John C. Wright

The SPARC tokamak is expected to robustly enter the burning plasma regime (Q > 5) during deuterium–tritium operations and will provide a unique platform to study novel effects of alpha heating in reactor-relevant plasma scenarios. This article presents the near-final design and characterization of the high-resolution magnetic proton recoil (MPR) neutron spectrometer for SPARC and discusses the opportunities for burning plasma studies enabled by this instrument. The MPR spectrometer will be positioned in the midplane line of sight of the poloidal neutron camera and view SPARC’s core plasma. The as-built instrumental response function is calculated based on measured magnetic fields, which have been optimized to maximize resolution and sensitivity constrained by limited space and power. The spectrometer has variable resolution and sensitivity, with settings ranging from high efficiency (2.22 × 10−6 counts per incident neutron) and low resolution (1070 keV) to low efficiency (1.48 × 10−7 counts per incident neutron) and high resolution (149 keV). We also present kinetic simulations of burning plasma effects, which we use to calculate synthetic neutron spectra to better understand the diagnostic capabilities of the instrument. Based on these simulations, the spectrometer is expected to diagnose core ion temperature with less than 7% uncertainty and time resolution less than 100 ms in break-even campaign experiments. Non-thermal alpha knock-on fusion is found to be a small contribution to overall fusion power; however, it does produce a measurable feature in the neutron spectrum that can be used to evaluate alpha heating and confinement in high-gain scenarios.

In high-gain reactor-relevant fusion plasmas, alpha heating dominates the power balance. As alpha particles thermalize, they transfer kinetic energy to the bulk plasma via collisions. At the MeV collision energies characteristic of alpha thermalization, nuclear elastic scattering cross sections become comparable to or exceed the Coulomb cross section, greatly enhancing the probability of large-angle scattering events. These nuclear interactions can accelerate a fuel ion to several MeV in a single collision, producing distinctive non-Maxwellian fast “knock-on” tails in the kinetic distribution functions that are characteristic of thermonuclear burn. This effect has been experimentally confirmed by the observation of fast neutron spectral tails at the Joint European Torus and at the National Ignition Facility. Here, we present the first kinetic simulations of alpha particle knock-on ion generation for the SPARC tokamak's Primary Reference Discharge, a 12.2 T, 8.7 MA H-mode scenario projected to achieve a scientific gain of ∼11, deep in the burning plasma regime. We couple the bounce-averaged Fokker–Planck solver CQL3D with the Monte Carlo reaction integral code DRESS, implementing a thermally broadened alpha source term, large-angle scattering corrections to CQL3D's collision operator for deuterons and tritons, and a synthetic neutron spectrum diagnostic. The knock-on ion tails evolve toward a kinetic steady state after about two alpha slowing-down times (∼ 600 ms) and comprise approximately 0.1% of the total fuel ion population, with the fast-deuterium density slightly exceeding fast-tritium, consistent with nuclear resonance in the α,d cross section below the alpha birth energy. Equivalent Maxwellian fits to the fast-ion distribution functions, assessed with log10-space coefficients of determination R log 2, are adequate for describing knock-on fuel ions (R log 2 = 0.64–0.89), but are fundamentally inappropriate for the alpha slowing-down distribution (R log 2≈0). Synthetic neutron emission spectra computed with DRESS predict a steady-state alpha knock-on neutron ratio of 8.8×10−5 and demonstrate that SPARC's magnetic proton recoil neutron spectrometer will be sensitive to the alpha knock-on neutron tail, providing a direct observational diagnostic of alpha confinement and thermalization in a magnetically confined burning plasma.

High magnetic field tokamaks, like SPARC, rely on ion cyclotron radio frequency heating (ICRF) to reach fusion relevant temperatures. The SPARC tokamak will have 14 ICRF antennas in 7 toroidal locations delivering > 20 MW of power to the plasma. New capabilities with the full wave cold plasma solver, Stix, now allow for resolving the wave-particle resonances using lower order thermal corrections to capture core absorption of Landau damping and ion resonances in devices like SPARC. Favorable comparisons to the TORIC codes give confidence in the single pass absorption of this model to accurately capture the strength of edge interactions of the RF. Using this new dielectric formulation in the Stix code, simulations of the 2D poloidal cross section of SPARC are completed for the first campaign and primary reference-like discharges (PRD-like). A scan of the minority ion concentrations of helium-3 is performed and shows the expected behavior that as the helium-3 decreases the amount of single pass absorption also decreases which is seen in both scenarios. Additionally, both scenarios show only slight differences in single-pass absorption for the range of 3% to 5% helium-3 allowing for more flexibility in experiments. This study also highlights the differences between the first campaign and PRD-like with the first campaign discharges showing much more multi-pass absorption and an effect of confining the wave to a smaller portion of the cross-section due to the fast wave cut-off. This latter result suggests that far-field sheath rectification at the high-field side would be minimal for the first campaign scenario.

