Session CO5: MF: SPARC and C-MOD

Overview of SPARC on the high-field path to fusion energy

The SPARC mission is to create and confine a plasma~that produces net fusion energy for the first time. High-temperature, high-field superconductors comprise the fundamental technology that enables SPARC to be built at a relatively small scale compared to other proposed net-energy tokamaks; the smaller scale enables it to be completed on a faster timeline. The two major milestones of the 3-year Phase 1 of the project to be completed in June 2021 are (1) design, construction, and operation of a SPARC-relevant toroidal field model coil and (2) a ready-to-construct engineering design of the SPARC tokamak and facility. The first year of R{\&}D was very successful, proving the robust performance of superconducting cables under SPARC-relevant conditions. The team has moved on to designing and preparing to construct the toroidal field model coil, which will retire most of the major integrated risks of the SPARC magnet system. In parallel, the physics and engineering design of the SPARC device has been progressing to a self-consistent ``V1'' design in which all major systems have a robust margin to engineering limits.   

Parameter Sensitivities and Physics Optimization for SPARC

SPARC, the fourth in the series of compact high-field tokamaks at MIT, will be a D-T burning experiment based on emerging HTS magnet technology. Using conservative plasma physics assumptions -- essentially the ITER baseline -- an initial design point was predicted to achieve a mission defined as Q\textgreater 2, with significant margin, and fusion power greater than 50 MW. Starting with that V0 design point, which had B$_{\mathrm{T}} \quad =$ 12T and R $=$ 1.65m, recent activities have focused on joint optimization of the physics and engineering of the device. These studies have looked at the dependence of fusion gain and power with machine parameters: magnetic field, safety factor, auxiliary power, aspect ratio, elongation and triangularity while assessing sensitivities to uncertainties in energy confinement L-H power threshold, density and temperature profile peaking and impurity content. Both 0D scaling and 1.5D simulations were used in these studies. Maintaining performance margin for the mission against these uncertainties is a key consideration. Physics performance is then balanced against the impact on device cost, mechanical stresses, thermal loads and neutron shielding. The outcome will be a new design point which will be the subject of detailed engineering design.   

Scenario Development for SPARC

Discharge scenarios in SPARC have been developed using the Tokamak Simulation Code (TSC), showing that the SPARC design can sustain the baseline plasma shape and current of 7.5 MA for 10 seconds. Like any tokamak, designing SPARC involves more than consideration of only the peak performance operating point. One must also be able to get to that operating point robustly, starting with plasma initiation, completing the plasma current ramp, and then eventually ramping the current down after the flattop. This presentation will describe time-dependent Grad-Shafranov simulations performed with TSC [S. C. Jardin et al., \emph{J. Comp. Phys.} 66, 481 (1986)] in order to determine the requirements on the central solenoid and poloidal field coils for SPARC. Included in these simulation are other time-dependent phenomena, such as plasma shaping control and feedback controlled vertical stability. Simulations show that a current ramp rate of 1 MA/s is feasible, giving a total discharge length of approximately 25 seconds. Further refinement of these simulations will inform the design of SPARC's central solenoid, poloidal field coils, vacuum vessel, and vertical stability feedback coils.   

Physics-Based Integrated Modeling and Exploration of Fusion Performance in SPARC Plasmas

SPARC is designed to be a high-field, medium-size machine (v0 parameters: B=12T, R=1.65m) aimed at achieving net energy gain with ICRF as its primary heating mechanism. Empirical predictions with conservative physics (H98=1.0) indicate that SPARC baseline plasmas will generate more than 50MW of fusion power, reaching $Q>2$. To build confidence that SPARC will realize its mission, physics-based integrated modeling has been performed. The TRANSP code coupled with the physics-based TGLF turbulence model confirms $Q>2$ operation is feasible for SPARC parameters. In this analysis, ion cyclotron waves are simulated with the full wave TORIC code and alpha heating is included with the Monte-Carlo fast ion NUBEAM module. Exploration of the parameter space also indicates that Q can be enhanced with small variations from baseline, providing a pathway to increase performance while moving away from stability boundaries. This talk presents the workflow to study SPARC plasmas, discusses assumptions and introduces trends of performance against geometric and engineering parameters.   

