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Reversed Field Pinch Research in MST (Final Technical Report)

This is the Final Technical Report for the cooperative agreement DE-FC02-05ER54814 titled “Reversed Field Pinch Research in MST” spanning the funding period 4/1/2005 to 12/14/2019. It summarizes key results from MST research, major publications and presentations, and the mentoring of graduate students and postdocs. The Madison Symmetric Torus (MST) is unique within the U.S. and world fusion plasma program. As one of just five operating reversed field pinch (RFP) experiments, and the only one in the U.S., MST has had an important role in advancing the fundamental understanding of the RFP plasma configuration. The MST research program targets topics that intersect with all three goals. While MST provides a unique opportunity to advance the science and fusion potential of the RFP, as a cousin to the tokamak and stellarator plasma configurations the RFP is a valuable partner in establishing validated predictive capability for fusion science more generally. Specific combinations of the major variables in toroidal confinement, like magnetic field strength, plasma current, and shaping, define the different configurations. By exploring adjacent regions in this major variable parameter space, the RFP exposes dependencies not otherwise accessible in the tokamak and stellarator. This diversity enlarges the arena for scientific discovery, both for fusion and plasma physics. The basic science emphasis for MST research has been the self-organizing behavior of RFP plasmas. This inspired MST’s participation in the NSF Physics Frontier Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas (CMSO), which ran from 2004-2016 and motivated a substantial fraction of MST’s research goals and capabilities. By all measures the MST Program has been remarkably successful in publications, community engagement, and mentoring of young scientists. While the DOE-FES’s proof-of-principle program for the RFP now languishes through the cessation of this cooperative agreement, operation of MST continues as one of two devices included in the new Wisconsin Plasma Physics Laboratory (WiPPL) basic science user facility. The scope of present research for MST in WiPPL is narrowed to the basic science associated with the RFP magnetic configuration and the advancement of specific fusion topics, which now includes studies of disruptions in tokamak plasmas. The world’s effort in RFP fusion research continues, despite a lack of U.S. federal support to investigate the RFP configuration for fusion application, most notably through a major upgrade to the RFX-mod2 facility in Italy [1] and the recent construction of the KTX facility at USTC in China. First plasmas for RFX-mod2 are anticipated in 2021.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experiments on plasma arcs at a water–air interface

An exploding water plasma experiment at UCLA investigated the expansion and morphology of a fireball with and without an external magnetic field. Diagnostics include photographs and movies (which may be downloaded) acquired with a framing camera, magnetic probes, and visible light spectra. The expansion and internal magnetic fields are very different from the unmagnetized case when a magnetic field of order 300G is applied along the expansion axis. Visible light spectra are brighter and additional lines are seen in the presence of the magnetic field. The experiment can serve as a platform for studies of interfacial mixing and possibly shed light on very different processes such as laser target physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. Here, an example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Combinatorial sputter deposition of ultrathick Au-Bi alloy films

We report gold-bismuth alloys are of interest as catalysts and catalytic sensing systems, electrochemical sensors, superconductors, and hohlraums for magnetically assisted inertial confinement fusion implosions. Radiation-hydrodynamics simulations with the Lasnex code of laser-driven hohlraums predict higher x-ray drive from Au-Bi alloys compared with cases of Au-Ta or pure Au and Bi hohlraums. Here, we use direct current magnetron sputtering in Ar gas, with co-sputtering from two elemental targets, to deposit Au-Bi alloys with Bi content of 9–77 at.% and thicknesses up to ~20 µm. Films are characterized by a combination of x-ray diffraction, Rutherford backscattering, scanning electron microscopy, substrate-curvature-based residual stress, and electronic transport measurements. Experiments are complemented by Monte Carlo simulations of ballistic sputtering and gas phase transport of depositing species and Ar gas atoms. Results show that all films are polycrystalline, with three distinct compositional regimes dominated by Au, Au 2 Bi, and Bi crystallographic phases. A metallic behavior of the temperature dependence of electrical resistivity is observed for all the films. Films with Bi content above ~30 at.% exhibit porosity, which is tolerable to hohlraum x-ray drive based on Lasnex simulations.

