No abstract

Stabilizing modes that limit plasma beta and reducing their deleterious effects on plasma rotation are key goals for efficient operation of a fusion reactor. Passive stabilization and active control of global kink/ballooning modes and resistive wall modes (RWM) have been demonstrated on NSTX and research now advances to understanding the stabilization physics and reliably maintaining the high beta plasma for confident extrapolation to ITER and CTF. Active n = 1 control experiments with an expanded sensor set, combined with low levels of n = 3 field phased to reduce error fields, reduced resonant field amplification and maintained plasma rotation, exceeded normalized beta = 6, and produced record discharge durations limited by magnet system constraints. Details of RWM active control show the mode being converted to a rotating kink that decays, or saturates leading to tearing modes. Discharges with rotation reduced by n = 3 magnetic braking suffer beta collapse at normalized beta = 4.2 approaching the no-wall limit, while normalized beta greater than 5.5 has been reached in these plasmas with n = 1 active control, in agreement with single-mode RWM theory. Advanced state-space control algorithms proposed for RWM control in ITER theoretically yield significant stabilization improvements. Values of relative phase between the measured n = 1 mode and the applied correction field that experimentally produce stability/instability agree with theory. Experimental mode destabilization occurs over a large range of plasma rotation, challenging the notion of a simple scalar critical rotation speed defining marginal stability. Stability calculations including kinetic modifications to ideal theory are applied to marginally stable experimental equilibria. Plasma rotation and collisionality variations are examined in the calculations. Intermediate rotation levels are less stable, consistent with experimental observations. Trapped ion resonances play a key role in this result. Recent experiments have demonstrated magnetic braking by non-resonant n = 2 fields. The observed rotation damping profile is broader than found for n = 3 fields. Increased ion temperature in the region of maximum braking torque increases the observed rate of rotation damping, consistent with theory.

Reduction or elimination of edge localized modes (ELMs) while maintaining high confinement is essential for future fusion devices, e.g., the ITER. An ELM-free regime was recently obtained in the National Spherical Torus Experiment, following lithium (Li) evaporation onto the plasma-facing components. Edge stability calculations indicate that the pre-Li discharges were unstable to low-n peeling or ballooning modes, while broader pressure profiles stabilized the post-Li discharges. Normalized energy confinement increased by 50% post Li, with no sign of ELMs up to the global stability limit.

Abstract. 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 analyze error fields, to measure error field amplification, and to detect resistive wall modes 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 favorable 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 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.

The resistive wall mode ͑RWM͒ instability in high-beta tokamaks is stabilized by energy dissipation mechanisms that depend on plasma rotation and kinetic effects. Kinetic modification of ideal stability calculated with the "MISK" code ͓B. Hu et al., Phys. Plasmas 12, 057301 ͑2005͔͒ is outlined. For an advanced scenario ITER ͓R. Aymar et al., Nucl. Fusion 41, 1301 ͑2001͔͒ plasma, the present calculation finds that alpha particles are required for RWM stability at presently expected levels of plasma rotation. Kinetic stabilization theory is tested in an experiment in the National Spherical Torus Experiment ͑NSTX͒ ͓M. Ono et al., Nucl. Fusion 40, 557 ͑2000͔͒ that produced marginally stable plasmas with various energetic particle contents. Plasmas with the highest and lowest energetic particle content agree with calculations predicting that increased energetic particle pressure is stabilizing but does not alter the nonmonotonic dependence of stability on plasma rotation due to thermal particle resonances. Presently, the full MISK model, including thermal particles and an isotropic slowing-down distribution function for energetic particles, overpredicts stability in NSTX experiments. Minor alteration of either effect in the theory may yield agreement; several possibilities are discussed.

Experimental observation of resistive wall mode (RWM) instability in the National Spherical Torus Experiment (NSTX) at plasma rotation levels intermediate to the ion precession drift and ion bounce frequencies suggests that low critical rotation threshold models are insufficient. Kinetic modifications to the ideal stability criterion yield a more complex relationship between plasma rotation and RWM stability. Good agreement is found between an experimental RWM instability at intermediate plasma rotation and the RWM marginal point calculated with kinetic effects included, by the MISK code. By self-similarly scaling the experimental plasma rotation profile and the collisionality in the calculation, resonances of the mode with the precession drift and bounce frequencies are explored. Experimentally, RWMs go unstable when the plasma rotation is between the stabilizing precession drift and bounce resonances.

Recent experiments on DIII-D ͓J. L. Luxon, Nucl. Fusion 42, 614 ͑2002͔͒ and National Spherical Torus Experiment ͑NSTX͒ ͓M. Ono et al., Nucl. Fusion 40, 557 ͑2000͔͒ have focused on investigating mechanisms of driving rotation in fusion plasmas. The so-called intrinsic rotation is generated by an effective torque, driven by residual stresses in the plasma, which appears to originate in the plasma edge. A clear scaling of this intrinsic drive with the H-mode pressure gradient is observed. Coupled with the experimentally inferred pinch of angular momentum, such an edge source is capable of producing sheared rotation profiles. Intrinsic drive is also possible directly in the core, although the physics mechanisms are much more complex. Another option which is being explored is the use of nonresonant magnetic fields for spinning the plasma. It is found beneficially that the torque from these fields can be enhanced at low rotation, which assists in spinning the plasma from rest, and offers increased resistance against plasma slowing.

The resistive-wall mode is actively stabilized in the National Spherical Torus Experiment in high-beta plasmas rotating significantly below the critical rotation speed for passive stability and in the range predicted for the International Thermonuclear Experimental Reactor. Variation of feedback stabilization parameters shows mode excitation or suppression. Stabilization of toroidal mode number unity did not lead to instability of toroidal mode number two. The mode can become unstable by deforming poloidally, an important consideration for stabilization system design.