Investigation of Core Physics in the SPARC Tokamak

Initial 1.5D modeling of the SPARC tokamak has enabled a first look at the physics regimes accessible during SPARC operation. This integrated modeling has begun to shed light on open scientific questions related to reactor-relevant, high field tokamak operation and reveals some of the unique scientific opportunities presented by the SPARC device. This talk will present a survey of results obtained from modeling of core and pedestal physics for the SPARC v0 design parameters. Physics-based transport models reveal stiff core transport, particularly in the ion channel, due to the existence of unstable long wavelength turbulence over a large part of the profile with well coupled electrons and ions existing in the outer half of the plasma. The observed stiff core transport implies that the modeling and assumptions made in the pedestal play a dominant role in determining the overall fusion performance. In this talk, we will discuss the balance of ion and electron energy, observations of the dominant turbulence as calculated by TGLF and CGYRO, the alpha particle physics accessed in SPARC including its relevance to the study burning plasma regimes, and the implications of these observations on the model fidelity required for accurate modeling of high field tokamak plasma conditions.   

The Edge Pedestal on the SPARC Tokamak

The SPARC tokamak is designed to operate in a high confinement regime with an edge transport barrier in order to meet its $Q>2$ objective. The highest pedestal pressure previously achieved is $\sim 80$kPa; the anticipated H-mode pedestal on SPARC will exceed this value by $>3$ and do so at reactor relevant collisionality. Because the pedestal is in a regime limited by current-driven kink/peeling modes, there is minimal degradation of the achievable temperature pedestal with increasing density. Possible relaxation mechanisms for the pedestal include both periodic edge localized modes (ELMs) and continuous fluctuations. We estimate the impact of ELM-suppressed operation on the pedestal height using documented results from existing devices. Experimental results from Alcator C-Mod are particularly informative, since it routinely operated at high field ($\leq$8T vs. 12T for SPARC v0) and density ($\leq$6x10$^{20}$m$^{-3}$, comparable to SPARC v0). C-Mod pushed into a reactor-relevant regime of neutral opaqueness, in which the capability of recycling neutrals to refuel the core plasma is strongly diminished. This regime of high neutral screening was compatible on C-Mod with edge pedestal formation, a very positive result when looking forward to SPARC.   

Developing solutions for GW/m$^{\mathrm{2}}$-level divertor heat fluxes for a 10 second flat top discharge in SPARC

The heat flux width in the SPARC tokamak is projected to be approximately 0.2 mm [1,2]. This implies that operation with the planned 100 MW of fusion power will result in unmitigated steady state parallel heat fluxes to the divertor that are roughly 30 GW/m$^{\mathrm{2}}$ and potentially higher during transients, presenting one of the most challenging power exhaust scenarios to date. Furthermore, the compact design and lack of a neutron shielding blanket means that there is limited space for advanced divertor geometries. The current baseline scenario involves the implementation of a rapid strike point sweep to spread the heat flux over a large divertor target surface area. Nevertheless, a modest level of divertor and core radiation is required to reduce surface heat fluxes. Because SPARC will operate with a 25 second pulse length, which includes a 10 second flat top, inertial cooling of target plate components can be employed. This eliminates the need for an active cooling system, greatly simplifying the design and reducing risk of component failure. UEDGE simulations of a preliminary divertor design concept will be presented and areas for further research and development identified. [1] T. Eich, et al., \textit{NF}, 58(9), 093031, 2013. [2] D. Brunner, et al., \textit{NF}, 58(7), 076010, 2018.   

