Search

The MANTA (Modular Adjustable Negative Triangularity ARC-class) design study investigated how negative-triangularity (NT) may be leveraged in a compact, fusion pilot plant (FPP) to take a ``power-handling first" approach. The result is a pulsed, radiative, ELM-free tokamak that satisfies and exceeds the FPP requirements described in the 2021 National Academies of Sciences, Engineering, and Medicine report ``Bringing Fusion to the U.S. Grid". A self-consistent integrated modeling workflow predicts a fusion power of 450 MW and a plasma gain of 11.5 with only 23.5 MW of power to the scrape-off layer (SOL). This low $P_\text{SOL}$ together with impurity seeding and high density at the separatrix results in a peak heat flux of just 2.8 MW/m$^{2}$. MANTA's high aspect ratio provides space for a large central solenoid (CS), resulting in ${\sim}$15 minute inductive pulses. In spite of the high B fields on the CS and the other REBCO-based magnets, the electromagnetic stresses remain below structural and critical current density limits. Iterative optimization of neutron shielding and tritium breeding blanket yield tritium self-sufficiency with a breeding ratio of 1.15, a blanket power multiplication factor of 1.11, toroidal field coil lifetimes of $3100 \pm 400$ MW-yr, and poloidal field coil lifetimes of at least $890 \pm 40$ MW-yr. Following balance of plant modeling, MANTA is projected to generate 90 MW of net electricity at an electricity gain factor of ${\sim}2.4$. Systems-level economic analysis estimates an overnight cost of US\$3.4 billion, meeting the NASEM FPP requirement that this first-of-a-kind be less than US\$5 billion. The toroidal field coil cost and replacement time are the most critical upfront and lifetime cost drivers, respectively.

A quasi-linear reduced transport model is developed from a database of high-$\beta$ electromagnetic nonlinear gyrokinetic simulations performed with Spherical Tokamak for Energy Production (STEP) relevant parameters. The quasi-linear model is fully electromagnetic and accounts for the effect of equilibrium flow shear using a novel approach. Its flux predictions are shown to agree quantitatively with predictions from local nonlinear gyrokinetic simulations across a broad range of STEP-relevant local equilibria. This reduced transport model is implemented in the T3D transport solver that is used to perform the first flux-driven simulations for STEP to account for transport from hybrid-KBM turbulence, which dominates over a wide region of the core plasma. Nonlinear gyrokinetic simulations of the final transport steady state from T3D return turbulent fluxes that are consistent with the reduced model, indicating that the quasi-linear model may also be appropriate for describing the transport steady state. Within the assumption considered here, our simulations support the existence of a transport steady state in STEP with a fusion power comparable to that in the burning flat-top of the conceptual design, but do not demonstrate how this state can be accessed.

Turbulent transport is regarded as one of the key issues in magnetic confinement nuclear fusion, both for tokamaks in stellarators. In this work, we show that a significant decrease in a microstability-based proxy, as opposed to a geometric one, for the turbulent heat flux, namely the quasilinear heat flux, can be obtained in an efficient manner by coupling stellarator optimization with linear gyrokinetic simulations. This is accomplished by computing the quasi-linear heat flux at each step of the optimization process, as well as the deviation from quasisymmetry, and minimizing their sum, leading to a balance between neoclassical and turbulent transport proxy., Comment: 8 pages, 6 figures, accepted in Physical Review E

GX is a code for solving the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for fusion reactor design and optimization along with wide-ranging physics exploration. This has led to several code and algorithm design decisions, specifically chosen to prioritize time to solution. First, we have used a discretization algorithm that is pseudo-spectral in the entire phase-space, including a Laguerre-Hermite pseudo-spectral formulation of velocity space, which allows for smooth interpolation between coarse gyrofluid-like resolutions and finer conventional gyrokinetic resolutions and efficient evaluation of a model collision operator. Additionally, we have built GX to natively target graphics processors (GPUs), which are among the fastest computational platforms available today. Finally, we have taken advantage of the reactor-relevant limit of small $\rho_*$ by using the radially-local flux-tube approach. In this paper we present details about the gyrokinetic system and the numerical algorithms used in GX to solve the system. We then present several numerical benchmarks against established gyrokinetic codes in both tokamak and stellarator magnetic geometries to verify that GX correctly simulates gyrokinetic turbulence in the small $\rho_*$ limit. Moreover, we show that the convergence properties of the Laguerre-Hermite spectral velocity formulation are quite favorable for nonlinear problems of interest. Coupled with GPU acceleration, which we also investigate with scaling studies, this enables GX to be able to produce useful turbulence simulations in minutes on one (or a few) GPUs. GX is open-source software that is ready for fusion reactor design studies., Comment: 39 pages, 12 figures

