FLEXO Simulations of Low-Density Plasma Behavior Around a New Combined Stability Platform for Z-Pinch ICF
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Woolstrum, Jeffrey Michael [Sandia National Labora↗
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Code-to-code comparison between FLASH and HYDRA in gas-puff Z-pinch modeling
The numerical modeling of gas-puff Z pinches involves the nonlinear coupling of a broad range of complex, multi-physics phenomena that makes such simulations challenging. The challenge is further compounded by nonlinear instabilities that can impact the dynamics of imploding gas-puff Z pinches, such as the magneto Rayleigh–Taylor instability (MRTI). If the growth rate and amplitude of the latter is comparable to the relevant timescales and properties of the imploding plasma, the MRTI can dramatically alter implosion dynamics, dictate pinch stability, and govern the plasma properties achievable in pulsed-power-driven laboratory experiments. National Laboratories and academic teams have developed numerical tools that can accurately model Z-pinch configurations and provide reliable design capabilities that can guide experimental choices and assist in interpreting experimental results. Most such tools, however, are not broadly available. Here, we present newly developed Z-pinch simulation capabilities of the publicly available FLASH code, applied in the study of MRTI growth and dynamical effects in gas-puff implosions. To verify the new implementations, we perform a comparison of FLASH gas-puff implosion simulations with previously published calculations with the HYDRA code from Lawrence Livermore National Laboratory, which have been validated with experimental data from the CESZAR pulsed-power driver at the University of California, San Diego. The experiments involved double- and triple-nozzle configurations, in an experimental attempt to stabilize the pinch to the MRTI. The code-to-code comparison shows similar results between the FLASH and HYDRA simulations, supporting the use of FLASH in the modeling of future gas-puff Z-pinch experiments at CESZAR.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Measuring dynamics of differentially rotating, unmagnetized, free-boundary plasma produced by soft x-ray irradiation
We present results from a new experiment, fielded on the MAGPIE pulsed power generator, producing a rotating, boundary-free plasma with no pre-imposed magnetic field. Angular momentum is introduced to the rotating system by the oblique collision of multiple plasma flows, which are driven by x-ray ablation of solid targets using the soft x-rays emitted from the implosion of wire array z-pinches. This produces a hydrodynamically stable plasma which undergoes ~2-3 rotations over the duration of the experiment, significantly more than previous pulsed-power platforms. Estimating the angular frequency from the electron density profile in the inner part of the rotating plasma shows that it has a quasi-Keplerian rotation profile. The system also allows for the addition of a controllable magnetic field. This, combined with the sufficiently large Reynolds (~10 5 ) and magnetic Reynolds (~10) numbers, will enable investigation of the effect of magnetic field on the structure and stability of the rotating plasma.
Physics - Plasma physics↗
Comprehensive analytical model of the dynamic 𝑍 pinch
In this work we present an analytical 1D axisymmetric model describing the evolution of the dynamic 𝑍 pinch. This model is capable of predicting the trajectories of the imploding sheath's magnetic piston and preceding shock front, along with the velocity, pressure, density, and magnetic field profiles, for any time-dependent current, spatially varying initial density profile, and weak initial axial field. The implosion is divided into stages, with each stage described by a set of coupled ordinary differential equations derived from the ideal MHD equations. Comparisons with experimental data from the COBRA pulsed-power facility are quite promising and imply this model could prove useful in designing and analyzing future pulsed-power experiments.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Doubling fusion power with volumetric optimization in magnetic confinement fusion devices
A technique, volumetric power optimization, is presented for enhancing the power output of magnetic confinement fusion devices. Applied to a tokamak, this approach involves shifting the burning plasma region to a larger plasma volume while introducing minimal perturbations to the plasma boundary shape. This edge perturbation—squareness—is analogous to pinching and stretching the edge boundary. Stability calculations confirm that this edge alteration is compatible with maintaining plasma stability. This optimization method for optimizing fusion power output could improve the performance of magnetic confinement fusion power plants.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Spot size measurement of a deuterium–tritium dense plasma focus using neutron radiography