ICRF Heating for SPARC

SPARC is designed to have a 30 MW coupled ICRF system as its sole proposed auxiliary heating method. SPARC RF scenarios are based on the successes of Alcator C-Mod as well as the TFTR and JET programs during their D-T operation. Among heating methods, ICRF is the only proven method that can effectively heat high density and high field plasmas in SPARC for both the pre-D-T and D-T operations. The single-pass-absorption for D-T burning plasma combining 2nd harmonic T heating and minority $^3$He heating will be $>$ 50\% under most conditions. Optimal $k_\|$ spectra for performance will be determined and incorporated detailed simulation results using TORIC and AORSA/CQL3D will be presented. These simulations will determine the power partition among species as the tail T and 3He ions slow down. In addition to operation at 120 MHz, we will discuss the possibility of 3-species scenario operation at a lower 80 MHz operation. Optimum fusion yield occurs for beam on target temperatures of 110 keV. This suggests tuning of ICRF scenarios to create tail energies for fuel ions in this range can be used to maximize the D-T burn rate. We will discuss possible scenarios for this as well as characterizing the general increase of the fusion rate in an ICRF heated plasma over the thermal D-T rate.   

Projections of ripple-loss of fast ions in SPARC

A major design consideration for the compact SPARC facility (R$=$1.65 m, a$=$0.50 m) is avoiding excessive first-wall heating from fast ions that are lost from the plasma. At full performance, the SPARC tokamak is projected to have 30 MW of energetic RF tail ions and up to 20 MW of alpha particles, yielding \textasciitilde 40 MW of banana-trapped energetic ions. These will be subject to radial transport and loss from the plasma by the ripple-trapping, collisional-banana, and stochastic banana-drift diffusion mechanisms. Full-orbit simulations of alpha loss expected in ITER by the ASCOT code (Nucl. Fusion \textbf{49} (2009) 095001) yielded an alpha-loss `footprint' that was highly concentrated both toroidally and poloidally on limiters mounted on the outer midplane, and such a concentration is expected in SPARC also. A rudimentary analysis suggests that the ITER ripple-loss calculations scale to maximum surface heating of \textasciitilde 1 MW/m$^{\mathrm{2}}$ in SPARC when $\delta_{\mathrm{max}} \quad =$ 0.5{\%}. Here we report full-orbit simulations of the ripple loss of RF-tail and alpha particles in SPARC by the ASCOT and SPIRAL codes, including simulations of the synergistic effect of sawteeth on ripple losses.   

Runaway electrons in SPARC

We explore the evolution and diagnosis of post-disruption runaway electrons (REs) in the SPARC V0 tokamak design [1]. The RE problem may be worsened by high plasma currents ($I_p\sim$~7.5~MA) better confining REs, and compact size ($R_0\sim$~1.65~m, $a\sim$~0.5 m) leading to faster current quench times. However, the high magnetic field ($B_0\sim$~12~T) will increase synchrotron power loss, $>5\times$ higher than ITER. The code GO [2] is used to model the electric field and RE current profiles during realistic SPARC disruption scenarios. Scans are performed in post-disruption plasma temperature, thermal quench time, and pre-disruption elongation. The kinetic equation solver CODE [3] is used to evolve the RE momentum space distribution function, giving expected energies of the RE plateau. Recent findings from \emph{quiescent} RE experiments in Alcator C-Mod indicate that the spectra, polarization, and images of RE synchrotron radiation can give insight into RE energy, pitch angle, and spatial distributions, respectively [4-6].\newline [1] Greenwald 2018 PSFC/RR-18-2 [2] Smith 2006 PoP 13 [3] Landreman 2014 CPC 185 [4] Tinguely 2018 NF 58 [5] Tinguely 2019 NF accepted [6] Tinguely 2018 PPCF 60   

Experimental Inference and Simulations of Impurity Transport in High-Performance Tokamak Plasmas

