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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Diii-D Research Advancing The Physics Basis For Optimizing The Tokamak Approach To Fusion Energy

DIII-D physics research addresses critical challenges for operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by integrating high performance core and boundary plasmas. Substantial increases in off-axis current drive efficiency from an innovative top launch system for EC power, and in pressure broadening for Alfven eigenmode control from a co-/counter-Ip steerable off-axis neutral beam, all improve the prospects for optimization of future long pulse/steady state high performance tokamak operation. Fundamental studies into the modes that drive the evolution of the pedestal pressure profile and electron vs. ion heat flux validate predictive models of pedestal recovery after ELMs. Understanding the physics mechanisms of ELM control and density pumpout by 3D magnetic perturbation fields leads to confident predictions for ITER and future devices. Validated modeling of high-Z shattered pellet injection for disruption mitigation, runaway electron dissipation, and techniques for disruption prediction and avoidance including machine learning, give confidence in handling disruptivity for future devices. With this physics understanding and suite of actuators, a high poloidal beta optimized-core scenario with an internal transport barrier that projects nearly to Q=10 in ITER at 9 MA was coupled to a detached divertor, and a near Super H-mode optimized-pedestal scenario with co-Ip beam injection, was coupled to a radiative divertor. The Hybrid core scenario was achieved directly, without the need for internal flux pumping, using off-axis current drive actuators, and a controller to avoid mode locking and disruptions in the ITER baseline scenario, based on plasma response to probing 3D fields, was demonstrated. Finally innovative tokamak operation using a negative triangularity shape showed many attractive features for future pilot plant operation.

Fenstermacher, M.↗
DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗
DOE OSTI2021

Efficient quantum algorithm for dissipative nonlinear differential equations

Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is &#x3B3; &#x3C4; A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of &#x3B3; &#x3C4; A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Kinetic Simulations of Instabilities and Particle Acceleration in Cylindrical Magnetized Relativistic Jets

Relativistic magnetized jets, such as those from AGN, GRBs, and XRBs, are susceptible to current- and pressure-driven MHD instabilities that can lead to particle acceleration and nonthermal radiation. Here, we investigate the development of these instabilities through 3D kinetic simulations of cylindrically symmetric equilibria involving toroidal magnetic fields with electron–positron pair plasma. Generalizing recent treatments by Alves et al. and Davelaar et al., we consider a range of initial structures in which the force due to toroidal magnetic field is balanced by a combination of forces due to axial magnetic field and gas pressure. We argue that the particle energy limit identified by Alves et al. is due to the finite duration of the fast magnetic dissipation phase. We find a rather minor role of electric fields parallel to the local magnetic fields in particle acceleration. In all investigated cases, a kink mode arises in the central core region with a growth timescale consistent with the predictions of linearized MHD models. In the case of a gas-pressure-balanced (Z-pinch) profile, we identify a weak local pinch mode well outside the jet core. We argue that pressure-driven modes are important for relativistic jets, in regions where sufficient gas pressure is produced by other dissipation mechanisms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

FIREFLY: heat load and particle exhaust approximations for rapid evaluation of divertor designs

The divertor in a magnetic confinement fusion reactor is an essential component for power dissipation and particle removal. The FIREFLY package for rapid evaluation of divertor designs is presented as an extension of the FLARE code for field line reconstruction from a flux tube mesh. First, divertor loads are approximated with a simplified heat transport model. Neutralized particles are then sampled from the resulting load distribution, and the EIRENE code is used to track molecules and atoms in a plasma background while accounting for dissociation, charge exchange and ionization. Particles are removed on pumping surfaces in order to estimate the exhaust efficiency for a given divertor geometry. Optimization of the divertor geometry for more efficient particle exhaust is explored by using W7-X as an example, and the sensitivity to model parameters for the plasma background in the proxy calculations is evaluated.

