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.
Recent U.S. fusion development strategy reports all recommend that the U.S. should pursue innovative science and technology to enable construction of a Fusion Pilot Plant (FPP) that produces net electricity from fusion at low capital cost. Compact tokamaks have been proposed as a means of potentially reducing the capital cost of a fusion pilot plant. However, compact steady-state tokamak FPPs face the challenge of integrating a high fraction of self-driven current with high core confinement, plasma pressure, and high divertor parallel heat flux. This integration is sufficiently challenging that a dedicated sustained-high-power-density (SHPD) tokamak facility is proposed by the U.S. community as the optimal way to close this integration gap. Performance projections for the steady-state tokamak FPP regime are presented and a preliminary SHPD device with substantial flexibility in lower aspect ratio (A=2-2.5), shaping, and divertor configuration to narrow gaps to a FPP is described.
Sharma, A. Y.; Cole, M. D. J.; Görler, T.; Chen, Y.; Hatch, D. R.; Guttenfelder, W.; Hager, R.; Sturdevant, B. J.; Ku, S.; Chang, C. S.
Abstract:
Plasma shaping may have a stronger effect on global turbulence in tight-aspect-ratio tokamaks than in conventional-aspect-ratio tokamaks due to the higher toroidicity and more acute poloidal asymmetry in the magnetic field. In addition, previous local gyrokinetic studies have shown that it is necessary to include parallel magnetic field perturbations in order to accurately compute growth rates of electromagnetic modes in tight-aspect-ratio tokamaks. In this work, the effects of elongation and triangularity on global, ion-scale, linear electromagnetic modes are studied at NSTX aspect ratio and high plasma beta using the global gyrokinetic particle-in-cell code XGC. The effects of compressional magnetic perturbations are approximated via a well-known modification to the particle drifts that was developed for flux-tube simulations [N. Joiner et al., Phys. Plasmas 17, 072104 (2010)], without proof of its validity in a global simulation. Magnetic equilibria are re-constructed for each distinct plasma profile that is used. Coulomb collision effects are not considered. Within the limitations imposed by the present study, it is found that linear growth rates of electromagnetic modes (collisionless microtearing modes and kinetic ballooning modes) are significantly reduced by NSTX-like shaping. For example, growth rates of kinetic ballooning modes at high beta are reduced to the level of that of collisionless trapped electron modes.
Stoltzfus-Dueck, T; Hornsby, W A; Grosshauser, S R
Abstract:
Ion Landau damping interacts with a portion of the E×B drift to cause a non-diffusive outward flux of co-current toroidal angular momentum. Quantitative evaluation of this momentum flux requires nonlinear simulations to determine fL, the fraction of fluctuation free energy that passes through ion Landau damping, in fully developed turbulence. Nonlinear gyrokinetic simulations with the GKW code confirm the presence of the systematic symmetry-breaking momentum flux. For simulations with adiabatic electrons, fL scales inversely with the ion temperature gradient, because only the ion curvature drift can transfer free energy to the electrostatic potential. Although kinetic electrons should in principle relax this restriction, the ion Landau damping measured in collisionless kinetic-electron simulations remained at low levels comparable with ion-curvature-drift transfer, except when magnetic shear was strong. A set of simulations scanning the electron pitch-angle scattering rate showed only a weak variation of fL with the electron collisionality. However, collisional-electron simulations with electron temperature greater than ion temperature unambiguously showed electron-curvature-drift transfer supporting ion Landau damping, leading to a corresponding enhancement of the symmetry-breaking momentum flux.
Wang, Yin; Gilson, Erik P.; Ebrahimi, Fatima; Goodman, Jeremy; Caspary, Kyle J.; Winarto, Himawan W.; Ji, Hantao
Abstract:
This dataset provides the source data of figures in the main text of the paper "Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability" accepted by Nature Communications.
