-heated plasmas: the effects of low-Z impurities

Confinement studies on the Impurity Study Experiment (ISX-B) in beam-heated plasmas contaminated with small quantities of low-Z impurities are reported. Experimental results on the correlation of particle and energy confinement are presented. A linear relationship of energy confinement and plasma density is observed. As density is increased further, this effect saturates and energy confinement becomes independent of electron density. The experiments have been extended to higher beam power, resulting in an expansion of the ISX-B operating space. Impurities other than neon (carbon and silicon) have been tried and do not produce an enhancement in confinement. Edge cooling by the introduction of impurities has been demonstrated. The change in confinement has been shown to be correlated with changes in the normalized poloidal field fluctuation level (θ/Bθ) but not with the density fluctuation level (ne/ne). The experimental results are compared with models of drift-wave and resistive ballooning turbulence and an explanation is offered for the difference between the results with recycling and non-recycling impurities.