36 MATERIALS SCIENCE↗

Spatially and temporally resolved plasma parameter estimations of laser heated MagLIF relevant gas pipes at NIF

The ability to control laser pre-heat is an integral part of the inertial confinement fusion concept known as Magnetized Liner Inertial Fusion. This process is studied at the National Ignition Facility (NIF) where 4 of the 192 laser beams are propagated through a 1-cm long gas cell where they deposit >20 kJ of energy into the gaseous fuel via inverse bremsstrahlung absorption. This process ionizes the gas, producing a plasma that follows behind the laser front and expands over the radius of the cell. Emission from this plasma, as viewed by a gated x-ray detector, can be used to build spatially and temporally resolved estimations of the pre-heat plasma's density and temperature profiles. This can then be used to estimate the plasma pressure, internal energy, and radiation losses. Estimations show the evolution of the plasma in magnetized and unmagnetized gas cells filled with ambient temperature neopentane (C5H12) +1% Ar, as well as unmagnetized cryogenically cooled (32 K) deuterium +1% Ne filled targets. This analysis shows the effects of initial gas-fill density, composition, and axial magnetization on the time-dependent plasma parameters. Previously, these parameters at the NIF had not been experimentally characterized, and these estimations provided a potential new means of testing radiation magneto-hydrodynamic predictive capability models. Results in unmagnetized targets have strong agreement with simulations. However, in targets with a 19 T applied axial magnetic field, this method yields electron temperatures up to 100% hotter than those predicted by HYDRA codes.

Bremsstrahlung↗

A Forward Analytic Model of Neutron Time-of-Flight Signals for Inferring Ion Temperatures from MagLIF Experiments

A forward analytic model is required to rapidly simulate the neutron time-of-flight (nToF) signals that result from magnetized liner inertial fusion (MagLIF) experiments at Sandia’s Z Pulsed Power Facility. Various experimental parameters, such as the burn-weighted fuel-ion temperature and liner areal density, determine the shape of the nToF signal and are important for characterizing any given MagLIF experiment. Extracting these parameters from measured nToF signals requires an appropriate analytic model that includes the primary deuterium-deuterium neutron peak, once-scattered neutrons in the beryllium liner of the MagLIF target, and direct beamline attenuation. Here, mathematical expressions for this model were derived from the general-geometry time- and energy-dependent neutron transport equation with anisotropic scattering. Assumptions consistent with the time-of-flight technique were used to simplify this linear Boltzmann transport equation into a more tractable form. Models of the uncollided and once-collided neutron scalar fluxes were developed for one of the five nToF detector locations at the Z-Machine. Numerical results from these models were produced for a representative MagLIF problem and found to be in good agreement with similar neutron transport simulations. Twenty experimental MagLIF data sets were analyzed using the forward models, which were determined to only be significantly sensitive to the ion temperature. The results of this work were also found to agree with values obtained separately using a zero scatter analytic model and a high-fidelity Monte Carlo simulation. Finally, inherent difficulties in this and similar techniques are identified, and a new approach forward is suggested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-speed feedback control of an oscillating magnetic helicity injector using a graphics processing unit

A real-time control system has been developed to control the amplitude, phase, and offset of bulk plasma parameters inside an oscillating magnetic helicity injector. Control software running entirely on an Nvidia Tesla P40 graphical processing unit is able to receive digitizer inputs and send response patterns to a Pulse Width Modulation (PWM) controller with a minimum control loop period of 12.8μs. With an input digitization rate of 10 MS/s, a three-parameter proportional integral differential controller is shown to be sufficient to inform the PWM controller to drive the desired oscillating plasma waveform with a frequency of 16.6 kHz that is located near the resonance of a coupled RLC circuit. In particular, the temporal phase of the injector waveform is held within 10 degrees of the target value. Control is demonstrated over the toroidal modal structure of the imposed magnetic perturbations of the helicity injection system, allowing a new class of discharges to be studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Solving the Pulsed-Power Driven Inertial Fusion Energy Standoff Problem (Abbreviated Final Report)

