Gerald A. Navratil

Modeling of active control of external magnetohydrodynamic instabilities

A general circuit formulation of resistive wall mode (RWM) feedback stabilization developed by Boozer [Phys. Plasmas 5, 3350 (1998)] has been used as the basis for the VALEN computer code that calculates the performance of an active control system in arbitrary geometry. The code uses a finite element representation of a thin shell structure in an integral formulation to model arbitrary conducting walls. This is combined with a circuit representation of stable and unstable plasma modes. Benchmark comparisons of VALEN results with large aspect ratio analytic model of the current driven kink mode are in very good agreement. VALEN also models arbitrary sensors, control coils, and the feedback logic connecting these sensors and control coils to provide a complete simulation capability for feedback control of plasma instabilities. VALEN modeling is in good agreement with experimental results on DIII-D [Garofalo et al., Nucl. Fusion 40, 1491 (2000)] and HBT-EP [Cates et al., Phys. Plasmas 7, 3133 (2000)]. VALEN ...

Sustained rotational stabilization of DIII-D plasmas above the no-wall beta limit

Sustained stabilization of the n=1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n=1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wal...

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.

Transport and performance in DIII-D discharges with weak or negative central magnetic shear

Discharges exhibiting the highest plasma energy and fusion reactivity yet realized in the DIII-D tokamak have been produced by combining the benefits of a hollow or weakly sheared central current profile with a high confinement (H-mode) edge. In these discharges, low power neutral beam injection heats the electrons during the initial current ramp, and {open_quotes}freezes in{close_quotes} a hollow or flat central current profile. When the neutral beam power is increased, formation of a region of reduced transport and highly peaked profiles in the core often results. Shortly before these plasmas would otherwise disrupt, a transition is triggered from the low (L-mode) to high (H-mode) confinement regimes, thereby broadening the pressure profile and avoiding the disruption. These plasmas continue to evolve until the high performance phase is terminated nondisruptively at much higher {beta}{sub T} (ratio of plasma pressure to toroidal magnetic field pressure) than would be attainable with peaked profiles and an L-mode edge. Transport analysis indicates that in this phase, the ion diffusivity is equivalent to that predicted by Chang-Hinton neoclassical theory over the entire plasma volume. This result is consistent with suppression of turbulence by locally enhanced E x B flow shear, and is supported by observations of reduced fluctuations in the plasma. Calculations of performance in these discharges extrapolated to a deuterium-tritium fuel mixture indicates that such plasmas could produce a DT fusion gain Q{sub DT} = 0.32.

Measurement and modeling of three-dimensional equilibria in DIII-D

A detailed experiment-theory comparison reveals that linear ideal MHD theory is in quantitative agreement with external magnetic and internal soft x-ray measurements of the plasma response to externally applied non-axisymmetric fields over a broad range of beta and rotation. This result represents a significant step toward the goal of advancing the understanding of three-dimensional tokamak equilibria. Both the magnetic and soft x-ray measurements show the driven plasma perturbation increases linearly with the applied perturbation, suggesting the relevance of linear plasma response models. The magnetic and soft x-ray measurements are made at multiple toroidal and poloidal locations, allowing well resolved measurements of the global structure. The comparison also highlights the need to include kinetic effects in the MHD model once beta exceeds 80% of the kink mode limit without a conducting wall. Two distinct types of response fields are identified by the linear ideal MHD model: one that consists of localized currents at the rational surfaces that cancel the applied resonant field and another that is excited by the components of the external field that couple to the kink mode. Numerical simulations show these two fields have similar amplitudes in ITER-shaped DIII-D discharges where n = 3 fields are used to suppress edge localized modes.

Comprehensive control of resistive wall modes in DIII-D advanced tokamak plasmas

The resistive wall mode (RWM) and neoclassical tearing mode (NTM) have been simultaneously suppressed in the DIII-D for durations of over 2 s at beta values 20% above the no-wall limit with modest electron cyclotron current drive and very low plasma rotation. The achieved plasma rotation was significantly lower than reported previously. However, in this regime where stable operation is obtained, it is not unconditionally guaranteed. Various MHD activities, such as edge localized modes (ELMs) and fishbones, begin to couple to the RWM branch near the no-wall limit; feedback has been useful in improving the discharge stability to such perturbations. Simultaneous operation of slow dynamic error field correction and fast feedback suppressed the pile-up of ELM-induced RWM at a series of ELM events. This result implies that successful feedback operation requires not only direct feedback against unstable RWM but also careful control of MHD-induced RWM aftermath, which is the dynamical response to a small-uncorrected error field near the no-wall beta limit. These findings are extremely useful in defining the challenge of control of the RWM and NTM in the unexplored physics territory of burning plasmas in ITER.

Measurement of resistive wall mode stability in rotating high-β DIII-D plasmas

Toroidal plasma rotation of the order of a few per cent of the Alfven velocity can stabilize the resistive wall mode (RWM) and extend the operating regime of tokamaks from the conventional, ideal magnetohydrodynamic (MHD) no-wall limit up to the ideal MHD ideal-wall limit. The stabilizing effect has been measured in DIII-D passively by measuring the critical plasma rotation required for stability and actively by probing the plasma with externally applied resonant magnetic fields. The comparison of these measurements to predictions of rotational stabilization of the sound wave damping and of the kinetic damping model using the MARS-F code results in qualitative agreement, but also indicates the need for further refinement of the measurements and models.

Suppression of resistive wall instabilities with distributed, independently controlled, active feedback coils

External kink instabilities are suppressed in a tokamak experiment by either (1) energizing a distributed array of independently controlled active feedback coils mounted outside a segmented resistive wall or (2) 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.

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.