Predicting resistive wall mode stability in NSTX through balanced random forests and counterfactual explanations

Recent progress in the disruption event characterization and forecasting framework has shown that machine learning guided by physics theory can be easily implemented as a supporting tool for fast computations of ideal stability properties of spherical tokamak plasmas. In order to extend that idea, a customized random forest (RF) classifier that takes into account imbalances in the training data is hereby employed to predict resistive wall mode (RWM) stability for a set of high beta discharges from the NSTX spherical tokamak. More specifically, with this approach each tree in the forest is trained on samples that are balanced via a user-defined over/under-sampler. The proposed approach outperforms classical cost-sensitive methods for the problem at hand, in particular when used in conjunction with a random under-sampler, while also resulting in a threefold reduction in the training time. In order to further understand the model’s decisions, a diverse set of counterfactual explanations based on determinantal point processes (DPP) is generated and evaluated. Via the use of DPP, the underlying RF model infers that the presence of hypothetical magnetohydrodynamic activity would have prevented the RWM from concurrently going unstable, which is a counterfactual that is indeed expected by prior physics knowledge. Given that this result emerges from the data-driven RF classifier and the use of counterfactuals without hand-crafted embedding of prior physics intuition, it motivates the usage of counterfactuals to simulate real-time control by generating the β N levels that would have kept the RWM stable for a set of unstable discharges

Exploration of the Equilibrium and Stability Properties of Spherical Tokamaks and Projection for MAST-U

In preparation for high fusion plasma performance operation of the newly operating spherical tokamak MAST-U, the equilibrium and stability properties of plasmas in the MAST database, as well as projections for MAST-U, are explored. The disruption event characterization and forecasting (DECAF) code is utilized to map disruptions in MAST, particularly with regard to vertical displacement events. Loss of vertical stability control was not found to be common in MAST, providing reassurance for MAST-U operation. MAST equilibria were reconstructed with magnetic diagnostics, adding kinetic diagnostics, or finally also adding magnetic pitch angle data. The reconstructions work well for MAST and the procedures are set up for MAST-U, including determination of the plasma current in the first MAST-U discharges. A 3D wall model of MAST-U has been constructed in the VALEN code, indicating that significant toroidal currents may be induced in the conducting structure. Rotation measurements may also be included in the reconstructions, and a test with the FLOW code of a rotating MAST plasma indicates a modest shift of the pressure contours off of the magnetic flux surfaces may be expected. Unstable resistive wall modes (RWMs) may constrain the performance of high pressure MAST-U plasmas. A machine learning (ML) assisted algorithm for stability calculation developed for the NSTX spherical tokamak has been applied to MAST plasmas. Improvements and expansion of the ML techniques continue, including semi-supervised learning techniques and a detection algorithm for unstable RWMs. Finally, projections of MAST-U plasma stability have been performed, indicating that a region of high pressure operational space exists in which the new passive stabilization plates act to stabilize ideal kink modes and RWMs may be stabilized by kinetic effects or active control

KSTAR equilibrium operating space and projected stabilization at high normalized beta

Along with an expanded evaluation of the equilibrium operating space of the Korea Superconducting Tokamak Advanced Research, KSTAR, experimental equilibria of the most recent plasma discharges were reconstructed using the EFIT code. In near-circular plasmas created in 2009, equilibria reached a stored energy of 54 kJ with a maximum plasma current of 0.34 MA. Highly shaped plasmas with near double-null configuration in 2010 achieved H-mode with clear edge localized mode (ELM) activity, and transiently reached a stored energy of up to 257 kJ, elongation of 1.96 and normalized beta of 1.3. The plasma current reached 0.7 MA. Projecting active and passive stabilization of global MHD instabilities for operation above the ideal no-wall beta limit using the designed control hardware was also considered. Kinetic modification of the ideal MHD n = 1 stability criterion was computed by the MISK code on KSTAR theoretical equilibria with a plasma current of 2 MA, internal inductance of 0.7 and normalized beta of 4.0 with simple density, temperature and rotation profiles. The steep edge pressure gradient of this equilibrium resulted in the need for significant plasma toroidal rotation to allow thermal particle kinetic resonances to stabilize the resistive wall mode (RWM). The impact of various materials and electrical connections of the passive stabilizing plates on RWM growth rates was analysed, and copper plates reduced the RWM passive growth rate by a factor of 15 compared with stainless steel plates at a normalized beta of 4.4. Computations of active RWM control using the VALEN code showed that the n = 1 mode can be stabilized at normalized beta near the ideal wall limit via control fields produced by the midplane in-vessel control coils (IVCCs) with as low as 0.83kW control power using ideal control system assumptions. The ELM mitigation potential of the IVCC, examined by evaluating the vacuum island overlap created by resonant magnetic perturbations, was analysed using the TRIP3D code. Using a combination of all IVCCs with dominant n = 2 field and upper/lower coils in an even parity configuration, a Chirikov parameter near unity at normalized poloidal flux 0.83, an empirically determined condition for ELM mitigation in DIII-D, was generated in theoretical high-beta equilibria. Chirikov profile optimization was addressed in terms of coil parity and safety factor profile.X112315sciescopu