The standoff problem in pulsed-power driven IFE (Inertial Fusion Energy) refers to the problem of electrically connecting a fusion target with the driver in a way that preserves the driver/target interface in the presence of a large fusion energy release (100’s of megajoules to 1000 megajoules). High yield fusion drivers for stockpile stewardship applications have similar concerns, but without the complication of the high repetition rate needed for energy production. All proposed IFE or high yield systems have the challenge of protecting the reactor vessel and driver from the energy release, but pulsed power drivers have the additional challenge of establishing an electrical connection in a way that does not create excessive debris or require costly/massive structures that must be expendable. Fortunately, there are conceptual solutions in the form of very low mass transmission lines, usually in the form of wires or foils, since very little mass is needed to overcome the magnetic forces driving the transmission lines apart or provide a low resistance pathway given the short pulse duration of the driver. Several important aspects of the standoff problem were analyzed in the course of this LDRD project. Conceptual means of introducing the low mass transmission lines into the reactor chamber were proposed, including analysis of methods to retain the power flow gap between the electrodes in the presence of the chamber environment. The energy losses due to ohmic dissipation and magnetic acceleration of the low mass transmission lines were evaluated for candidate driver pulses and different transmission line masses, and the fluence of x-ray and neutron energy on the persistent power flow structures that must survive the pulse of energy were evaluated. Finally, means of rapidly pumping down the chamber were explored as a way to return the system to low pressure following the multi-atmosphere post-pulse pressure rise. The overall conclusion from the analysis is that, while the reactor environment creates stressful conditions for a low mass transmission line standoff system, there are concepts expending 10 kg or less of electrode mass each pulse with the potential to mitigate the stresses and successfully drive fusion targets. Whether such a system could lead to a practical and economical fusion reactor would require extensive research and development beyond the scope of the feasibility study.

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THz Radiation Generation to Enable Internal Magnetic Field Measurement of Burning Plasmas (Final Scientific Report)

A one-year experimental program was performed using the Multi-TeraWatt (MTW) laser at the Laboratory for Laser Energetics (LLE) to investigate the efficiency and physical process of laser-driven—wire THz generation. This process was evaluated as a potential high-repetition-rate source of powerful THz pulses for use in THz pulsed polarimetry of a moderate-density magnetic-confinement fusion concept developed by TAE. The goal was to develop a source for short pulses in the THz regime (150 μm wavelength) containing 10’s of mJ. The campaign tested the impact of Cu wire diameter (25, 75, 160 μm), length (250 – 750 μm), and laser irradiation orientation on THz production efficiency in comparison to 20-μm thick Cu foils. Of these targets, the 160 µm diameter, 750 µm long wires with sharpened tips and irradiated at the base were found to produce the highest energy and shortest wavelength THz pulses, exceeding 2.5 Joule/sr and meeting the requirements for the polarimetry diagnostic. The brightest THz signal was radiated in the direction of the sharpened wire tip. A combination of two models – a traveling wave antenna combined with coherent transition radiation – describes the emission pattern, pulse energy, and spectrum observed in the experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Drift kinetic effects on plasma response to resonant magnetic perturbation for EU DEMO design

Abstract A systematic investigation of the plasma response to an externally applied resonant magnetic perturbation (RMP) field, for the purpose of controlling edge localized modes, is carried out for an EU DEMO reference plasma. Particular emphasis is placed on the role of kinetic effects associated with both thermal particles and fusion-born alphas. The single fluid, resistive model predicts a large peak amplification of the n = 1 ( n is the toroidal mode number) plasma response to the target equilibrium, which is found to be close to the Troyon no-wall limit. A more advanced response model, including kinetic resonances between the RMP perturbation and drift motions of thermal and energetic particles, on the other hand, finds a strong suppression of the n = 1 field amplification. A major role is played by the precessional drift resonance of fusion-born alphas. A strong parallel sound wave damping model is found to well reproduce the full kinetic response results for the DEMO plasma, in terms of both the resonant field response amplitude and the plasma displacement. Finally, both fluid and kinetic models produce similar responses for the n = 2 and 3 RMP fields for the considered DEMO plasma, whilst kinetic effects again become important for the n = 4 RMP due to proximity of the reference plasma to the no-wall limit for the n = 4 ideal kink instability.