mesh generation, magnetic field lines, scrape-off ↗
DOE OSTI2025

On reduced modelling of the modulational dynamics in magnetohydrodynamics

This paper explores structure formation in two-dimensional magnetohydrodynamic (MHD) turbulence as a modulational instability (MI) of turbulent fluctuations. We focus on the early stages of structure formation and consider simple backgrounds that allow for a tractable model of the MI while retaining the full chain of modulational harmonics. This approach allows us to systematically examine the validity of popular closures such as the quasilinear approximation and other low-order truncations. We find that, although such simple closures can provide quantitatively accurate approximations of the MI growth rates in some regimes, they can fail to capture the modulational dynamics in adjacent regimes even qualitatively, falsely predicting MI when the system is actually stable. We find that this discrepancy is due to the excitation of propagating spectral waves (PSWs) which can ballistically transport energy along the modulational spectrum, unimpeded until dissipative scales, thereby breaking the feedback loops that would otherwise sustain MIs. The PSWs can be self-maintained as global modes with real frequencies and drain energy from the primary structure at a constant rate until the primary structure is depleted. To describe these waves within a reduced model, we propose an approximate spectral closure that captures them and MIs on the same footing. We also find that introducing corrections to ideal MHD, conservative or dissipative, can suppress PSWs and reinstate the accuracy of the quasilinear approximation. In this sense, ideal MHD is a ‘singular’ system that is particularly sensitive to the accuracy of the closure within mean-field models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Plasma heating by electron cyclotron wave and the temperature effects on lower hybrid current drive on EAST

This paper presents the progress in the long—pulse operation of the electron cyclotron (EC) system and the achievements in high—electron temperature plasmas by the combined EC and lower hybrid (LH) waves heating since the EC system was built in 2015. An electron temperature of up to 12 keV with a duration over 100 s was realized by the simultaneous heating of EC and LH waves at the line-averaged density ${\bar n_{\text{e}}}$ ~1.8 × 10 19 m –3 . The plasma heating effect strongly depends on the location of EC power deposition. H-mode plasmas with solely EC wave auxiliary heating have been obtained on EAST for the first time. These H-mode discharges show an enhanced confinement factor H 98(y,2) around 1.0, which is higher than the previous H-mode using LH power alone (Xu et al 2011 Nucl. Fusion 51 072001). The total heating power is very close to the threshold value for L–H transition according to the international tokamak scaling. In addition to the temperature effects inside the separatrix, higher electron temperature produced by EC wave is found to reduce the LH power loss in the scrape-off layer due to collisional absorption, which is beneficial to further increase the LH current drive efficiency. Ray-tracing/Fokker–Planck modeling results indicate that higher electron temperature can shorten the LH wave propagation on EAST in a multiple-pass regime, thus decreasing the collisional dissipation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A novel path to runaway electron mitigation via deuterium injection and current-driven MHD instability

Relativistic electron (RE) beams at high current density (low safety factor, qa) yet very low free-electron density accessed with D2 secondary injection in the DIII-D and JET tokamak are found to exhibit large-scale MHD instabilities that benignly terminate the RE beam. In JET, this technique has enabled termination of MA-level RE currents without measurable first-wall heating. This scenario thus offers an unexpected alternate pathway to achieve RE mitigation without collisional dissipation. Benign termination is explained by two synergistic effects. First, during the MHD-driven RE loss events both experiment and MHD orbit-loss modeling supports a significant increase in the wetted area of the RE loss. Second, as previously identified at JET and DIII-D, the fast kink loss timescale precludes RE beam regeneration and the resulting dangerous conversion of magnetic to RE kinetic energy. During the termination, the RE kinetic energy is lost to the wall, but the current fully transfers to the cold bulk thus enabling benign Ohmic dissipation of the magnetic energy on longer timescales via a conventional current quench. Hydrogenic (D2) secondary injection is found to be the only injected species that enables access to the benign termination. D2 injection: 1) facilitates access to low qa in existing devices (via reduced collisionality & resistivity), 2) minimizes the RE avalanche by ‘purging’ the high-Z atoms from the RE beam, 3) drives recombination of the background plasma, reducing the density and Alfven time, thus accelerating the MHD growth. Furthermore, this phenomenon is found to be accessible when crossing the low qa stability boundary with rising current, falling toroidal field, or contracting minor radius - the latter being the expected scenario for vertically unstable RE beams in ITER. While unexpected, this path scales favorably to fusion-grade tokamaks and offers a novel RE mitigation scenario in principle accessible with the day-one disruption mitigation system (DMS) of ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Impurity leakage and radiative cooling in the first nitrogen and neon seeding study in the closed DIII-D SAS configuration