Using a recently installed impurity powder dropper (IPD), boron powder (< 150 μm) was injected into lower single null (LSN) L-mode discharges in WEST. IPDs possibly enable real-time wall conditioning of the plasma-facing components and may help to facilitate H-mode access in the full-tungsten environment of WEST. The discharges in this experiment featured Ip = 0.5 MA, BT = 3.7 T, q95 = 4.3, tpulse = 12–30 s, ne,0 ~ 4×1019 m-2, and PLHCD ~ 4.5 MW. Estimates of the deuterium and impurity particle fluxes, derived from a combination of visible spectroscopy measurements and their corresponding S/XB coefficients, showed decreases of ~ 50% in O+, N+, and C+ populations during powder injection and a moderate reduction of these low-Z impurities (~ 50%) and W (~ 10%) in the discharges that followed powder injection. Along with the improved wall conditions, WEST discharges with B powder injection observed improved confinement, as the stored energy WMHD, neutron rate, and electron temperature Te increased significantly (10–25% for WMHD and 60–200% for the neutron rate) at constant input power. These increases in confinement scale up with the powder drop rate and are likely due to the suppression of ion temperature gradient (ITG) turbulence from changes in Zeff and/or modifications to the electron density profile.
The growth of magnetic islands in NSTX is modeled successfully, with the consideration of passing fast ions. It is shown that a good quantitative agreement between simulation and experimental measurement can be achieved when the uncompensated cross-field current induced by passing fast ions is included in the island growth model. The fast ion parameters,
along with other equilibrium parameters, are obtained self-consistently using the TRANSP code with the assumptions of the ‘kick’ model (Podestà et al 2017 Plasma Phys. Control. Fusion 59 095008). The results show that fast ions can contribute to overcoming the stabilizing effect of polarization current for magnetic island growth.
Non-axisymmetric magnetic fields arising in a tokamak either by external or internal perturbations can induce complex non-ideal MHD responses in their resonant surfaces while remaining ideally evolved elsewhere. This layer response can be characterized in a linear regime by a single parameter called the inner-layer Delta, which enables outer-layer matching and the prediction of torque balance to non-linear island regimes. Here, we follow strictly one of the most comprehensive analytic treatments including two-fluid and drift MHD effects and keep the fidelity of the formulation by incorporating the numerical method based on the Riccati transformation when quantifying the inner-layer Delta. The proposed scheme reproduces not only the predicted responses in essentially all asymptotic regimes but also with continuous transitions as well as improved accuracies. In particular, the Delta variations across the inertial regimes with viscous or semi-collisional effects have been further resolved, in comparison with additional analytic solutions. The results imply greater shielding of the electromagnetic torque at the layer than what would be expected by earlier work when the viscous or semi-collisional effects can compete against the inertial effects, and also due to the intermediate regulation by kinetic Alfven wave resonances as rotation slows down. These are important features that can alter the nonaxisymmetric plasma responses including the field penetration by external fields or island seeding process in rotating tokamak plasmas.
Liquid metal can create a renewable protective surface on plasma facing components (PFC), with an additional advantage of deuterium pumping and the prospect of tritium extraction if liquid lithium (LL) is used and maintained below 450 C, the temperature above which LL vapor pressure begins to contaminate the plasma. LM can also be utilized as an efficient coolant, driven by the Lorentz force created with the help of the magnetic field in fusion devices. Capillary porous systems can serve as a conduit of LM and simultaneously provide stabilization of the LM flow, protecting against spills into the plasma. Recently a combination of a fast-flowing LM cooling system with a porous plasma facing wall (CPSF) was investigated [Khodak and Maingi (2021)]. The system takes an advantage of a magnetohydrodynamics velocity profile, as well as attractive LM properties to promote efficient heat transfer from the plasma to the LL at low pumping energy cost, relative to the incident heat flux on the PFC. In case of a disruption leading to excessive heat flux from the plasma to the LM PFCs, LL evaporation can stabilize the PFC surface temperature, due to high evaporation heat and apparent vapor shielding. The proposed CPSF was optimized analytically for the conditions of a Fusion Nuclear Science Facility [Kessel et al. (2019)]: 10T toroidal field and 10 MW/m2 peak incident heat flux. Computational fluid dynamics analysis confirmed that a CPSF system with 2.5 mm square channels can pump enough LL so that no additional coolant is needed.