We present the first-of-its-kind coupling of a continuum full-f gyrokinetic turbulence model with a 6D continuum model for kinetic neutrals, carried out using the Gkeyll code. Our objective is to improve the first-principles understanding of the role of neutrals in plasma fueling, detachment, and their interaction with edge plasma profiles and turbulence statistics. Our model includes only atomic hydrogen and incorporates electron-impact ionization, charge exchange, and wall recycling. These features have been successfully verified with analytical predictions and benchmarked with the DEGAS2 Monte Carlo neutral code. We carry out simulations for a scrape-off layer (SOL) with simplified geometry and NSTX parameters. We compare these results to a baseline simulation without neutrals and find that neutral interactions reduce the normalized density fluctuation levels and associated skewness and kurtosis, while increasing auto-correlation times. A flatter density profile is also observed, similar to the SOL density shoulder formation in experimental scenarios with high fueling.

The effect of varying magnetic shear on scrape-off layer turbulence and profiles is studied via electromagnetic gyrokinetic simulations of a helical scrape-off layer model. We develop a model helical geometry with magnetic shear and a corresponding field-aligned coordinate system, which is used for simulations with the Gkeyll code. We find that perpendicular transport is reduced in cases with stronger shear, resulting in higher peak particle and heat fluxes to the endplates. Electromagnetic effects slightly increase transport in strong shear cases., Comment: 11 pages, 9 figures. arXiv admin note: text overlap with arXiv:2112.06880

We demonstrate that cross-field transport in the scrape-off layer (SOL) can be moderately increased by electromagnetic effects in high-beta regimes, resulting in a broader electron heat-flux width on the endplates. This conclusion is taken from full-$f$ electromagnetic gyrokinetic simulations of a helical SOL model that roughly approximates the SOL of the National Spherical Torus Experiment (NSTX). The simulations have been performed with the Gkeyll code, which recently became the first code to demonstrate the capability to simulate electromagnetic gyrokinetic turbulence on open magnetic field lines with sheath boundary conditions. We scan the source rate and thus $\beta$ so that the normalized pressure gradient (the MHD ballooning parameter $\alpha \propto \partial \beta / \partial r \propto \beta / L_p$) is scanned over an experimentally-relevant range, $\alpha = 0.3-1.5$. While there is little change in the pressure gradient scale length $L_p$ near the midplane as beta is increased, a 10% increase in cross-field transport near the midplane results in an increase in the electron heat-flux width $\lambda_q$ and a 25% reduction of the peak electron heat flux to the endplates., Comment: 13 pages, 10 figures

We present an energy-conserving discontinuous Galerkin scheme for the full-$f$ electromagnetic gyrokinetic system in the long-wavelength limit. We use the symplectic formulation and solve directly for $\partial A_\parallel/\partial t$, the inductive component of the parallel electric field, using a generalized Ohm's law derived directly from the gyrokinetic equation. Linear benchmarks are performed to verify the implementation and show that the scheme avoids the Amp\`ere cancellation problem. We perform a nonlinear electromagnetic simulation in a helical open-field-line system as a rough model of the tokamak scrape-off layer using parameters from the National Spherical Torus Experiment (NSTX). This is the first published nonlinear electromagnetic gyrokinetic simulation on open field lines. Comparisons are made to a corresponding electrostatic simulation., Comment: 38 pages, 11 figures

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution 3D gyrofluid representation and the conventional but more expensive 5D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre-Hermite velocity-space basis. We discuss issues related to collisions, closures, and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre-Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts, and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence, and transport in a wide range of geometries, including tokamaks and stellarators.

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A two-fold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity., Comment: 32 pages, 8 figures, accepted to JPP