Stellarators offer a promising path towards fusion reactors, but their design and construction are complicated by stringent tolerance requirements on highly complex 3D coils. A potential way to simplify the engineering requirements for stellarators is to use simple planar toroidal field coils along with permanent magnet arrays to generate shaping fields. In order to ensure sufficient field accuracy while minimizing engineering complexity and system cost, new techniques are required to correct the field produced by the permanent magnet arrays to within requirements set by plasma physics. This work describes a novel correction method developed for this purpose. This analysis is applied to the design of a quasi-axisymmetric stellarator that employs a combination of permanent magnets and planar toroidal field coils to generate its magnetic field. Analysis techniques and initial results using the method for error correction on a proposed permanent magnet stellarator are shown, and it is demonstrated that the method successfully meets the design requirements of the project.
Zhu, Hongxuan; Stoltzfus-Dueck, T; Hager, R; Ku, S; Chang, C. S.
Abstract:
Ion orbit loss has been used to model the formation of a strong negative radial electric field Er in the tokamak edge, as well as edge momentum transport and toroidal rotation. To quantitatively measure ion orbit loss, an orbit-flux formulation has been developed and numerically applied to the gyrokinetic particle-in-cell code XGC. We study collisional ion orbit loss in an axisymmetric DIII-D L-mode plasma using gyrokinetic ions and drift-kinetic electrons. Numerical simulations, where the plasma density and temperature profiles are maintained through neutral ionization and heating, show the formation of a quasisteady negative Er in the edge. We have measured a radially outgoing ion gyrocenter flux due to collisional scattering of ions into the loss orbits, which is balanced by the radially incoming ion gyrocenter flux from confined orbits on the collisional time scale. This suggests that collisional ion orbit loss can shift Er in the negative direction compared to that in plasmas without orbit loss. It is also found that collisional ion orbit loss can contribute to a radially outgoing (counter-current) toroidal-angular-momentum flux, which is not balanced by the toroidal-angular-momentum flux carried by ions on the confined orbits. Therefore, the edge toroidal rotation shifts in the co-current direction on the collisional time scale.
Hager, Robert; Ku, Seung-Hoe; Sharma, Amil Y.; Churchill, Randy Michael; Chang, C. S.; Scheinberg, Aaron
Abstract:
The simplified delta-f mixed-variable/pull-back electromagnetic simulation algorithm implemented in XGC for core plasma simulations by Cole et al. [Phys. Plasmas 28, 034501 (2021)] has been generalized to a total-f electromagnetic algorithm that can include, for the first time, the boundary plasma in diverted magnetic geometry with neutral particle recycling, turbulence and neoclassical physics.
The delta-f mixed-variable/pull-back electromagnetic implementation is based on the pioneering work by Kleiber and Mischenko et al. [Kleiber et al., Phys. Plasmas 23, 032501 (2016); Mishchenko et al., Comput. Phys. Commun. 238, 194 (2019)].
An electromagnetic demonstration simulation is performed in a DIII-D-like, H-mode boundary plasma, including a corresponding comparative electrostatic simulation, which confirms that the electromagnetic simulation is necessary for a higher fidelity understanding of the electron particle and heat transport even at the low-beta pedestal foot in the vicinity of the magnetic separatrix.
Coronal mass ejections (CMEs) are some of the most energetic and violent events in our solar system. The prediction and understanding of CMEs is of particular importance due to the impact that they can have on Earth-based satellite systems, and in extreme cases, ground-based electronics. CMEs often occur when long-lived magnetic flux ropes (MFRs) anchored to the solar surface destabilize and erupt away from the Sun. One potential cause for these eruptions is an ideal magnetohydrodynamic (MHD) instability such as the kink or torus instability. Previous experiments on the Magnetic Reconnection eXperiment (MRX) revealed a class of MFRs that were torus-unstable but kink-stable, which failed to erupt. These “failed-tori” went through a process similar to Taylor relaxation where the toroidal current was redistributed before the eruption ultimately failed. We have investigated this behavior through additional diagnostics that measure the current distribution at the foot points and the energy distribution before and after an event. These measurements indicate that ideal MHD effects are sufficient to explain the energy distribution changes during failed torus events. This excludes Taylor relaxation as a possible mechanism of current redistribution during an event. A new model that only requires non-ideal effects in a thin layer above the electrodes is presented to explain the observed phenomena. This work broadens our understanding of the stability of MFRs and the mechanism behind the failed torus through the improved prediction of the torus instability and through new diagnostics to measure the energy inventory and current profile at the foot points.
Trinczek, Silvia; Parra, Felix I.; Catto, Peter J.; Calvo, Iván; Landreman, Matt
Abstract:
We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.
The MAST-U fusion plasma research device, the upgrade to the Mega Amp Spherical Tokamak, has recently completed its first campaign of physics operation. MAST-U operated with Ohmic, or one or two neutral beams for heating, at 400-800 kA plasma current, in conventional or “SuperX” divertor configurations. Equilibrium reconstructions provide key plasma physics parameters vs. time for each discharge, and diagrams are produced which show where the prevalence of operation occurred as well as the limits in various operational spaces. When compared to stability limits, the operation of MAST-U so far has generally stayed out of the low q, low density instability region, and below the high density Greenwald limit, high beta global stability limits, and high elongation vertical stability limit. MAST-U still has the potential to reach higher elongation, which could benefit the plasma performance. Despite the majority of operation happening below established stability limits, disruptions did occur in the flat-top phase of MAST-U plasmas. The reasons for these disruptions are highlighted, and possible strategies to avoid them and to extend the operational space of MAST-U in future campaigns are discussed.
