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The SPARC tokamak is a critical next step towards commercial fusion energy. SPARC is designed as a high-field ($B_0 = 12.2$ T), compact ($R_0 = 1.85$ m, $a = 0.57$ m), superconducting, D-T tokamak with the goal of producing fusion gain $Q>2$ from a magnetically confined fusion plasma for the first time. Currently under design, SPARC will continue the high-field path of the Alcator series of tokamaks, utilizing new magnets based on rare earth barium copper oxide high-temperature superconductors to achieve high performance in a compact device. The goal of $Q>2$ is achievable with conservative physics assumptions ($H_{98,y2} = 0.7$) and, with the nominal assumption of $H_{98,y2} = 1$, SPARC is projected to attain $Q \\approx 11$ and $P_{\\textrm {fusion}} \\approx 140$ MW. SPARC will therefore constitute a unique platform for burning plasma physics research with high density ($\\langle n_{e} \\rangle \\approx 3 \\times 10^{20}\\ \\textrm {m}^{-3}$), high temperature ($\\langle T_e \\rangle \\approx 7$ keV) and high power density ($P_{\\textrm {fusion}}/V_{\\textrm {plasma}} \\approx 7\\ \\textrm {MW}\\,\\textrm {m}^{-3}$) relevant to fusion power plants. SPARC's place in the path to commercial fusion energy, its parameters and the current status of SPARC design work are presented. This work also describes the basis for global performance projections and summarizes some of the physics analysis that is presented in greater detail in the companion articles of this collection.

SPARC is being designed to operate with a normalized beta of $\\beta _N=1.0$, a normalized density of $n_G=0.37$ and a safety factor of $q_{95}\\approx 3.4$, providing a comfortable margin to their respective disruption limits. Further, a low beta poloidal $\\beta _p=0.19$ at the safety factor $q=2$ surface reduces the drive for neoclassical tearing modes, which together with a frozen-in classically stable current profile might allow access to a robustly tearing-free operating space. Although the inherent stability is expected to reduce the frequency of disruptions, the disruption loading is comparable to and in some cases higher than that of ITER. The machine is being designed to withstand the predicted unmitigated axisymmetric halo current forces up to 50 MN and similarly large loads from eddy currents forced to flow poloidally in the vacuum vessel. Runaway electron (RE) simulations using GO+CODE show high flattop-to-RE current conversions in the absence of seed losses, although NIMROD modelling predicts losses of ${\\sim }80$ %; self-consistent modelling is ongoing. A passive RE mitigation coil designed to drive stochastic RE losses is being considered and COMSOL modelling predicts peak normalized fields at the plasma of order $10^{-2}$ that rises linearly with a change in the plasma current. Massive material injection is planned to reduce the disruption loading. A data-driven approach to predict an oncoming disruption and trigger mitigation is discussed.

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error. Optical analogues of gravitational systems probe general relativity in the laboratory, yet exactly mimicking black holes remains challenging. The authors model light propagating in optical analogues of equatorial Kerr–Newman black holes with regular materials, with clear advantages to realization.

The operation of a 3D coil--passively driven by the current quench loop voltage--for the deconfinement of runaway electrons is modeled for disruption scenarios in the SPARC and DIII-D tokamaks. Nonlinear MHD modeling is carried out with the NIMROD code including time-dependent magnetic field boundary conditions to simulate the effect of the coil. Further modeling in some cases uses the ASCOT5 code to calculate advection and diffusion coefficients for runaway electrons based on the NIMROD-calculated fields, and the DREAM code to compute the runaway evolution in the presence of these transport coefficients. Compared with similar modeling in Tinguely, et al [2021 Nucl. Fusion 61 124003], considerably more conservative assumptions are made with the ASCOT5 results, zeroing low levels of transport, particularly in regions in which closed flux surfaces have reformed. Of three coil geometries considered in SPARC, only the \\(n=1\\) coil is found to have sufficient resonant components to suppress the runaway current growth. Without the new conservative transport assumptions, full suppression of the RE current is maintained when the TQ MHD is included in the simulation or when the RE current is limited to 250kA, but when transport in closed flux regions is fully suppressed, these scenarios allow RE beams on the order of 1-2MA to appear. Additional modeling is performed to consider the effects of the close ideal wall. In DIII-D, the current quench is modeled for both limited and diverted equilibrium shapes. In the limited shape, the onset of stochasticity is found to be insensitive to the coil current amplitude and governed largely by the evolution of the safety-factor profile. In both devices, prediction of the q-profile evolution is seen to be critical to predicting the later time effects of the coil.

