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Final report for DOE DE-SC0014113, which supported experimental work on pressure-gradient driven turbulence in a magnetized laboratory plasma, specifically focusing on the effects of finite beta and of multi-ion species.
The E x B shear instability of a two-dimensional (2D) filament (i.e., a thin, rectangular strip perpendicular to the magnetic field) of magnetized pure electron plasma is investigated experimentally in the presence of an externally imposed strain flow. Data are acquired using a specialized Penning–Malmberg trap in which strain flows can be applied in 2D by biasing segmented electrodes surrounding the plasma. The E x B drift dynamics are well-described by the Drift-Poisson equations, which are isomorphic to the 2D Euler equations describing ideal fluids. Thus, the experimental results correspond to the Rayleigh instability of a shear layer in a 2D ideal fluid, where the electron density is analogous to the fluid vorticity. Shear layers are prepared by stretching initially axisymmetric electron vortices using a strong, applied strain flow. The data at early times are in quantitative agreement with a linear model which extends Rayleigh’s work to account for the influence of an external strain flow. In the presence of weak strain, the system approximately maintains a phase relationship that corresponds to an instantaneous Rayleigh eigenmode. The instability develops into the nonlinear regime later in time and at smaller spatial scales as the strain rate is increased. A secondary vortex pairing instability is observed, but it is suppressed when the strain-to-vorticity ratio exceeds roughly 0.025. In this way, vorticity transport perpendicular to the filament is diminished due to the applied strain.
Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.
While high-Z solid plasma-facing components (PFCs) are the leading candidates for reactors, it is unclear that they can survive the intense plasma material interaction (PMI). Liquid metals (LM) PFCs offer potential solutions since they are not susceptible to the same type of damage, and can be “self-healing”. Following the Fusion Energy System Study on Liquid Metal Plasma Facing Components study that recently was completed by Kessel et al. (Fusion Sci Technnol 75:886, 2019) a domestic LM PFC design program has been initiated to develop reactor-relevant LM PFC concepts. This program seeks to evaluate LM PFC concepts for a Fusion Nuclear Science Facility (FNSF) or a Compact Pilot Plant via engineering design calculations, modeling of PMI and PFC components and laboratory experiments. The latter involves experiments in dedicated test stands and confinement devices and seeks to identify and answer open questions in LM PFC design. The new national LM PFC program is first investigating lithium as the plasma facing material for a flowing divertor PFC concept. Several flow speeds will be evaluated, ranging from ~ cm/s to m/s. The surface temperature will initially be held below the strongly evaporative limit in the first design; higher temperatures with strong evaporation will be considered in future concepts. Other topics of interest include: understanding of the hydrogen and helium interaction with the liquid lithium; single effect experiments on wetting, compatibility and embrittlement; and prototypical experiments for control and characterization of flowing LM. A path to plasma and future tokamak exposure of these concepts will be developed.
Here we report on the development of a Brewster angle-cavity ringdown spectroscopy (BA-CRDS) system for low temperature plasma diagnostics. The system can measure gas species in solutions, with a detection limit (minimum detectable absorbance) of 9.1 × 10 -5 , which is equivalent to a detection limit of 0.04 parts per billion for measuring OH radicals in water at 308 nm. With higher reflectivity ringdown mirrors and improved design of a Brewster angle cell, the detection limit can potentially be up to 10 -6 or lower. In this exploratory study, the absorption cross sections of HgBr 2 and H 2 O 2 in the aqueous phase at 256 nm are measured to be (1.8 ± 0.1) × 10 -18 cm 2 and (5.2 ± 0.5) × 10 -20 cm 2 , respectively. Furthermore, temporal profiles of absorbance from distilled water, HgBr 2 , and H 2 O 2 solutions when interacting with a helium atmospheric plasma jet are individually characterized at different plasma powers, gas flow rates, and/or solute concentrations. The observed linear temporal profiles of absorbance from the plasma-interacted water suggest formation of H 2 O 2 from plasma-generated OH radicals, while the nonlinear temporal profiles from the plasma-treated HgBr 2 solutions reveal possible removal of HgBr 2 by OH radicals. Our results demonstrate that the new BA-CRDS system is a powerful tool for quantification of reactive plasma species in multiphases or other complex settings.
