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Spatiotemporal forecasting of the edge localized modes in tokamak plasmas using neural networks

Artificial intelligence techniques have been increasingly adopted by the plasma and fusion science to address problems like plasma reconstruction, surrogate modeling, and tokamak/stellarator optimization. A key focus in sustained fusion research is the prediction and mitigation of edge-localized-modes (ELMs), instabilities that occur in short, periodic bursts and can cause erosion to the tokamak vessel wall. Recent research has demonstrated the power of neural networks in approximating continuous functions. In this work, we build spatiotemporal forecasting models that can predict the onset of ELMs and their evolution at early stages. We leverage recent advances in generative modeling, sequence-to-sequence modeling, and Fourier neural operators to propose architectures and training strategies that can learn to forecast short to long term dynamics of the noisy signals due to ELMs. We benchmark the developed model against a state-of-the-art foundation model using the beam emission spectroscopy (BES) data that captures the plasma fluctuations due to ELMs over a 8 x 8 spatial grid. Our models demonstrate high accuracy, outperforming the baselines, in predicting the evolution of BES signals during ELM events. Furthermore, the developed models exhibit high accuracy in predicting the rapid rise and relaxation of the signals due to ELMs within 30–80 µs.

edge localized modes↗

Achievement of a high-density, high-confinement, and high-beta tokamak plasma regime in DIII-D, and implications for a lower-current path for ITER and FPP

Experiments on DIII-D have demonstrated a density-confinement synergy that enables sustainment of high performance in a previously unattained parameter regime of simultaneous very high energy confinement quality (H 98y2 ≥ 1.5), very high line-average density Greenwald fraction (ƒ Gr = πa 2 < n >/I P ≥ 1.4), and high toroidal beta (β T ≥ 3%). Tokamak operation in this regime is essential for a compact steady-state FPP, as well as for Q=10 with 500 MW of fusion power in ITER at I P << 15 MA. These experiments leveraged the knowledge that, in the high-poloidal-beta (β P ) regime, impurity and density gradients can enhance turbulence stabilization caused by high α MHD (α MHD ~(dβ P )⁄dr). This was described by theoretical predictions and gyrokinetic transport simulations [M.T. Kotschenreuther et al, 2024 Nucl. Fusion, 64 076033], and later confirmed by experiments on DIII-D [S. Ding et al, 2024 Nature 629 555]. To increase both β P and β T , the new experiments increased the ideal-wall stability β N -limit by using a smaller plasma-outer wall distance and higher triangularity in the plasma cross section (top/bottom average δ~0.9), enabled by the recent “shape & volume rise” (SVR) modification to the DIII-D divertor. The higher triangularity also contributed to achieving higher ƒ Gr by enabling higher pedestal density. At high density, the pedestal is ballooning limited and exhibits small and frequent ELMs, while the divertor is near detachment even without any impurity seeding. High plasma performance was attained and sustained reproducibly, with the eventual terminations brought about by an MHD mode destabilized as the current profile slowly continued to evolve. A path to stationary fully noninductive operation might include ECH injection to reduce both core impurity accumulation and the electron collisionality, thus increasing the bootstrap current. These experiments provide the first experimental demonstration of the ƒ Gr , H 98y2 , and β T values required simultaneously for ITER Q = 10 at I P < 10 MA, pointing to practical ways to improve the energy confinement in a fusion reactor.

Garofalo, Andrea M. [General Atomics, San Diego, C↗

Integrated deep learning framework for unstable event identification and disruption prediction of tokamak plasmas

Abstract The ability to identify underlying disruption precursors is key to disruption avoidance. In this paper, we present an integrated deep learning (DL) based model that combines disruption prediction with the identification of several disruption precursors like rotating modes, locked modes, H-to-L back transitions and radiative collapses. The first part of our study demonstrates that the DL-based unstable event identifier trained on 160 manually labeled DIII-D shots can achieve, on average, 84% event identification rate of various frequent unstable events (like H-L back transition, locked mode, radiative collapse, rotating MHD mode, large sawtooth crash), and the trained identifier can be adapted to label unseen discharges, thus expanding the original manually labeled database. Based on these results, the integrated DL-based framework is developed using a combined database of manually labeled and automatically labeled DIII-D data, and it shows state-of-the-art (AUC = 0.940) disruption prediction and event identification abilities on DIII-D. Through cross-machine numerical disruption prediction studies using this new integrated model and leveraging the C-Mod, DIII-D, and EAST disruption warning databases, we demonstrate the improved cross-machine disruption prediction ability and extended warning time of the new model compared with a baseline predictor. In addition, the trained integrated model shows qualitatively good cross-machine event identification ability. Given a labeled dataset, the strategy presented in this paper, i.e. one that combines a disruption predictor with an event identifier module, can be applied to upgrade any neural network based disruption predictor. The results presented here inform possible development strategies of machine learning based disruption avoidance algorithms for future tokamaks and highlight the importance of building comprehensive databases with unstable event information on current machines.

