A.C. Sontag

Progress in understanding error-field physics in NSTX spherical torus plasmas

The low-aspect ratio, low magnetic field and wide range of plasma beta of NSTX plasmas provide new insight into the origins and effects of magnetic field errors. An extensive array of magnetic sensors has been used to analyse error fields, to measure error-field amplification and to detect resistive wall modes (RWMs) in real time. The measured normalized error-field threshold for the onset of locked modes shows a linear scaling with plasma density, a weak to inverse dependence on toroidal field and a positive scaling with magnetic shear. These results extrapolate to a favourable error-field threshold for ITER. For these low-beta locked-mode plasmas, perturbed equilibrium calculations find that the plasma response must be included to explain the empirically determined optimal correction of NSTX error fields. In high-beta NSTX plasmas exceeding the n = 1 no-wall stability limit where the RWM is stabilized by plasma rotation, active suppression of n = 1 amplified error fields and the correction of recently discovered intrinsic n = 3 error fields have led to sustained high rotation and record durations free of low-frequency core MHD activity. For sustained rotational stabilization of the n = 1 RWM, both the rotation threshold and the magnitude of the amplification are important. At fixed normalized dissipation, kinetic damping models predict rotation thresholds for RWM stabilization to scale nearly linearly with particle orbit frequency. Studies for NSTX find that orbit frequencies computed in general geometry can deviate significantly from those computed in the high-aspect ratio and circular plasma cross-section limit, and these differences can strongly influence the predicted RWM stability. The measured and predicted RWM stability is found to be very sensitive to the E × B rotation profile near the plasma edge, and the measured critical rotation for the RWM is approximately a factor of two higher than predicted by the MARS-F code using the semi-kinetic damping model.

Improved understanding of physics processes in pedestal structure, leading to improved predictive capability for ITER

Joint experiment/theory/modelling research has led to increased confidence in predictions of the pedestal height in ITER. This work was performed as part of a US Department of Energy Joint Research Target in FY11 to identify physics processes that control the H-mode pedestal structure. The study included experiments on C-Mod, DIII-D and NSTX as well as interpretation of experimental data with theory-based modelling codes. This work provides increased confidence in the ability of models for peeling–ballooning stability, bootstrap current, pedestal width and pedestal height scaling to make correct predictions, with some areas needing further work also being identified. A model for pedestal pressure height has made good predictions in existing machines for a range in pressure of a factor of 20. This provides a solid basis for predicting the maximum pedestal pressure height in ITER, which is found to be an extrapolation of a factor of 3 beyond the existing data set. Models were studied for a number of processes that are proposed to play a role in the pedestal ne and Te profiles. These processes include neoclassical transport, paleoclassical transport, electron temperature gradient turbulence and neutral fuelling. All of these processes may be important, with the importance being dependent on the plasma regime. Studies with several electromagnetic gyrokinetic codes show that the gradients in and on top of the pedestal can drive a number of instabilities.

Effect of plasma shaping on performance in the National Spherical Torus Experiment

The National Spherical Torus Experiment (NSTX) has explored the effects of shaping on plasma performance as determined by many diverse topics including the stability of global magnetohydrodynamic (MHD) modes (e.g., ideal external kinks and resistive wall modes), edge localized modes (ELMs), bootstrap current drive, divertor flux expansion, and heat transport. Improved shaping capability has been crucial to achieving βt∼40%. Precise plasma shape control has been achieved on NSTX using real-time equilibrium reconstruction. NSTX has simultaneously achieved elongation κ∼2.8 and triangularity δ∼0.8. Ideal MHD theory predicts increased stability at high values of shaping factor S≡q95Ip∕(aBt), which has been observed at large values of the S∼37[MA∕(m∙T)] on NSTX. The behavior of ELMs is observed to depend on plasma shape. A description of the ELM regimes attained as shape is varied will be presented. Increased shaping is predicted to increase the bootstrap fraction at fixed Ip. The achievement of strong shaping ...