It has recently been demonstrated experimentally that a turbulent plasma created by the collision of two inhomogeneous, asymmetric, weakly magnetized, laser-produced plasma jets can generate strong stochastic magnetic fields via the small-scale turbulent dynamo mechanism, provided the magnetic Reynolds number of the plasma is sufficiently large. In this paper, we compare such a plasma with one arising from two pre-magnetized plasma jets whose creation is identical save for the addition of a strong external magnetic field imposed by a pulsed magnetic field generator. We investigate the differences between the two turbulent systems using a Thomson-scattering diagnostic, x-ray self-emission imaging, and proton radiography. The Thomson-scattering spectra and x-ray images suggest that the external magnetic field has a limited effect on the plasma dynamics in the experiment. Although the external magnetic field induces collimation of the flows in the colliding plasma jets and although the initial strengths of the magnetic fields arising from the interaction between the colliding jets are significantly larger as a result of the external field, the energies and morphologies of the stochastic magnetic fields post-amplification are indistinguishable. We conclude that, for turbulent laser-plasmas with supercritical magnetic Reynolds numbers, the dynamo-amplified magnetic fields are determined by the turbulent dynamics rather than the seed fields or modest changes in the initial flow dynamics of the plasma, a finding consistent with theoretical expectations and simulations of turbulent dynamos.
Spark plasma discharges induce vortex rings and a hot gas kernel. We develop a model to describe the late stage of the spark-induced flow and the role of the vortex rings in the entrainment of cold ambient gas and the cooling of the hot gas kernel. The model is tested in a plasma-induced flow using density and velocity measurements obtained from simultaneous stereoscopic particle image velocimetry and background oriented schlieren. We show that the spatial distribution of the hot kernel follows the motion of the vortex rings, whose radial expansion increases with the electrical energy deposited during the spark discharge. Here, the vortex ring cooling model establishes that entrainment in the convective cooling regime is induced by the vortex rings and governs the cooling of the hot gas kernel, and the rate of cooling increases with the electrical energy deposited during the spark discharge.
The SOLPS-ITER code is utilized to analyze the boundary plasma associated with a fast-flow lithium (Li) divertor configuration in the fusion nuclear science facility (FNSF) tokamak and identify operational regimes with acceptable divertor and core conditions. Plasma transport from the SOLPS-ITER code has been coupled with a liquid metal (LM) MHD/heat transfer code to model a Li open-surface divertor design and assess its impact on the scrape-off-layer (SOL) and core plasma performance. Simulations with only Neon (Ne) impurity seeding have been conducted to evaluate its impact on meeting FNSF design demands for the divertor and upstream plasma parameters. Simulation results indicate that Ne seeding significantly mitigates divertor heat flux but potentially reduces both upstream electron and main ion density due to fuel dilution. The combined application of Ne seeding and deuterium (D 2 ) puffing is required to satisfy the FNSF design requirements on upstream density ($n^{OMP}_{e,sep}$~1× 10 20 m -3 ) and divertor energy flux ($q^{Odiv}_{\bot,max}$<10 MW m -2 ). D 2 puffing plays a role in counteracting upstream density drops and augmenting energy and momentum losses through atomic and molecular processes. The inlet Li flow velocity is systematically varied across a wide range to identify acceptable flows and corresponding LM surface temperatures. This comprehensive analysis identifies the acceptable Li flow parameters, LM surface temperature, and emitted Li fluxes necessary to meet the major design constraints. The emitted Li fluxes exhibit minimal impact on the main plasma at surface temperatures up to approximately ~525 °C, corresponding emitted Li fluxes of up to φ Li ~2X10 23 atoms s -1 . Uncertainties in the Li emission processes from the surface are also investigated, primarily influencing Li loss in the lower surface temperature range (<525 °C), with simulation results indicating a minor impact on the divertor and upstream plasma. Conversely, evaporation predominantly drives the Li loss processes at higher surface temperature ranges (>525 °C), contaminating both the divertor and upstream plasma.