In [V.A. Izzo et al 2022 Nucl. Fusion 62 096029], state-of-the-art modeling of thermal and current quench (CQ) MHD coupled with a self-consistent evolution of runaway electron (RE) generation and transport showed that a non-axisymmetric (n = 1) in-vessel coil could passively prevent RE beam formation during disruptions in SPARC, a compact high-field tokamak projected to achieve a fusion gain Q > 2 in DT plasmas. However, such suppression requires finite transport of REs within magnetic islands and re-healed flux surfaces; conservatively assuming zero transport in these regions leads to an upper bound of RE current ~1 MA compared to ~8.7 MA of pre-disruption plasma current. Further investigation finds that core-localized electrons, within r/a < 0.3 and with kinetic energies 0.2-15 MeV, contribute most to the RE plateau formation. Yet only a relatively small amount of transport, i.e. a diffusion coefficient ~18 \\(\\mathrm{m^2/s}\\), is needed in the core to fully mitigate these REs. Properly accounting for (i) the CQ electric field's effect on RE transport in islands and (ii) the contribution of significant RE currents to disruption MHD may help achieve this.

In this paper, we present a new deep learning disruption prediction algorithm based on important findings from explorative data analysis which effectively allows knowledge transfer from existing devices to new ones, thereby predicting disruptions using very limited disruptive data from the new devices. The explorative data analysis conducted via unsupervised clustering techniques confirms that time-sequence data are much better separators of disruptive and non-disruptive behavior than the instantaneous plasma state data with further advantageous implications for a sequence-based predictor. Based on such important findings, we have designed a new algorithm for multi-machine disruption prediction that achieves high predictive accuracy on the C-Mod (AUC=0.801), DIII-D (AUC=0.947) and EAST (AUC=0.973) tokamaks with limited hyperparameter tuning. Through numerical experiments, we show that boosted accuracy (AUC=0.959) is achieved on EAST predictions by including in the training only 20 disruptive discharges, thousands of non-disruptive discharges from EAST, and combining this with more than a thousand discharges from DIII-D and C-Mod. The improvement of predictive ability obtained by combining disruptive data from other devices is found to be true for all permutations of the three devices. Furthermore, by comparing the predictive performance of each individual numerical experiment, we find that non-disruptive data are machine-specific while disruptive data from multiple devices contain device-independent knowledge that can be used to inform predictions for disruptions occurring on a new device.

In the Alcator C-Mod tokamak, relativistic runaway electron (RE) generation can occur during the flattop current phase of low density, diverted plasma discharges. Due to the high toroidal magnetic field (B = 5.4 T), RE synchrotron radiation is measured by a wide-view camera in the visible wavelength range (~400-900 nm). In this paper, a statistical analysis of over one thousand camera images is performed to investigate the plasma conditions under which synchrotron emission is observed in C-Mod. In addition, the spatiotemporal evolution of REs during one particular discharge is explored in detail via a thorough analysis of the distortion-corrected synchrotron images. To accurately predict RE energies, the kinetic solver CODE [Landreman et al 2014 Comput. Phys. Commun. 185 847-855] is used to evolve the electron momentum-space distribution at six locations throughout the plasma: the magnetic axis and flux surfaces q = 1, 4/3, 3/2, 2, and 3. These results, along with the experimentally-measured magnetic topology and camera geometry, are input into the synthetic diagnostic SOFT [Hoppe et al 2018 Nucl. Fusion 58 026032] to simulate synchrotron emission and detection. Interesting spatial structure near the surface q = 2 is found to coincide with the onset of a locked mode and increased MHD activity. Furthermore, the RE density profile evolution is fit by comparing experimental to synthetic images, providing important insight into RE spatiotemporal dynamics.