Wang, Yin; Gilson, Erik; Ebrahimi, Fatima; Goodman, Jeremy; Ji, Hantao
Abstract:
Source data for the article "Observation of Axisymmetric Standard Magnetorotational Instability in the Laboratory" published in Physical Review Letters.
Kraus, B. Frances; Gao, Lan; Hill, K. W.; Bitter, M.; Efthimion, P. C.; Hollinger, R.; Wang, Shoujun; Song, Huanyu; Nedbailo, R.; Rocca, J. J.; Mancini, R. C.; MacDonald, M. J.; Beatty, C. B.; Shepherd, R.
Abstract:
A high-resolution x-ray spectrometer was coupled with an ultrafast x-ray streak camera to produce time-resolved line shape spectra measured from hot, solid-density plasmas. A Bragg crystal was placed near a laser-produced plasma to maximize throughput; alignment tolerances were established by raytracing. The streak camera produced single-shot time-resolved spectra, heavily sloped due to photon time-of-flight differences, with sufficient reproducibility to accumulate photon statistics. The images are time-calibrated by the slope of streaked spectra and dewarped to generate spectra emitted at different times defined at the source. The streaked spectra demonstrate the evolution of spectral shoulders and other features on ps timescales, showing the feasibility of plasma parameter measurements on the rapid timescales necessary to study high-energy-density plasmas.
Hill, K. W.; Gao, L.; Kraus, B. F.; Bitter, M.; Efthimion, P. C.; Pablant, N. A.; Schneider, M. B.; Thorn, D. B.; Chen, H.; Kauffman, R. L.; Liedahl, D. A.; MacDonald, M. J.; MacPhee, A. G.; Scott, H. A.; Stoupin, S.; Doron, R.; Stambulchik, E.; Maron, Y.; Lahmann, B.
Abstract:
Numerical data used to draw the figures in the manuscript
This is the supplemental material for the manuscript "Verification, validation, and results of an approximate model for the stress of a Tokamak toroidal field coil at the inboard midplane" submitted to Fusion Engineering and Design. This material includes PDF writeups of the derivations of the axisymmetric extended plane strain model, the elastic properties smearing model, and 20+ MATLAB scripts and functions which implement the model and generate the figures in the paper.
Schwartz, Jacob A.; Nelson, A. O.; Kolemen, Egemen
Abstract:
Shaping a tokamak plasma to have a negative triangularity may allow operation in an ELM-free L-mode regime and with a larger strike-point radius, ameliorating divertor power-handling requirements. However, the shaping has a potential drawback in the form of a lower no-wall ideal beta limit, found using the MHD codes CHEASE and DCON. Using the new fusion systems code FAROES, we construct a steady-state DEMO2 reactor model. This model is essentially zero-dimensional and neglects variations in physical mechanisms like turbulence, confinement, and radiative power limits, which could have a substantial impact on the conclusions deduced herein. Keeping its shape otherwise constant, we alter the triangularity and compute the effects on the levelized cost of energy (LCOE). If the tokamak is limited to a fixed B field, then unless other means to increase performance (such as reduced turbulence, improved current drive efficiency or higher density operation) can be leveraged, a negative-triangularity reactor is strongly disfavored in the model due to lower \beta_N limits at negative triangularity, which leads to tripling of the LCOE. However, if the reactor is constrained by divertor heat fluxes and not by magnet engineering, then a negative-triangularity reactor with higher B0 could be favorable: we find a class of solutions at negative triangularity with lower peak heat flux and lower LCOE than those of the equivalent positive triangularity reactors.