A comparative study of nitrogen versus neon has been carried out to analyze the impact of the two radiative species on power dissipation, SOL impurity distribution, divertor and pedestal characteristics. The experimental results show that N remains compressed in the divertor, thereby providing high radiative losses without affecting the pedestal profiles and displacing carbon as dominant radiator. Neon, instead, radiates more upstream than N thus reducing the power flux through the separatrix leading to a reduced ELM frequency and compression in the divertor. A significant amount of neon is measured in the plasma core leading to a steeper density gradient. The different behavior between the two impurities is confirmed by SOLPS-ITER modeling which for the first time at DIII-D includes multiple impurity species and a treatment of full drifts, currents and neutral–neutral collisions. The impurity transport in the SOL is studied in terms of the parallel momentum balance showing that N is mostly retained in the divertor whereas Ne leaks out consistent with its higher ionization potential and longer mean free path. This is also in agreement with the enrichment factor calculations which indicate lower divertor enrichment for neon. The strong ionization source characterizing the SAS divertor causes a reversal of the main ions and impurity flows. The flow reversal together with plasma drifts and the effect of the thermal force contribute significantly in the shift of the impurity stagnation point affecting impurity leakage. This work provides a demonstration of the impurity leakage mechanism in a closed divertor structure and the consequent impact on pedestal. Since carbon is an intrinsic radiator at DIII-D, in this paper we have also demonstrated the different role of carbon in the N vs Ne seeded cases both in the experiments and in the numerical modeling. Here, carbon contributes more when neon seeding is injected compared to when nitrogen is used. Finally, the results highlight the importance of accompanying experimental studies with numerical modeling of plasma flows, drifts and ionization profile to determine the details of the SOL impurity transport as the latter may vary with changes in divertor regime and geometry. In the cases presented here, plasma drifts and flow reversal caused by high level of closure in the slot upper divertor at DIII-D play an important role in the underlined mechanism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Chaotic saddles and interior crises in a dissipative nontwist system

Here, we consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems; they are responsible for chaotic transients, fractal basin boundaries, and chaotic scattering, and they mediate interior crises. In this work we discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. We show how the presence of two saddles increases the transient times and we analyze the phenomenon of crisis induced intermittency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The advanced tokamak path to a compact net electric fusion pilot plant

Abstract Physics-based simulations project a compact net electric fusion pilot plant with a nuclear testing mission is possible at modest scale based on the advanced tokamak concept, and identify key parameters for its optimization. These utilize a new integrated 1.5D core-edge approach for whole device modeling to predict performance by self-consistently applying transport, pedestal and current drive models to converge fully non-inductive stationary solutions, predicting profiles and energy confinement for a given density. This physics-based approach leads to new insights and understanding of reactor optimization. In particular, the levering role of high plasma density is identified, which raises fusion performance and self-driven ‘bootstrap currents’, to reduce current drive demands and enable high pressure with net electricity at a compact scale. Solutions at 6–7 T, ∼4 m radius and 200 MW net electricity are identified with margins and trade-offs possible between parameters. Current drive comes from neutral beam and ultra-high harmonic (helicon) fast wave, though other advanced approaches are not ruled out. The resulting low recirculating power in a double null configuration leads to a divertor heat flux challenge that is comparable to ITER, though reactor solutions may require more dissipation. Strong H-mode access (x2 margin over L–H transition scalings) and ITER-like heat fluxes are maintained with ∼20%–60% core radiation, though effects on confinement need further analysis. Neutron wall loadings appear tolerable. The approach would benefit from high temperature superconductors, as higher fields would increase performance margins while potential for demountability may facilitate nuclear testing. However, solutions are possible with conventional superconductors. An advanced load sharing and reactive bucking approach in the device centerpost region provides improved mechanical stress handling. The prospect of an affordable test device which could close the loop on net-electric production and conduct essential nuclear materials and breeding research is compelling, motivating research to validate the techniques and models employed here.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Persistent mysteries of jet engines, formation, propagation, and particle acceleration: Have they been addressed experimentally?

Here, the physics of astrophysical jets can be divided into three regimes: (i) engine and launch (ii) propagation and collimation, (iii) dissipation and particle acceleration. Since astrophysical jets comprise a huge range of scales and phenomena, practicality dictates that most studies of jets intentionally or inadvertently focus on one of these regimes, and even therein, one body of work may be simply boundary condition for another. We first discuss long standing persistent mysteries that pertain the physics of each of these regimes, independent of the method used to study them. This discussion makes contact with frontiers of plasma astrophysics more generally. While observations theory, and simulations, and have long been the main tools of the trade, what about laboratory experiments? Jet related experiments have offered controlled studies of specific principles, physical processes, and benchmarks for numerical and theoretical calculations. We discuss what has been accomplished on these fronts. Although experiments have indeed helped us to understand certain processes, proof of principle concepts, and benchmarked codes, they have yet to solved an astrophysical jet mystery on their own. A challenge is that experimental tools used for jet-related experiments so far, are typically not machines originally designed for that purpose, or designed with specific astrophysical mysteries in mind. This presents an opportunity for a different way of thinking about the development of future platforms: start with the astrophysical mystery and build an experiment to address it.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Bifurcation-like transition of divertor conditions induced by X-point radiation in KSTAR L-mode plasmas *