High performance tokamak operation is strongly constrained by the purity of core plasmas. This motivates model validation across multiple transport channels to understand the behavior of heavy ions. We present novel methods to obtain impurity transport radial diffusion and convection coefficients using Bayesian inference via nested sampling in high-dimensional and multi-modal parameter spaces. Fully-marginalized Bayesian estimates are obtained with free knot locations and nuisance parameters that reduce reliance on uncertain experimental details. We compare EDA H-mode and I-mode high-performance scenarios with an L-mode discharge in Alcator C-Mod. In these experiments, trace amounts of calcium (Z$=$20) were introduced with laser blow-off injections and diagnosed via measurements of Ca17$+$/18$+$ emission. To interpret data, the STRAHL impurity transport code [Dux PPCF 2003] was optimized for iterative operation, resulting in fundamental advantages in parallel execution and additional physics fidelity in sawtoothing discharges. Bayesian model selection and uncertainty quantification enable improved comparison of experimentally-inferred transport with neoclassical NEO [Belli PPCF 2008], as well as turbulent TGLF [Staebler PoP 2007] and CGYRO [Candy JCP 2016] simulations.   

Impact of density fluctuations on LHCD power deposition profile on Alcator C-Mod

Lower hybrid current drive (LHCD) experiments on Alcator C-Mod have demonstrated efficient current drive at a reactor-relevant density in a divertor configuration for the first time. A detailed experimental study [Mumgaard, MIT PhD Thesis (2016)] indicates that the injected wave power is centrally deposited with a self-similar power deposition profile that is insensitive to the input wave and plasma parameters. This contrasts with standard model analysis that generally predicts an off-axis power deposition in the C-Mod multi-pass damping regime. Since density fluctuations are always present in the tokamak boundary region, an interaction of the LH wave with the density fluctuation may modify wave propagation behavior by rotating the wave perpendicular wave-vector, k$_{\mathrm{\bot }}$ [P. T. Bonoli and E. Ott, Phys. Rev. Lett. \textbf{46}, 424 (1981)]. In order to assess such an effect, a phenomenological model that introduces a spread in k$_{\mathrm{\bot \thinspace }}$is examined using a GENRAY/CQL3D ray-tracing/Fokker-Planck model in the $\pi $-scope workflow. Modeling results indicate that, with a judicious choice of k$_{\mathrm{\bot }}$ rotation, the ray exhibits enhanced first-pass radial penetration, leading to on-axis wave power deposition. A comparison of the model with the experimental result will be presented.   

Parameter of Merit for Experiments Aiming at DT Ignition

Given the importance of reaching ignition conditions in magnetically confined plasmas [1] it is appropriate to identify parameters of merits for the design of future machines. One considered for the Ignitor experiment is ${{P}_{mI}}=B_{p}^{2}{{I}_{T}}$, where ${{I}_{T}}$ is the toroidal plasma current and ${{B}_{p}}$ is the average poloidal field, aiming for about 100 (T2 MA). The starting point for ${{T}_{e}}\simeq {{T}_{i}}$, is $\Re \simeq {{\alpha }_{T}}nTD_{\bot }^{th}/{{a}^{2}}\ $ where $\Re $ is the D-T reactivity, $\Re \propto {{\alpha }_{F}}{{n}^{2}}{{T}^{2}}$ and a is the mean plasma radius. Assuming $D_{\bot }^{th}\propto {{\alpha }_{D}}/n\ $ and $n\propto {{\alpha }_{L}}J$, where $J$ is the current density,${{\alpha }_{F}}{{n}^{2}}{{T}^{2}}\simeq {{\alpha }_{T}}nT{{\alpha }_{D}}/\left( J{{a}^{2}}{{\alpha }_{L}} \right)\ $ and, for $nT\propto {{\alpha }_{c}}B_{p}^{2}$ we obtain $B_{p}^{2}{{I}_{p}}\propto \left( {{\alpha }_{D}}{{\alpha }_{T}} \right)/\left( {{\alpha }_{F}}{{\alpha }_{c}}{{\alpha }_{L}} \right)\ $. The introduced $\alpha $-parameters involve weaker dependences on plasma and machine characteristics than those given already. \\ $[1]$ B. Coppi and the Ignitor Team, Nucl. Fus. 55, 053001 (2015).