Gilson, Erik; Lee, H; Bortolon, A; Choe, W; Diallo, A; Hong, SH; Lee, HM; Maingi, R; Mansfield, DK; Nagy, A; Park, SH; Song, IW; Song, JI; Yun, SW; Nazikian, R
Abstract:
Results from KSTAR powder injection experiments, in which tens of milligrams of boron nitride (BN) were dropped into low-power H-mode plasmas, show an improvement in wall conditions in subsequent discharges and, in some cases, a reduction or elimination of edge-localized modes (ELMs). Injected powder is distributed by the plasma flow and is deposited on the wall and, over the course of several discharges, was observed to gradually reduce recycling by 33%, and decrease both the ELM amplitude and frequency. This is the first demonstration of the use of BN for ELM mitigation. In all of these experiments, an Impurity Powder Dropper (IPD) was used to introduce precise, controllable amounts of the materials into ELMy H-mode KSTAR discharges. The plasma duration was between 10 s and 15 s, 𝐼𝑝 = 500 kA, 𝐵𝑇 = 1.8 T, 𝑃NBI = 1.6 MW, and 𝑃ECH = 0.6 MW. Plasma densities were between 2 and 3 × 1019 m−3. In all cases, the pre-fill and startup gas-fueling was kept constant, suggesting that the decrease in baseline D𝛼 emission is in fact due to a reduction in recycling. The results presented herein highlight the viability of powder injection for intra-shot and between-shot wall conditioning.
The engineering limits of plasma facing components (PFCs) constrain the allowable operational space of tokamaks. Poorly managed heat fluxes that push the PFCs beyond their limits not only degrade core plasma performance via elevated impurities, but can also result in PFC failure due to thermal stresses or melting. Simple axisymmetric assumptions fail to capture the complex interaction between 3D PFC geometry and 2D or 3D plasmas. This results in fusion systems that must either operate with increased risk or reduce PFC loads, potentially through lower core plasma performance, to maintain a nominal safety factor. High precision 3D heat flux predictions are necessary to accurately ascertain the state of a PFC given the evolution of the magnetic equilibrium. A new code, the Heat flux Engineering Analysis Toolkit (HEAT), has been developed to provide high precision 3D predictions and analysis for PFCs. HEAT couples many otherwise disparate computational tools together into a single open source python package. Magnetic equilibrium, engineering CAD, finite volume solvers, scrape off layer plasma physics, visualization, high performace computing, and more, are connected in a single web-based user interface. Linux users may use HEAT without any software prerequisites via an appImage. This manuscript introduces HEAT, discusses the software architecture, presents first HEAT results, and outlines physics modules in development.
The Kelvin-Helmholtz (KH) instability of magnetohydrodynamic surface waves at the low latitude boundary layer is examined using both an eigenfrequency analysis and a time-dependent wave simulation. The analysis includes the effects of sheared flow and Alfven velocity gradient. When the magnetosheath flows are perpendicular to the ambient magnetic field direction, unstable KH waves that propagate obliquely to the sheared flow direction occur at the sheared flow surface when the Alfv\'en Mach number is higher than an instability threshold. Including a shear transition layer between the magnetosphere and magnetosheath leads to secondary KH waves (driven by the sheared flow) that are coupled to the resonant surface Alfven wave. There are remarkable differences between the primary and the secondary KH waves including wave frequency, the growth rate, and the ratio between transverse and the compressional component. The secondary KH wave energy is concentrated near the shear Alfven wave frequency at the magnetosheath with a lower frequency than the primary KH waves. Although the growth rate of the secondary KH waves is lower than the primary KH waves, the threshold condition is lower, so it is expected that these types of waves will dominate at lower Mach number. Because the transverse component of the secondary KH waves is stronger than the primary KH waves, more efficient wave energy transfer from the boundary layer to the inner magnetosphere is also predicted.