plasma instabilities↗

Effects of external kink and fishbone-like modes on energetic particle transport in tokamak plasmas

Transport and loss of beam injected energetic particles (EPs) due to three-dimensional perturbations, associated with the external kink (XK) instability and fishbone-like mode (FLM), are numerically investigated utilizing the guiding center following code ORBIT for static toroidal plasmas in HL-2A. The perturbation structure for the XK is computed by the MARS-F code and then mapped to the Boozer coordinates as defined in ORBIT. The simulation shows that the EP profile experiences a significant change in the middle of the plasma column, when the XK-induced radial magnetic field perturbation amplitude, normalized by the equilibrium field, exceeds a threshold value of about 10 -2 . The EP transport is found to be dominated by a diffusion process instead of convection. Furthermore, by scanning the perturbation frequency as a free parameter while maintaining the XK mode structure (thus mimicking the FLM as observed in DIII-D and JT-60U tokamaks), redistribution and loss of EPs are found to be substantially enhanced due to strong resonances between the FLM and EPs, when the mode frequency exceeds a threshold value of ~2 kHz for the case considered. For either XK or FLM, the response of passing EPs to the perturbation is dominant due to the assumed tangential neutral beam injection. Most lost EPs due to these instabilities are initially passing particles but are eventually lost through trapped orbits.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Physics↗

Stability of a tokamak plasma with diffuse toroidal rotation

The present work considers the stability of a high- $\beta$ , large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas , vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high- $\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

Physics↗

Suprathermal electron transport studies in radio-frequency-heated tokamak plasmas

This contribution reports on the study of suprathermal electron radial transport enhancement in the presence of electron-heating radio-frequency waves, such as electron-cyclotron waves or lower-hybrid waves. Since suprathermal electrons emit hard X-rays from Bremsstrahlung, experimental data from hard X-ray measurements are used to follow their dynamics. In particular, electron-cyclotron power modulation experiments performed in TCV show that this transport depends on the total electron-cyclotron power. These results are corroborated by experimentally constrained Fokker-Planck simulations [J. Cazabonne et al, Plasma Phys. Control. Fusion 65, 104001 (2023)]. Similar experiments have been performed in WEST with lower-hybrid waves, and are reported for the first time. Preliminary analyses show potential evidence of suprathermal electron transport, but no clear dependence on wave power nor photon energy at this stage.

Cazabonne, Jean [CEA, IRFM, Saint Paul Lez Durance↗

Stable compression of a spherical tokamak plasma

In this study, an analysis of toroidal plasma compression by a collapsing flux conserver reveals linearly stable scenarios of operation to high compression ratios. The resistive and ideal MHD stability is calculated in full toroidal geometry using the asymptotic matching method in realistic conditions. A time dependent MHD simulation of the compression is conducted to confirm the conservation principles used to calculate the equilibrium states for the analysis. The near edge current profile, controlled by toroidal field ramping during compression, is shown to be critical to stability due to coupling between poloidal components of the least stable mode. Two cases with slight differences in edge current are examined, one with a stable corridor to high compression and one without.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of negative triangularity on tearing mode stability in tokamak plasmas

Abstract The influence of negative triangularity (NT) of the plasma shape on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability has been numerically investigated, with results compared to that of the positive triangularity (PT) counterpart. By matching the safety factor profile for a series of toroidal equilibria, several important plasma parameters, including the triangularity, the plasma equilibrium pressure, the plasma resistivity as well as the toroidal rotation, have been varied. The TM localized near the plasma edge is found to be more unstable in the NT plasmas as compared to the PT counterpart. The fundamental reason for this difference is the lack of favorable average curvature stabilization in NT configurations. Direct comparison of the Mercier index corroborates this conclusion. For the core-localized mode, where the difference in the local triangularity between NT and PT becomes small and the curvature stabilization is significantly reduced, larger Shafranov shift in the plasma core associated with the NT configuration results in more stable TM. The plasma toroidal flow generally stabilizes the TM in plasmas with both NTs and PTs. The flow stabilization is however weaker in the case of negative triangularity with finite plasma pressure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Density pedestal prediction model for tokamak plasmas

