A Reduced Resistive Wall Mode Kinetic Stability Model for Disruption Forecasting

Kinetic modification of ideal stability theory from stabilizing resonances of mode-particle interaction has had success in explaining resistive wall mode (RWM) stability limits in tokamaks. With the goal of real-time stability forecasting, a reduced kinetic stability model has been implemented in the new Disruption Event Characterization and Forecasting (DECAF) code, which has been written to analyze disruptions in tokamaks. The reduced model incorporates parameterized models for ideal limits on beta, a ratio of plasma pressure to magnetic pressure, which are shown to be in good agreement with DCON code calculations. Increased beta between these ideal limits causes a shift in the unstable region of delta W_K space, where delta W_K is the change in potential energy due to kinetic effects that is solved for by the reduced model, such that it is possible for plasmas to be unstable at intermediate beta but stable at higher beta. Gaussian functions for delta W_K are defined as functions of E cross B frequency and collisionality, with parameters reflecting the experience of the National Spherical Torus Experiment (NSTX). The reduced model was tested on a database of discharges from NSTX and experimentally stable and unstable discharges were separated noticeably on a stability map in E cross B frequency, collisionality space. The reduced model only failed to predict an unstable RWM in 15.6% of cases with an experimentally unstable RWM and performed well on predicting stability for experimentally stable discharges as well.Readme, digital data file

Application of Benchmarked Kinetic Resistive Wall Mode Stability Codes to ITER, Including Additional Physics

Leading resistive wall mode (RWM) stability codes MARS-K [Y. Liu, et al., Phys. Plasmas 15, 112503 (2008)] and MISK [B. Hu, et al., Phys. Plasmas 12, 057301 (2005)] have been previously benchmarked. The benchmarking has now been extended to include additional physics, and used to project the stability of ITER in a realistic operating space. Due to ITER's relatively low plasma rotation and collisionality, collisions and non-resonance rotational effects were both found to have little impact on stability, and these non-resonance rotational effects also will not self-consistently affect the ITER RWM eigenfunction. Resonances between thermal ions and electrons and the expected level of ITER toroidal rotation were found to be important to stability, as were alpha particles, which are not in rotational resonance. MISK calculations show that without alpha particles, ITER is projected to be unstable to the RWM, but the expected level of alphas is calculated to provide a sufficient level of stability.readme, digital data file

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 7 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

Scenario Development During Commissioning Operations on the National Spherical Torus Experiment Upgrade

The National Spherical Torus Experiment Upgrade (NSTX-U) will advance the physics basis required for achieving steady-state, high-beta, and high-confinement conditions in a tokamak by accessing high toroidal field (1 T) and plasma current (1.0 - 2.0 MA) in a low aspect ratio geometry (A = 1.6 - 1.8) with flexible auxiliary heating systems (12 MW NBI, 6 MW HHFW). This paper describes progress in the development of L- and H-mode discharge scenarios and the commissioning of operational tools in the first ten weeks of operation that enable the scientific mission of NSTX-U. Vacuum field calculations completed prior to operations supported the rapid development and optimization of inductive breakdown at different values of ohmic solenoid current. The toroidal magnetic field (B_T0 = 0.65 T) exceeded the maximum values achieved on NSTX and novel long-pulse L-mode discharges with regular sawtooth activity exceeded the longest pulses produced on NSTX (tpulse > 1.8s). The increased flux of the central solenoid facilitated the development of stationary L-mode discharges over a range of density and plasma current (Ip). H-mode discharges achieved similar levels of stored energy, confinement (H98y,2 > 1) and stability (beta_N/beta_N-nowall > 1) compared to NSTX discharges for Ip 2.2) and achieving long periods of MHD quiescent operations. The rapid progress in developing L- and H-mode scenarios in support of the scientific program was enabled by advances in real-time plasma control, efficient error field identification and correction, effective conditioning of the graphite wall and excellent diagnostic availability.readme, digital data file

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 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

Investigation of MHD instabilities and control in KSTAR preparing for high beta operation

Initial H-mode operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) is expanded to higher normalized beta and lower plasma internal inductance moving towards design target operation. As a key supporting device for ITER, an important goal for KSTAR is to produce physics understanding of MHD instabilities at long pulse with steady-state profiles, at high normalized beta, and over a wide range of plasma rotation profiles. An advance from initial plasma operation is a significant increase in plasma stored energy and normalized beta, with W-tot = 340 kJ, beta(N) = 1.9, which is 75% of the level required to reach the computed ideal n = 1 no-wall stability limit. The internal inductance was lowered to 0.9 at sustained H-mode duration up to 5 s. In ohmically heated plasmas, the plasma current reached 1 MA with prolonged pulse length up to 12 s. Rotating MHD modes are observed in the device with perturbations having tearing rather than ideal parity. Modes with m/n = 3/2 are triggered during the H-mode phase but are relatively weak and do not substantially reduce W-tot. In contrast, 2/1 modes to date only appear when the plasma rotation profiles are lowered after H-L back-transition. Subsequent 2/1 mode locking creates a repetitive collapse of beta(N) by more than 50%. Onset behaviour suggests the 3/2 mode is close to being neoclassically unstable. A correlation between the 2/1 mode amplitude and local rotation shear from an x-ray imaging crystal spectrometer suggests that the rotation shear at the mode rational surface is stabilizing. As a method to access the ITER-relevant low plasma rotation regime, plasma rotation alteration by n = 1, 2 applied fields and associated neoclassical toroidal viscosity (NTV) induced torque is presently investigated. The net rotation profile change measured by a charge exchange recombination diagnostic with proper compensation of plasma boundary movement shows initial evidence of non-resonant rotation damping by the n = 1, 2 applied field configurations. The result addresses perspective on access to low rotation regimes for MHD instability studies applicable to ITER. Computation of active RWM control using the VALEN-3D code examines control performance using midplane locked mode detection sensors. The LM sensors are found to be strongly affected by mode and control coil-induced vessel current, and consequently lead to limited control performance theoreticallyclose3

NSTX-U theory, modeling and analysis results

The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 s, and has available up to 15 MW of neutral beam injection power at different tangency radii and 6 MW of high harmonic fast wave heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvenic ions in beam-heated NSTX-U plasmas access energetic particle (EP) parameter space that is relevant for both α-heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, EP stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control