Physics↗

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electromagnetic turbulence simulation of tokamak edge plasma dynamics and divertor heat load during thermal quench

Abstract The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal-quench phase of tokamak disruptions, are numerically investigated with BOUT++’s flux-driven six-field electromagnetic turbulence model. Here, transient yet intense particle and energy sources are applied at the pedestal top to mimic the plasma power drive at the edge induced by a core thermal collapse, which flattens the core temperature profile. Interesting features, such as surging of divertor heat load (up to 50 times) and broadening of heat-flux width (up to four times) on the outer-divertor target plate, are observed in the simulation, in qualitative agreement with experimental observations. The dramatic changes in divertor heat load and width are due to the enhanced plasma turbulence activities inside the separatrix. Two cross-field transport mechanisms, namely, the E × B turbulent convection and the stochastic parallel advection/conduction, are identified to play important roles in this process. First, an elevated edge pressure gradient drives instabilities and subsequent turbulence in the entire pedestal region. The enhanced turbulence not only transports particles and energy radially across the separatrix via the E × B convection, which causes the initial divertor heat-load burst, but it also induces amplified magnetic fluctuation B ˜ . Once themagnetic fluctuation is large enough to break the magnetic flux surface, magnetic flutter effect provides an additional radial transport channel. In the late stage of our simulation, | B ˜ r / B 0 | reaches to 10 −4 level that completely breaks magnetic flux surfaces such that stochastic field lines are directly connecting pedestal top plasma to the divertor target plates or first wall, further contributing to the divertor heat-flux width broadening.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Overview of the physics basis for the ARC fusion power plant

Commonwealth Fusion Systems plans to build ARC as the first fusion power plant at a site in Chesterfield County, Virginia, USA by the early 2030s. We present an overview of analysis comprising the physics basis of the ARC V3A design, a high-magnetic-field tokamak with 𝐵 0 =11.4 T, 𝐼 𝑝 =12.0 MA, 𝑅 0 =4.62 m, 𝑎 =1.18 m. ARC V3A is designed to produce 𝑃 𝑓⁡𝑢⁢𝑠 ≈1.13 GW DT fusion power and deliver ⩾400 MW net electric power to the grid. This overview includes quantitative analysis of fundamental issues for design of and operational plasma scenarios for a tokamak power plant, and lays out the design targets and strategic choices for ARC, including empirical fusion performance projections, assessment of H-mode access, ion cyclotron resonance heating simulations, alpha particle physics and time-dependent full-pulse simulations. This is complemented by topical papers on fusion performance and transport, disruption physics, boundary physics and magnetohydrodynamic stability. Critically, these studies identify key model uncertainties and physics risks to be retired through SPARC operation. Due to the modular nature of ARC, early results from SPARC can be incorporated into the design of the first ARC as well as subsequent replacements of the ARC vacuum vessel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploration of Rayleigh-Taylor seeding mechanisms in laser- and pulsed-power-driven inertial fusion

The ubiquitous Rayleigh-Taylor instability (RTI) has been observed in fluids and plasmas in a wide range of parameter regimes from astrophysical to laboratory plasmas. In high-energy-density (HED) laboratory plasmas, such as laser-driven inertial confinement fusion (ICF) plasmas, the RTI can have a detrimental impact on achieving fusion ignition through the generation of hydrodynamic mix. Hence, an understanding of the seeding mechanisms that produce the RTI and identifying ways to mitigate hydrodynamic mix is of critical importance. Appropriately aligned magnetic fields have been known to stabilize short-wavelength RTI. A number of numerical and experimental studies have demonstrated the benefits of using imposed magnetic fields in laser-driven ICF to achieve higher ion temeratures, higher neutron yields, and a relaxation of the ignition criteria. This work addresses seeding mechanisms in laser-driven implosions to understand critical early-stage physics that ultimately leads to substantial growth of the RTI along with mechanisms for mitigation of this growth. Surface perturbations due to machining tolerances and single-feature seeds (for example due to fill tubes) can produce substantial RTI growth in the ignition-relevant high-convergence ratio targets for laser- driven ICF implosions. RTI growth from single-feature seeding in laser-based implosions has the potential to be mitigated through appropriately aligned externally applied magnetic fields and the goal of this work has been to quantify that numerically and experimentally. Resistive-magnetohydrodynamic (MHD) simu- lations are used to study the seeding and evolution of the RTI leveraging previous support from the DOE HEDLP program. Furthermore, experimental data has been obtained and applied towards code validation of unmagnetized and magnetized evolution of single-feature seeded RTI growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetic Signatures of Radiation-Driven Double Ablation Fronts