Abstract A model for the pedestal density prediction based on neutral penetration combined with pedestal transport is presented. The model is tested against a pedestal database of JET-ILW Type I ELMy H-modes showing good agreement over a wide range of parameters both in standalone modelling (using the experimental temperature profile) and in full Europed modelling that predicts both density and temperature pedestals simultaneously. The model is further tested for ASDEX Upgrade and MAST-U Type I ELMy H-modes and both are found to agree with the same model parameters as for JET-ILW. The JET-ILW experiment where the isotope of the main ion is varied in a D/T scan at constant gas rate and constant β N is successfully modelled as long as the separatrix density ( n e,sep ) and pedestal transport coefficient ratio ( D / χ ) are varied in accordance with the experimentally observed variation of n e,sep and the isotope dependence of D / χ found in gyrokinetic simulations. The predictions are found to be sensitive to n e,sep which is why the model is combined with an n e,sep model to predict the pedestal for the STEP fusion reactor.

Physics↗

Saturation of fishbone instability through zonal flows driven by energetic particle transport in tokamak plasmas

Gyrokinetic and kinetic-MHD simulations are performed for the fishbone instability in the DIII-D discharge #178631, chosen for validation of first-principles simulations to predict the energetic particle (EP) transport in an ITER prefusion baseline scenario. Fishbone modes are found to generate zonal flows, which dominate the fishbone saturation. The underlying mechanisms of the two-way fishbone-zonal flows nonlinear interplay are discussed in details. Numerical and analytical analyses identify the fishbone-induced EP redistribution as the dominant generation mechanism for zonal flows. The zonal flows modify the nonlinear dynamics of phase space zonal structures, which reduces the amount of EPs able to resonate with the mode, leading to an early fishbone saturation. Simulation results including zonal flows agree quantitatively with DIII-D experimental measurements of the fishbone saturation amplitude and EP transport, supporting this novel saturation mechanism by self- generated zonal flows. Moreover, the wave-particle mode-locking mechanism is shown to determine quantitatively the fishbone frequency down-chirping, as evident in GTC simulation results in agreement with predictions from analytical theory. Finally, the&#xD;fishbone-induced zonal flows are possibly responsible for the formation of an ion-ITB in the DIII-D discharge. Based on the low EP transport and the large zonal flow shearing rates associated with the fishbone instability in gyrokinetic simulations of the ITER scenario, it is conjectured that high performance scenarios could be designed in ITER burning plasmas through fishbone-induced ITBs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hyperdiffusion of dust particles in a turbulent tokamak plasma

The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number $St\propto a_d/n_0$, with $a_d$ the dust radius and $n_0$ the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories $\Delta r^2$ is shown to depend on the ratio $Ku/St$, with $Ku\propto u_{rms}$ the Kubo number and $u_{rms}$ the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting $\Delta r^2\propto (Ku/St)^2t^3$, or $\Delta r^2\propto (u_{rms}n_0/a_d)^2t^3$. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.

dust↗

Stability and Control of Burning Tokamak Plasmas with Resistive Walls (Second Year Report/ Final Report)

This research will focus on quantitative prediction of the stability, control, and equilibrium state evolution in toroidal burning plasmas. The stability of long pulse burning plasmas is highly sensitive to the physics of resonant layers in the plasma, sources of momentum and ow, kinetic effects of energetic particles, and boundary conditions at the wall, including feedback control and error fields. In ITER in particular, the low toroidal ow equilibrium state, sustained primarily by energetic alpha particles from fusion reactions, will require the consideration of all of these key elements to predict quantitatively the stability and evolution. The principal investigators on this proposal are leading experts in the relevant theoretical and computational areas, and aim to perform computations guided by analytic modeling, to address this physics in realistic configurations. The overall goal is to understand the key physics mechanisms that describe resistive toroidal burning plasmas, surrounded by a resistive wall, under active feedback control. With the physics of the energetic ions, resonant layers, resistive wall, and toroidal momentum transport included, this study will extend from recent publications in theory and simulation of individual effects and move toward predictive modeling for burning plasmas.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Fast Particle-Wave Interactions and Alfvén Eigenmodes in JET Tokamak Plasmas