The lithium vapor-box divertor is a possible fusion power exhaust solution.It uses condensation pumping to create a gradient of vapor density in a divertor slot; this should allow a stable detachment front without active feedback.As initial explorations of the concept, two test stands which take the form of three connected cylindrical stainless steel boxes are being developed: one without plasma at PPPL, to test models of lithium evaporation and flow; and one for the linear plasma device Magnum-PSI (at DIFFER in Eindhoven, The Netherlands) to test the ability of a lithium vapor cloud to induce volumetric detachment and redistribute the plasma power.The first experiment uses boxes with diameters of 6 cm, joined by apertures with diameters of 2.2 cm. Up to 1 g of Li is placed in one box, which is heated to up to 600 degrees C. The Li evaporates, then flows to and condenses in the two other, cooler boxes over several minutes. The quantity of Li transported is assessed by weighing the boxes before and after the heating cycle, and is compared to the quantity predicted to flow for the box at its measured temperature using a Direct Simulation Monte Carlo code, SPARTA. With good experimental conditions, the two values agree to within 15%.The experiment on Magnum-PSI is in the conceptual design stage.The design is assessed by simulations using the code B2.5-Eunomia.They show that when the hydrogen-ion plasma beam, with n_e = 4e20 per cubic meter, T_e = 1.5 eV, and r = 1 cm, is passed through a 16 cm long, 12 Pa, 625 degree C Li vapor cloud, the plasma heat flux and pressure on the target are significantly reduced compared to the case without Li.With the Li present, the plasma is cooled by excitation of Li neutrals followed by radiation until it volumetrically recombines, lowering the heat flux from 3.7 MW/m^2 to 0.13 MW/m^2, and the pressure is reduced by 93%, largely by collisions of hydrogen ions with neutral Li.
Lampert,Mate; Diallo,Ahmed; Myra,James R.; Zweben, Stewart J.
Abstract:
Edge localized modes (ELMs) are routinely observed in H-mode plasma regimes of the National Spherical Torus Experiment (NSTX). Due to the explosive nature of the instability, only diagnostics with high temporal and spatial resolution could provide a detailed insight into the dynamics associated with the ELMs. Gas-puff imaging (GPI) at NSTX provides 2D measurements of the magnetic field aligned fluctuations (e.g. ELM filaments) in the scrape-off layer and the at the plasma edge with 2.5 us temporal and 10 mm optical resolution.A novel analysis technique was developed to estimate the frame-by-frame velocities and the spatial parameters of the dominant structures associated with the ELMs. The analysis was applied to single ELM events to characterize the ELM crash dynamics, and then extended to a database of 169 ELM events.Statistical analysis was performed in order to find the characterizing dynamics of the ELM crash. The results show that on average an ELM crash consists of a filament with a circular cross-section which is propelled outwards with a characterizing peak radial velocity of ~3.3 km/s. The radial velocity was found to be linearly dependent on the distance of the filament from the separatrix, which has never been seen before. The ELM filament is characterized by propagation in the ion-diamagnetic direction poloidally with a peak velocity of 11.4 km/s. The ELM crash lasts for approximately 100us until the radial propulsion settles back to the pre-ELM level. The experimental findings were compared with analytical theory. Two possible mechanisms were identified for explaining the observations: the curvature interchange model and the current-filament interaction model.
Data supporting the manuscript "Enhancement of edge turbulence concomitant with ELM suppression during boron powder injection in EAST" published in Plasma of Physics, 2021.
A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfven Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes are found in simulations -- co-CAEs, cntr-GAEs, and co-GAEs -- with differing spectral and stability properties. The simulations reveal that unstable GAEs are more ubiquitous than unstable CAEs, consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from simulations and estimated analytically for relevant sources not present in the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.
Nespoli, Federico; Kaganovich, Igor; Autricque, Adrien; Marandet, Yannick; Tamain, Patrick
Abstract:
The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number $St\propto a_d/n_0$, with $a_d$ the dust radius and $n_0$ the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories $\Delta r^2$ is shown to depend on the ratio $Ku/St$, with $Ku\propto u_{rms}$ the Kubo number and $u_{rms}$ the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting $\Delta r^2\propto (Ku/St)^2t^3$, or $\Delta r^2\propto (u_{rms}n_0/a_d)^2t^3$. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.