In experiments performed with the OMEGA EP laser system, magnetic field generation in double ablation fronts was observed. Proton radiography measured the strength, spatial profile, and temporal dynamics of self-generated magnetic fields as the target material was varied between plastic (CH), aluminum, copper, and gold. Two distinct regions of magnetic field are generated in mid-Z targets -- one produced by gradients from electron thermal transport and the second from radiation-driven gradients. Extended magnetohydrodynamic simulations including radiation transport reproduced key aspects of the experiment, including field generation and double ablation front formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Sputter deposition of high electrical resistivity Au-Ta alloy coatings on rotating substrates

Sputter deposition of gold-tantalum alloy coatings is a key process for manufacturing hohlraums for magnetically-assisted inertial confinement fusion implosions. In this report we describe direct current magnetron sputter deposition of ~ 10 - μ~ 10 - μm-thick films of Au-80 at.% Ta onto rotating sphero-cylindrical hohlraum and planar Si witness substrates. Emphasis is given to how film microstructure and properties are affected by main deposition parameters, including argon working gas pressure, substrate bias, and the source composition (a single alloyed target compared to co-sputtering from two elemental targets). Experimental findings are correlated with distributions of landing energies and incident angles of depositing species calculated by Monte Carlo simulations of ballistic collisions and gas phase atomic transport. Deposition conditions characterized by low energetics of depositing species favor the formation of a β-Ta-like phase. Implications of these results to hohlraum fabrication are discussed.

36 MATERIALS SCIENCE↗

The effect of laser entrance hole foil thickness on MagLIF-relevant laser preheat

The magnetized liner inertial fusion (MagLIF) scheme relies on coupling laser energy into an underdense fuel raising the fuel adiabat at the start of the implosion. To deposit energy into the fuel, the laser must first penetrate a laser entrance hole (LEH) foil which can be a significant energy sink and introduce mix. In this paper, we report on experiments investigating laser energy coupling into MagLIF-relevant gas cell targets with LEH foil thicknesses varying from 0.5 μm to 3 μm. Two-dimensional (2D) axisymmetric simulations match the experimental results well for 0.5 μm and 1 μm thick LEH foils but exhibit whole-beam self-focusing and excessive penetration of the laser into the gas for 2 μm and 3 μm thick LEH foils. Additionally, better agreement for the 2 μm-thick foil is found when using a different thermal conductivity model in 2D simulations, while only 3D Cartesian simulations come close to matching the 3 μm-thick foil experiments. The study suggests that simulations may over-predict the tendency for the laser to self-focus during MagLIF preheat when thicker LEH foils are used. This effect is pronounced with 2D simulations where the azimuthally symmetric density channel effectively self-focuses the rays that are forced to traverse the center of the plasma. The extra degree of freedom in 3D simulations significantly reduces this effect. The experiments and simulations also suggest that, in this study, the amount of energy coupled into the gas is highly correlated with the laser propagation length regardless of the LEH foil thickness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Demonstration of improved laser preheat with a cryogenically cooled magnetized liner inertial fusion platform

We report on progress implementing and testing cryogenically cooled platforms for Magnetized Liner Inertial Fusion (MagLIF) experiments. Two cryogenically cooled experimental platforms were developed: an integrated platform fielded on the Z pulsed power generator that combines magnetization, laser preheat, and pulsed-power-driven fuel compression and a laser-only platform in a separate chamber that enables measurements of the laser preheat energy using shadowgraphy measurements. The laser-only experiments suggest that ~89% ± 10% of the incident energy is coupled to the fuel in cooled targets across the energy range tested, significantly higher than previous warm experiments that achieved at most 67% coupling and in line with simulation predictions. The laser preheat configuration was applied to a cryogenically cooled integrated experiment that used a novel cryostat configuration that cooled the MagLIF liner from both ends. Furthermore, the integrated experiment, z3576, coupled 2.32 ± 0.25 kJ preheat energy to the fuel, the highest to-date, demonstrated excellent temperature control and nominal current delivery, and produced one of the highest pressure stagnations as determined by a Bayesian analysis of the data.

47 OTHER INSTRUMENTATION↗