An electron temperature bifurcation is observed in the small angle slot divertor, which has been developed to enhance neutral cooling across the divertor target by coupling a closed slot structure with appropriate target shaping. Experiments in the DIII-D tokamak and associated SOLPS-ITER modeling with full drifts find a strong interplay between drifts and divertor geometry on divertor dissipation. The coupling of divertor geometry and drift flows can strongly affect the path towards divertor detachment onset as the plasma density is raised. With the strike point on the inner slanted surface and ion B × ∇B away from the magnetic X-point, bifurcative transitions were observed with sharp decrease of T e towards detachment onset both experimentally and computationally. This differs from the situation for the open divertor where the T e cliff was only observed for ion B × ∇B towards the X-point. SOLPS-ITER modeling with full drifts demonstrates that the magnitude of the E × B drift flow is comparable with the main plasma flow. The reversal of both the poloidal and radial E × B flows near the strike point leads to rapid density accumulation right near the separatrix, which results in bifurcative step transition of divertor conditions with cold plasma across the entire divertor target plate. Furthermore, these results indicate that the interplay between geometry and drifts should be fully taken into account in future fusion reactor divertor designs.
Here, this work introduces the “potential vorticity bucket brigade,” a mechanism for explaining the resilience of vortex structures in magnetically confined fusion plasmas and geophysical flows. Drawing parallels with zonal jet formation, we show how inhomogeneous patterns of mixing can reinforce, rather than destroy non-zonal flow structure. We accomplish this through an exact stochastic Lagrangian representation of vorticity transport, together with a near-integrability property, which relates coherent flow topology to fluid relabeling symmetries. We demonstrate these ideas in the context of gradient-driven magnetized plasma turbulence, though the tools we develop here are model-agnostic and applicable beyond the system studied here.
The multi-region relaxed magnetohydrodynamics (MRxMHD) has been successful in the construction of equilibria in three-dimensional (3D) configurations. In MRxMHD, the plasma is sliced into sub-volumes separated by ideal interfaces, each undergoing relaxation, allowing the formation of islands and chaos. The resulting equilibrium has a stepped pressure profile across sub-volumes. The stepped pressure equilibrium code (SPEC) was developed to calculate MRxMHD equilibria numerically. In this work, we have extended the SPEC code to compute MRxMHD equilibria with field-aligned flow and rotation, following the theoretical development to incorporate cross-helicity and angular momentum constraints. The code has been verified for convergence and compared to a Grad–Shafranov solver in 2D. We apply our new tool to study the flow profile change before and after the sawtooth crash of a reversed-field pinch discharge, in which data of the parallel flow is available. We find the promising result that under the constraints of cross-helicity and angular momentum, the parallel flow profile in post-crash SPEC equilibrium is flat in the plasma core and the amplitude of the flow matches experimental observations. Lastly, we provide an example equilibrium with a 3D helical field structure as the favored lower energy state. This will be the first 3D numerical equilibrium in which the flow effects are self-consistently calculated.
In laboratory and natural plasmas of practical interest, the spatial scale Δ d at which magnetic field lines lose distinguishability differs enormously from the scale a of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives a/Δ d ~ 10 12 , which is the magnetic Reynold number R m . The traditional resolution of the paradox of disparate scales is for the current density j associated with the reconnecting field Brec to be concentrated by a factor of Rm by the ideal evolution, so j ~ B rec /µ 0 Δ d . A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, Δ max /Δ min , when calculated at various points in time. Reconnection becomes inevitable where Δ max /Δ min ~ R m . A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for Δ max /Δ min . Reconnection occurs on a time scale and with a current density enhanced by only ln(a/Δ d ) from the ideal evolution time and from the current density B rec /µ 0 a. In both resolutions, once a sufficiently wide region, Δ r , has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfv´enic time scale. The Alfv´enic evolution is intrinsically ideal but expands the region in which Δ max /Δ min is large.
Abstract Resonant layers in a tokamak respond to non-axisymmetric magnetic perturbations by amplifying the mode amplitude and balancing the plasma rotation through magnetic reconnection and force balance, respectively. This resonant response can be characterized by local layer parameters and especially by a single quantity in the linear regime, the so-called inner-layer Δ. The computation of Δ under two-fluid drift-MHD formalism has been progressed by reducing the order of the system in the phase space, where the shielding current is approximated as being only carried by electrons, a posteriori . In this study, we relax the approximation and compute Δ accounted for by the parallel flow associated with the ion shielding current. The posteriori is numerically verified in great agreement with the original SLAYER developed in a previous paper (J.-K. Park 2022 Phys. Plasmas 29 072506). Extending the resonant layer response theory to high β plasmas, our research findings answer two important questions: how the parallel flow influences the resonant layer response and why the parallel flow effect appears in high β plasmas. The complicated plasma compression in high β regime allows the parallel flow response to give rise to the ion shielding current, which not only shifts the zero-crossing condition of the ExB flow but also enhances the field penetration threshold. Technically, the Riccati matrix transformation method is adapted to handle the numerical stiffness due to the increased order of the system. The high fidelity of this numerical method makes use of further extension of the model to higher-order systems to take other physical phenomena into account. This work is envisaged to predict the resonant layer response under high β fusion reactor conditions.