This document serves as the closeout report of DOE Grant Award No. DE-FG02-99ER54563 with project period 1 April 2015 through 31 March 2020. The project comprised the international collaboration between MIT and EU scientists on the JET facility to improve our understanding of the physics of energetic particle-wave interactions by measuring the damping rates of stable Alfvén Eigenmodes (AEs) and unstable energetic particle driven modes. More specifically, this project involved the continued participation of MIT, the Culham Centre for Fusion Energy, the Swiss Plasma Center, and theorists from various European laboratories and from UC Irvine. Past contributions from the University of São Paulo are gratefully acknowledged. The Alfvén Eigenmode Active Diagnostic (AEAD) on JET discharges was successfully upgraded in this period and has extracted physically useful information, in primarily deuterium plasma discharges. It is expected that such experiments would be continued during the DT campaign in CY 2021 to assess the damping rates of similar modes in the presence of alpha particles, a product of fusing burning plasma. Only JET would carry out such experiments in the near term in the world. It is important to note that this collaboration was continued under DOE Grant Award No. DE-SC0014264 from 1 April 2020 through the present. In this grant period, the AEAD was upgraded with a set of individual amplifiers for each of a set of six antennas in two toroidally opposite locations. These new amplifiers allowed targeted selection of the antennas’ toroidal spectrum for AEs of interest with toroidal mode number | n | ≤ 20. The resonant detection and measurement of the damping rates of AEs was obtained from magnetic probes that could be compared with theory and simulations. This is a key topic of investigation for ITER and all other next-step fusion experiments, where such modes will interact with energetic particles produced by fusion reactions (alpha particles), Neutral Beam Injection (NBI) and Ion Cyclotron Resonance Heating (ICRH). The majority of the observations during this period were of Toroidal Alfvén Eigenmodes (TAEs) as these are most commonly observed on JET; a number of measurements were made during dedicated TAE experiments. However, a new set of lower frequency band filters were procured with the goal of studying Geodesic Acoustic Modes (GAMs), Beta (Acoustic) AEs (BAE/BAAEs), and Reverse Shear AEs (RSAEs), also predicted by theory. Commissioning and optimizations were successfully completed in this period, and the diagnostic has been in operation during the more recent JET campaigns. Initial results have been obtained in dedicated TAE experiments and successfully compared to drift-kinetic theory. A wide range of theoretical studies have been undertaken in support of the upcoming JET campaigns experiments. To supplement the ongoing use of ideal MHD codes, such as MISHKA during the studies of TAEs, gyrokinetic simulations of low frequency AEs were performed in collaboration with UC Irvine. The Gyrokinetic Toroidal Code (GTC) was used to determine the structure, frequencies and stability of AEs in JET plasmas. Thus, a solid scientific foundation has been laid for future DT campaigns in JET in the 2021 operation period when the damping rates of relevant modes in the presence of alpha particles could be assessed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stability and Control of Burning Tokamak Plasmas with Resistive Walls (Final Report)

This research has focused on quantitative prediction of the stability, control, and equilibrium state evolution in toroidal burning plasmas. The stability of long pulse burning plasmas is highly sensitive to the physics of resonant layers in the plasma, sources of momentum and flow, kinetic effects of energetic particles, and boundary conditions at the wall, including feedback control and error fields. In ITER in particular, the low toroidal flow equilibrium state, sustained primarily by energetic alpha particles from fusion reactions, will require the consideration of all of these key elements to predict quantitatively the stability and evolution. The principal investigators on this proposal are leading experts in the relevant theoretical and computational areas, and aimed to perform computations guided by analytic modeling, to address this physics in realistic configurations. The overall goal is to understand the key physics mechanisms that describe resistive toroidal burning plasmas, surrounded by a resistive wall, under active feedback control. With the physics of the energetic ions, resonant layers, resistive wall, and toroidal momentum transport included, this study will extend from recent publications in theory and simulation of individual effects and move toward predictive modeling for burning plasmas.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