The dynamic interplay between the core and the edge plasma has important consequences in the confinement and heating of fusion plasma. The transport of the Scrape-Off-Layer (SOL) plasma imposes boundary conditions on the core plasma, and neutral transport through the SOL influences the core plasma sourcing. In order to better study these effects in a self-consistent, time-dependent fashion with reasonable turn-around time, a reduced model is needed. In this paper we introduce the SOL Box Model, a reduced SOL model that calculates the plasma temperature and density in the SOL given the core-to-edge particle and power fluxes and recycling coefficients. The analytic nature of the Box Model allows one to readily incorporate SOL physics in time-dependent transport solvers for pulse design applications in the control room. Here we demonstrate such a coupling with the core transport solver TRANSP and compare the results with density and temperature measurements, obtained through Thomson scattering and Langmuir probes, of an NSTX discharge. Implications for future interpretive and predictive simulations are discussed.
The data set consists of the figures in a manuscript titled Thermal ion kinetic effects and Landau damping in fishbone modes, and plotting script used for figure generation. There are 16 figures with captions.
Schwartz, Jacob A.; Ricks, Wilson; Kolemen, Egemen; Jenkins, Jesse D.
Abstract:
Fusion could be a part of future decarbonized electricity systems, but it will need to compete with other technologies.
In particular, pulsed tokamaks plants have a unique operational mode, and evaluating
which characteristics make them economically competitive can help select between design pathways.
Using a capacity expansion and operations model,
we determined cost thresholds for pulsed tokamaks to reach a range of penetration levels in a future decarbonized US Eastern Interconnection.
The required capital cost to reach a fusion capacity of 100 GW varied from $3000 to $7200/kW,
and the equilibrium penetration increases rapidly with decreasing cost.
The value per unit power capacity depends on the variable operational cost and on cost of its competition, particularly fission, much more than on the pulse cycle parameters.
These findings can therefore provide initial cost targets for fusion more generally in the United States.
The usage of permanent magnets to shape the confining field of a stellarator has the potential to reduce or eliminate the need for non-planar coils. As a proof-of-concept for this idea, we have developed a procedure for designing an array of cubic permanent magnets that works in tandem with a set of toroidal-field coils to confine a stellarator plasma. All of the magnets in the design are constrained to have identical geometry and one of three polarization types in order to simplify fabrication while still producing sufficient field accuracy. We present some of the key steps leading to the design, including the geometric arrangement of the magnets around the device, the procedure for optimizing the polarizations according to three allowable magnet types, and the choice of magnet types to be used. We apply these methods to design an array of rare-Earth permanent magnets that can be paired with a set of planar toroidal-field coils to confine a quasi-axisymmetric plasma with a toroidal magnetic field strength of about 0.5 T on axis.
Zhu, Hongxuan; Stoltzfus-Dueck, T; Hager, R; Ku, S; Chang, C. S.
Abstract:
Ion orbit loss is considered important for generating the radially inward electric field Er in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code XGC. As the first application of this diagnostic, a neoclassical DIII-D H-mode plasma is studied using gyrokinetic ions and adiabatic electrons. The validity of the diagnostic is demonstrated by studying the collisional relaxation of Er in the core. After this demonstration, the loss-orbit current is numerically measured in the edge pedestal in quasisteady state. In this plasma, it is found that the radial electric force on ions from Er approximately balances the ion radial pressure gradient in the edge pedestal, with the radial force from the plasma flow term being a minor component. The effect of orbit loss on Er is found to be only mild.
A new model for electron temperature gradient (ETG) modes is developed as a component of the Multi-Mode anomalous transport module [T. Rafiq \textit{et al.,} Phys Plasmas \textbf{20}, 032506 (2013)] to predict a time dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, $\beta$ and gradient of $\beta$ $(\betap)$, collisionality, safety factor, and toroidicity, where $\beta$ is the ratio of plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.
An important goal of stellarator optimization is to achieve good confinement of
energetic particles such as, in the case of a reactor, alphas created by Deuterium-Tritium
(D-T) fusion. In this work, a fixed-boundary stellarator equilibrium was re-optimized for
energetic particle confinement via a two-step process: first, by minimizing deviations from quasi-axisymmetry (QA) on a single flux surface near the mid-radius, and secondly by maintaining
this improved quasi-axisymmetry while minimizing the analytical quantity ΓC , which represents
the angle between magnetic flux surfaces and contours of J||, the second adiabatic invariant.
This was performed multiple times, resulting in a group of equilibria with significantly reduced
energetic particle losses, as evaluated by Monte Carlo simulations of alpha particles in scaled-up
versions of the equilibria. This is the first time that energetic particle losses in a QA stellarator
have successfully been reduced by optimizing ΓC . The relationship between energetic particle
losses and metrics such as QA error (Eqa) and ΓC in this set of equilibria were examined via
statistical methods and a nearly linear relationship between volume-averaged ΓC and prompt
particle losses was found.