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Multi-species flow takes place when two or more gases, plasmas or fluids are flowing and interacting with one another through particle collisions, chemical reactions, turbulence, and thermonuclear processes; this list is not exhaustive. It has a wide range of applications in geological, biological and engineering systems. In what follows species refers to different species of atoms or molecules that may or may not be partially or fully ionized. The interactions between these species takes place at an atomic or molecular level. The species are electrically neutral. These are very important points, because the coupling between species that are interacting on a mesoscale level or are immiscible would be very different than what is being considered in this work. In addition, in section 4, we present a heuristic argument to enhance the collisional mean free path to incorporate the effects of turbulent eddies by use of Prandtl’s assumption that the integral scale length of a turbulent boundary layer is proportional to the width of the turbulent layer. This leads to coupling terms that are non-Newtonian, because they are a function of the dynamics of the flow. It is also assumed that the turbulent stress terms are much smaller than the species partial pressures. This may be a good assumption if the species are hot, dense plasmas that exist in ICF targets.
Divertors are a critical concept for all magnetically confined fusion systems. The W7-X stellarator has an island divertor as do many of the privately funded stellarator reactor designs, but non-resonant divertors have many advantages, which are defined in the paper OSTI ID: 3021689, “Stellarators with enhanced tritium confinement and edge radiation control” and discussed in OSTI ID: 3021687, 3021688, 3021692, and 3021695. The three basic advantages are: (1) Resilience, the location at which the diverted plasma reaches the walls is insensitive to plasma conditions, unlike island divertors. (2) The width of the region at the plasma edge that flows into the divertor has a controllable width. It can be made sufficiently broad to avoid neutrals impending on the plasma from charge exchanging with high energy plasma particles. The resulting high energy neutrals erode the walls. (3) The controllable width and confinement of non-resonant divertors allow high-Z impurities to be added. The shortness of their confinement time limits their diffusion into the plasma interior. High-Z impurity radiation at the plasma edge seems the only way to sufficiently spread the outcoming power over the walls. The lack of experiments is a major impediment to application of non-resonant divertors, although the small experiment STAR_LITE is being built at Hampton University to study them.
Reduced models for approximating the impact of kinetic electron behavior on the transport of thermal energy and magnetic field are investigated. The thermal flux limiter has improved agreement with Vlasov–Fokker–Planck data when a harmonic form is used that adjusts the electron mean free path to account for electron–electron collisions; these results apply to both unmagnetized and magnetized plasmas. Once a magnetic field is incorporated, the mean free path should also be modified using the electron gyroradius. A flux limiter on Nernst advection of magnetic fields is also required; a form that limits Nernst by the same fraction as the thermal heat-flow best reproduces kinetic simulations. A flux limiter form for the cross terms (Righi–Leduc and cross-gradient-Nernst) is also suggested. Hohlraum simulations relevant to fusion experiments on the National Ignition Facility are found to be sensitive to all of these details.
Understanding the physics of collisionless, magnetized plasmas is key to unlocking a number of important problems in space and astrophysics. Magnetic reconnection is a fundamental mechanism which can explosively release stored magnetic energy, convert it to plasma heat and flows, and accelerate particles. In this project we developed technique and conducted experiments and simulations of magnetic reconnection in laser produces plasmas. Through this project, we also developed experimental techniques to generate magnetized collisionless shocks, and we therefore expanded the scope of the project to develop these experiments. These projects make fundamental progress on understanding the dynamics of magnetized laser-produced plasmas. In additional to plasma astrophysics, these results have broad interest for laboratory high energy density plasmas, since magnetic fields can be used to confine and control plasmas in many contexts and may offer new capabilities toward laboratory ignited plasmas.