Overview of NSTX Upgrade initial results and modelling highlights

The National Spherical Torus Experiment (NSTX) has undergone a major upgrade, and the NSTX Upgrade (NSTX-U) Project was completed in the summer of 2015. NSTX-U first plasma was subsequently achieved, diagnostic and control systems have been commissioned, the H-mode accessed, magnetic error fields identified and mitigated, and the first physics research campaign carried out. During ten run weeks of operation, NSTX-U surpassed NSTX record pulse-durations and toroidal fields (TF), and high-performance ∼1 MA H-mode plasmas comparable to the best of NSTX have been sustained near and slightly above the n = 1 no-wall stability limit and with H-mode confinement multiplier H98y,2 above 1. Transport and turbulence studies in L-mode plasmas have identified the coexistence of at least two ion-gyro-scale turbulent micro-instabilities near the same radial location but propagating in opposite (i.e. ion and electron diamagnetic) directions. These modes have the characteristics of ion-temperature gradient and micro-tearing modes, respectively, and the role of these modes in contributing to thermal transport is under active investigation. The new second more tangential neutral beam injection was observed to significantly modify the stability of two types of Alfven eigenmodes. Improvements in offline disruption forecasting were made in the areas of identification of rotating MHD modes and other macroscopic instabilities using the disruption event characterization and forecasting code. Lastly, the materials analysis and particle probe was utilized on NSTX-U for the first time and enabled assessments of the correlation between boronized wall conditions and plasma performance. These and other highlights from the first run campaign of NSTX-U are described

NSTX/NSTX-U theory, modeling and analysis results

The mission of the spherical tokamak NSTX-U is to explore the physics that drives core and pedestal transport and stability at high-β and low collisionality, as part of the development of the spherical tokamak (ST) concept towards a compact, low-cost ST-based pilot plant. NSTX-U will ultimately operate at up to 2 MA and 1 T with up to 12 MW of neutral beam injection power for 5 s. NSTX-U will operate in a regime where electromagnetic instabilities are expected to dominate transport, and beam-heated NSTX-U plasmas will explore a portion of energetic particle parameter space that is relevant for both _-heated conventional and low aspect ratio burning plasmas. NSTX-U will also develop the physics understanding and control tools to ramp-up and sustain high performance plasmas in a fullynoninductive fashion. NSTX-U began research operations in 2016, but a failure of a divertor magnetic field coil after ten weeks of operation resulted in the suspension of operations and initiation of recovery activities. During this period, there has been considerable work in the area of analysis, theory and modeling of data from both NSTX and NSTX-U, with a goal of understanding the underlying physics to develop predictive models that can be used for high-confidence projections for both ST and higher aspect ratio regimes. These studies have addressed issues in thermal plasma transport, macrostability, energetic particlet-driven instabilities at ion-cyclotron frequencies and below, and edge and divertor physics

Overview of physics results from NSTX

In the last two experimental campaigns, the low aspect ratio NSTX has explored physics issues critical to both toroidal confinement physics and ITER. Experiments have made extensive use of lithium coatings for wall conditioning, correction of non-axisymmetric field errors and control of n = 1 resistive wall modes (RWMs) to produce high-performance neutral-beam heated discharges extending to 1.7 s in duration with non-inductive current fractions up to 0.7. The RWM control coils have been used to trigger repetitive ELMs with high reliability, and they have also contributed to an improved understanding of both neoclassical tearing mode and RWM stabilization physics, including the interplay between rotation and kinetic effects on stability. High harmonic fast wave (HHFW) heating has produced plasmas with central electron temperatures exceeding 6 keV. The HHFW heating was used to show that there was a 20-40% higher power threshold for the L-H transition for helium than for deuterium plasmas. A new diagnostic showed a depletion of the fast-ion density profile over a broad spatial region as a result of toroidicity-induced Alfvén eigenmodes (TAEs) and energetic-particle modes (EPMs) bursts. In addition, it was observed that other modes (e.g. global Alfvén eigenmodes) can trigger TAE and EPM bursts, suggesting that fast ions are redistributed by high-frequency AEs. The momentum pinch velocity determined by a perturbative technique decreased as the collisionality was reduced, although the pinch to diffusion ratio, Vpinch/χ, remained approximately constant. The mechanisms of deuterium retention by graphite and lithium-coated graphite plasma-facing components have been investigated. To reduce divertor heat flux, a novel divertor configuration, the 'snowflake' divertor, was tested in NSTX and many beneficial aspects were found. A reduction in the required central solenoid flux has been realized in NSTX when discharges initiated by coaxial helicity injection were ramped in current using induction. The resulting plasmas have characteristics needed to meet the objectives of the non-inductive start-up and ramp-up program of NSTX. © 2011 IAEA, Vienna