We are adapting the all-orders spectral algorithm (AORSA) [Jaeger Phys. Plasmas 8 (2001)] from tokamak geometry to axisymmetric magnetic mirror geometry. We will use the modified AORSA to study ion cyclotron range of frequency (ICRF) heating in the Wisconsin HTS Axisymmetric Mirror (WHAM) magnetic mirror device [D. Endrizzi J. Plasma Phys. 5 (2023)]. ICRF power will be used in WHAM to accelerate high-energy neutral beam injected deuterium ions with ion cyclotron absorption at the second to fourth harmonics of deuterium. At these harmonics, for the spatial scales present in WHAM, full-wave simulations most accurately capture wave propagation, including transmission, reflection, and absorption at the cyclotron layer. The antenna is modeled as a single strap with m = 0 excitation, where m is the azimuthal mode number. We present some preliminary results for wave coupling and heating.

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λi≫1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R2∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

A real-time capable core Ion Cyclotron Range of Frequencies (ICRF) heating model on NSTX and WEST is developed. The model is based on two nonlinear regression algorithms, the random forest ensemble of decision trees and the multilayer perceptron neural network. The algorithms are trained on TORIC ICRF spectrum solver simulations of the expected flat-top operation scenarios in NSTX and WEST assuming Maxwellian plasmas. The surrogate models are shown to successfully capture the multi-species core ICRF power absorption predicted by the original model for the high harmonic fast wave and the ion cyclotron minority heating schemes while reducing the computational time by six orders of magnitude. Although these models can be expanded, the achieved regression scoring, computational efficiency and increased model robustness suggest these strategies can be implemented into integrated modeling frameworks for real-time control applications.

Reproducing fast-ion enhanced fusion rates from ion-cyclotron resonance heating (ICRH) in tokamaks requires the self-consistent coupling of a full-wave solver and a Fokker–Planck solver, which evolves multiple simultaneously resonant ion species. We introduce a new self-consistent model that iterates the TORIC full-wave solver with the CQL3D Fokker–Planck solver using the integrated plasma simulator (IPS). This model evolves the bounce-averaged ion distribution functions in both parallel and perpendicular velocity-space with a quasilinear radio frequency (RF) diffusion operator valid in the ion finite Larmor radius (FLR) limit and the RF electric fields with the resultant non-Maxwellian FLR dielectric tensor. This produces non-Maxwellian ICRH simulations that are fully self-consistent, fast, and interoperable with integrated modeling frameworks, such as TRANSP/GACODE/IPS-FASTRAN. We demonstrate our model's capabilities by validating it against experimental data in Alcator C-Mod. We then perform the first RF heating simulations of SPARC using self-consistent non-Maxwellian ion distributions to investigate the potential to enhance fusion rates using ion cyclotron resonance heating generated fast ions.

As the Ion Cyclotron Radio Frequency range (ICRF) heating becomes more favorable in fusion devices, the urgency of predicting and mitigating impurity generation that arises from it becomes more pressing. In the ICRF regime, rectified Radio Frequency (RF) sheaths are known to form at antenna and material edges that influence negative effects like sputtering and a decrease in heating efficiency. Methods to mitigate the formation of these RF sheaths through RF image currents cancellation have been experimentally studied. A power-phasing scan done on Alcator C-Mod in which the amount of power on the two inner straps (P _in) versus the total 4 straps (P _tot) was varied showed a minimization of enhanced potentials between P in / P tot ∼ 0.7–0.9 while impurities were minimized for P in / P tot ∼ 0.5–0.8. New capabilities in the realm of representing the RF sheath numerically now allow for these experiments to be simulated. Given the size of the sheath relative to the scale of the device, it can be approximated as a Boundary Condition (BC). A new parallelized cold-plasma wave equation solver called Stix implements a non-linear sheath impedance model BC formulated by Myra et al (2015 Phys. Plasmas 22 062507) through the method of finite elements using the MFEM library [http://mfem.org]. It is seen that Stix shows qualitative agreement with the measured C-Mod enhanced potentials.

Ion cyclotron radio frequency range (ICRF) power plays an important role in heating and current drive in fusion devices. However, experiments show that in the ICRF regime there is a formation of a radio frequency (RF) sheath at the material and antenna boundaries that influences sputtering and power dissipation. Given the size of the sheath relative to the scale of the device, it can be approximated as a boundary condition (BC). Electromagnetic field solvers in the ICRF regime typically treat material boundaries as perfectly conducting, thus ignoring the effect of the RF sheath. Here we describe progress on implementing a model for the RF sheath based on a finite impedance sheath BC formulated by J. Myra and D. A. D'Ippolito, Physics of Plasmas 22 (2015) which provides a representation of the RF rectified sheath including capacitive and resistive effects. This research will discuss the results from the development of a parallelized cold-plasma wave equation solver Stix that implements this non-linear sheath impedance BC through the method of finite elements in pseudo-1D and pseudo-2D using the MFEM library. The verification and comparison of the sheath BC from Stix with results from H. Kohno and J. Myra, Computer Physics Communications 220 129-142 (2017) will also be discussed.