In the Alcator C-Mod tokamak, runaway electron (RE) experiments have been performed during low density, flattop plasma discharges at three magnetic fields: 2.7, 5.4, and 7.8 T, the last being the highest field to-date at which REs have been generated and measured in a tokamak. Time-evolving synchrotron radiation spectra were measured in the visible wavelength range (~300-1000 nm) by two absolutely-calibrated spectrometers viewing co- and counter-plasma current directions. In this paper, a test particle model is implemented to predict momentum-space and density evolutions of REs on the magnetic axis and q = 1, 3/2, and 2 surfaces. Drift orbits and subsequent loss of confinement are also incorporated into the evolution. These spatiotemporal results are input into the new synthetic diagnostic SOFT [M. Hoppe, et al., Nucl. Fusion 58(2), 026032 (2018)] which reproduces experimentally-measured spectra. For these discharges, it is inferred that synchrotron radiation dominates collisional friction as a power loss mechanism and that RE energies decrease as magnetic field is increased. Additionally, the threshold electric field for RE generation, as determined by hard X-ray and photo-neutron measurements, is compared to current theoretical predictions.

Next generation high performance (HP) tokamaks risk damage from unmitigated disruptions at high current and power. Achieving reliable disruption prediction for a device's HP operation based on its low performance (LP) data is key to success. In this letter, through explorative data analysis and dedicated numerical experiments on multiple existing tokamaks, we demonstrate how the operational regimes of tokamaks can affect the power of a trained disruption predictor. First, our results suggest data-driven disruption predictors trained on abundant LP discharges work poorly on the HP regime of the same tokamak, which is a consequence of the distinct distributions of the tightly correlated signals related to disruptions in these two regimes. Second, we find that matching operational parameters among tokamaks strongly improves cross-machine accuracy which implies our model learns from the underlying scalings of dimensionless physics parameters like q_{95}, \\beta_{p} and confirms the importance of these parameters in disruption physics and cross machine domain matching from the data-driven perspective. Finally, our results show how in the absence of HP data from the target devices, the best predictivity of the HP regime for the target machine can be achieved by combining LP data from the target with HP data from other machines. These results provide a possible disruption predictor development strategy for next generation tokamaks, such as ITER and SPARC, and highlight the importance of developing on existing machines baseline scenario discharges of future tokamaks to collect more relevant disruptive data.

This paper presents the first experimental analysis of polarized synchrotron emission from relativistic runaway electrons (REs) in a tokamak plasma. Importantly, we show that the polarization information of synchrotron radiation can be used to diagnose spatially-localized RE pitch angle distributions. Synchrotron-producing REs were generated during low density, Ohmic, diverted plasma discharges in the Alcator C-Mod tokamak. The ten-channel Motional Stark Effect diagnostic was used to measure spatial profiles of the polarization angle \\(\\theta_{\\mathrm{pol}}\\) and the fraction \\(\\mathrm{f}_{\\mathrm{pol}}\\) of detected light that was linearly-polarized. Spatial transitions in \\(\\theta_{\\mathrm{pol}}\\) of 90\\(\\deg\\)---from horizontal to vertical polarization and vice versa---are observed in experimental data and are well-explained by the gyro-motion of REs and high directionality of synchrotron radiation. Polarized synchrotron emission is modeled with the synthetic diagnostic SOFT; its output Green's (or detector response) functions reveal a critical RE pitch angle at which \\(\\theta_{\\mathrm{pol}}\\) flips by 90\\(\\deg\\) and \\(\\mathrm{f}_{\\mathrm{pol}}\\) is minimal. Using SOFT, we determine the dominant RE pitch angle which reproduces measured \\(\\theta_{\\mathrm{pol}}\\) and \\(\\mathrm{f}_{\\mathrm{pol}}\\) values. The spatiotemporal evolutions of \\(\\theta_{\\mathrm{pol}}\\) and \\(\\mathrm{f}_{\\mathrm{pol}}\\) are explored in detail for one C-Mod discharge. For channels viewing REs near the magnetic axis and flux surfaces \\(q\\) = 1 and 4/3, disagreements between synthetic and experimental signals suggest that the sawtooth instability may be influencing RE dynamics. Furthermore, other sources of pitch angle scattering, not considered in this analysis, could help explain discrepancies between simulation and experiment.