Abstract Density ramps with ion grad B drift directed into lower single null KSTAR L-mode plasmas are associated with a simultaneous and abrupt reduction of the divertor particle flux on both low- and high-field-side targets when the mid-plane line averaged electron density reaches a given level. Target embedded Langmuir probe signals show a clear ‘cliff edge’ behavior similar to that observed in the divertor target electron temperature in DIII-D H-mode plasmas (Eldon et al 2017 Nucl. Fusion 57 066039; McLean et al 2015 J. Nucl. Mater. 463 533–6). The collapse of the particle flux is observed along the whole divertor target area (from private flux region to the far scrape-off layer (SOL)). The critical upstream density of this target flux cliff is invariant under fuel gas throughput modulation. The transition along the cliff occurs in tens of milliseconds. With the cliff, carbon impurities and deuterium neutrals transported through the X-point to the core produce a strong radiation spot near the X-point, seen on bolometric signals, and increase the upstream density. The experimental observations are consistent with time-dependent SOLPS-ITER simulations, which also demonstrate an abrupt transition of the target flux and upstream density with the increase in X-point radiation. The timescale of the cliff predicted by SOLPS-ITER is consistent with the experiment, although, it is influenced by gas throughput or time-dependent numerical methods. In the L-mode phase space of separatrix electron density and temperature, branches are divided based on target temperature, because the latter is strongly coupled to the radiation front and ionization front due to the monotonic characteristic of the parallel electron temperature distribution. Since the H-mode condition operates at a much higher upstream density and electron temperature in phase space, dissipation from sputtered carbon alone leads to the density limit before reaching the X-point radiation condition. This is therefore consistent with the fact that cliffs have never been observed in H-mode KSTAR experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The impact of magnetic fields on momentum transport and saturation of shear-flow instability by stable modes

The Kelvin–Helmholtz (KH) instability of a shear layer with an initially uniform magnetic field in the direction of flow is studied in the framework of 2D incompressible magnetohydrodynamics with finite resistivity and viscosity using direct numerical simulations. The shear layer evolves freely, with no external forcing, and thus broadens in time as turbulent stresses transport momentum across it. As with hydrodynamic KH, the instability here features a conjugate stable mode for every unstable mode in the absence of dissipation. Stable modes are shown to transport momentum up its gradient, shrinking the layer width whenever they exceed unstable modes in amplitude. In simulations with weak magnetic fields, the linear instability is minimally affected by the field, but enhanced small-scale fluctuations relative to the hydrodynamic case are observed. These enhanced fluctuations coincide with increased energy dissipation and faster layer broadening, with these features more pronounced in simulations with stronger fields. These trends result from the magnetic field reducing the effects of stable modes relative to the transfer of energy to small scales. As field strength increases, stable modes become less excited, thus transporting less momentum against its gradient. Furthermore, the energy that would otherwise transfer back to the driving shear because of the stable modes is instead allowed to cascade to small scales, where it is lost to dissipation. Approximations of the turbulent state in terms of a reduced set of modes are explored. While the Reynolds stress is well-described using just two modes per wavenumber at large scales, the Maxwell stress is not.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

An inclusive framework for joined Hamiltonian and dissipative dynamical systems that are thermodynamically consistent, i.e., preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket , a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

Physics↗
DOE OSTI2024

Benefits of the Super-X divertor configuration for scenario integration on MAST Upgrade

The integration of good core and edge/pedestal confinement with strong dissipation of heat and particles in the divertors is a significant challenge for the development of fusion energy. Alternative divertor configurations offer potential advantages by broadening the operational space where a device can operate with detached divertors and acceptable power exhaust. First results from MAST Upgrade are presented from high confinement mode experiments with outer divertors in the Super-X divertor configuration, showing that the outer divertors naturally detach when the Super-X is formed with no discernible impact on the plasma core and pedestal. These initial findings confirm predicted benefits of the Super-X configuration in terms of facilitating scenario integration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