Progress in the development of ELM pace-making with non-axisymmetric magnetic perturbations in NSTX

The application of non-axisymmetric magnetic perturbations has been shown to destabilize edge-localized modes (ELMs) in the National Spherical Torus Experiment. This ELM-triggering effect is used to controllably introduce ELMs into lithium-enhanced ELM-free H-mode discharges, reducing the typical impurity accumulation while maintaining high energy confinement. Recent improvements to the triggering techniques are described. The perturbation waveform has been improved, with large amplitude, short duration perturbations allowing rapid, highly reliable triggering, with reduced braking of toroidal rotation. The rapid triggering allowed the ELM frequency to be increased to over 60 Hz, leading to a reduction in the average ELM size. Combined with improved gas fuelling, this method has resulted in periods of stationary global conditions, although plasma profiles do continue to evolve.

Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks

Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad?Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.

Dynamical evolution of pedestal parameters in ELMy H-mode in the National Spherical Torus Experiment

Characterizations of the pedestal parameter dynamics throughout the edge localized mode (ELM) cycles are performed on the National Spherical Torus Experiment (NSTX, (Ono et al 2000 Nucl. Fusion 40 557)). A clear buildup of the pedestal height between ELMs is observed for three different plasma currents. This buildup tends to saturate at low and medium plasma currents. Similarly, the pedestal width increases with no clear evidence of saturation during an ELM cycle. The maximum pedestal gradient increases as a function of plasma current, reaches a nominal value after the ELM crash, and remains constant until the end of the ELM cycle. The pedestal height just prior to the onset of ELM is shown to increase quadratically with plasma current. The pedestal width (Δ) scales as with the poloidal β at the top of the pedestal. Coherent density fluctuations strongly increasing at the plasma edge are observed to be maximum after the ELM crash and to decay during the rest of the ELM cycle. Finally, the evolution of the pedestal height and width during the ELM cycle as well as the scaling with Ip of the pedestal pressure prior to the onset ELM are found to be qualitatively consistent with the peeling–ballooning theory.

First observation of ELM pacing with vertical jogs in a spherical torus

Experiments in a number of conventional aspect ratio tokamaks have been successful in pacing edge localized modes (ELMs) by rapid vertical jogging of the plasma. This paper demonstrates the first pacing of ELMs in a spherical torus plasma. Applied 30 Hz vertical jogs synchronized the ELMs with the upward motion of the plasma. 45 Hz jogs also lead to an increase in the ELM frequency, though the synchronization of the ELMs and jogs was unclear. A reduction in the ELM energy was observed at the higher driven ELM frequencies.

Connection between plasma response and resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression in DIII-D

Calculations of the plasma response to applied non-axisymmetric fields in several DIII-D discharges show that predicted displacements depend strongly on the edge current density. This result is found using both a linear two-fluid-MHD model (M3D-C1) and a nonlinear ideal-MHD model (VMEC). Furthermore, it is observed that the probability of a discharge being edge localized mode (ELM)-suppressed is most closely related to the edge current density, as opposed to the pressure gradient. It is found that discharges with a stronger kink response are closer to the peeling–ballooning stability limit in ELITE simulations and eventually cross into the unstable region, causing ELMs to reappear. Thus for effective ELM suppression, the RMP has to prevent the plasma from generating a large kink response, associated with ELM instability. Experimental observations are in agreement with the finding; discharges which have a strong kink response in the MHD simulations show ELMs or ELM mitigation during the RMP phase of the experiment, while discharges with a small kink response in the MHD simulations are fully ELM suppressed in the experiment by the applied resonant magnetic perturbation. The results are cross-checked against modeled 3D ideal MHD equilibria using the VMEC code. The procedure of constructing optimal 3D equilibria for diverted H-mode discharges using VMEC is presented. Kink displacements in VMEC are found to scale with the edge current density, similar to M3D-C1, but the displacements are smaller. A direct correlation in the flux surface displacements to the bootstrap current is shown.