Neutron radiography is a technique uniquely suited to applications in nuclear diagnostics, non-destructive testing, and subcritical experiments. The spatial resolution of neutron radiographs is degraded by optical blur in the imaging system and the neutron source size, where the ideal source is point-like to optimize the point-spread function. A potential neutron source for radiography is the dense plasma focus (DPF), a coaxial Z-pinch that produces thermonuclear and beam-target neutrons. To assess if the source size is suitable for radiography, a neutron imaging system was used to measure the source size of the 4 MA Sodium DPF at the Nevada National Security Site operating with deuterium–tritium gas-fill. The source size was measured using the edge-spread function of tungsten objects, each having a rolled (convex) edge. The spot size was found to be 7–12 mm full-width at half-max (FWHM) assuming a Gaussian source, though comparison is presented for Lorentzian and Bennett distributions. The average FWHM was found to be 8.6 ± 1.2 mm vertically and 10.8 ± 1.2 mm horizontally with respect to the image plane, averaging over varied edges and alignments. The results were sensitive to source alignment and edge metrology, which introduced notable uncertainties. These results are consistent with separate experimental measurements as well as magnetohydrodynamics simulations of this DPF, which suggest that neutron production can originate from pinches ∼5–7 mm off-axis. These results suggest that the DPF should be used for radiography at low magnification (M < 1) where spot size does not dominate spatial blur.
47 OTHER INSTRUMENTATION↗
Plasma-induced collective effects in muon ionization cooling
Muon ionization cooling is a critical process that determines the achievable beam brightness and overall performance of a muon collider. In this study, we investigate collective effects induced by high-intensity muon beams inside the absorber, effects that have not been included in previous ionization cooling simulations. We show that beam-induced plasma can neutralize the beam space-charge field, while the self-generated azimuthal magnetic field can introduce additional beam focusing through a z-pinch-like mechanism. We also demonstrate that sufficiently high plasma densities may modify the stopping-power rate. The implications of these plasma-induced phenomena for ionization cooling performance are discussed.
Yonehara, Katsuya [Fermilab] (ORCID:00000002544041↗
An implicit particle code with exact energy and charge conservation for studies of dense plasmas in axisymmetric geometries
A collisional particle code based on implicit energy- and charge-conserving methods in axisymmetric geometries is presented. A new particle pusher for axisymmetric systems is introduced that is compatible with exact energy and charge conservation and yields improved accuracy compared to other methods. How to appropriately treat all aspects of the algorithm near the r = 0 axis of symmetry is described in detail. Here, the axisymmetric model is verified by simulating the free expansion of a plasma sphere in 2D cylindrical and 1D spherical geometries. The algorithm's ability to study the dynamic compression of a dense plasma is illustrated by simulating the dynamic Z-pinch in 1D cylindrical geometry.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Time-resolved measurement of neutron energy isotropy in a sheared-flow-stabilized Z pinch
Previous measurements of neutron energy using fast plastic scintillators while operating the Fusion Z Pinch Experiment (FuZE) constrained the energy of any yield-producing deuteron beams to less than 4.65 keV. FuZE has since been operated at increasingly higher input power, resulting in increased plasma current and larger fusion neutron yields. A detailed experimental study of the neutron energy isotropy in these regimes applies more stringent limits to possible contributions from beam-target fusion. The FuZE device operated at -25 kV charge voltage has resulted in average plasma currents of 370 kA and D–D fusion neutron yields of $4\times10^7 \pm 4\times10^6$ neutrons per discharge. Measurements of the neutron energy isotropy under these operating conditions demonstrates the energy of deuteron beams is less than $7.4 \pm 5.6^\mathrm{(stat)} \pm 3.7^\mathrm{(syst)}$ keV. Characterization of the detector response has reduced the number of free parameters in the fit of the neutron energy distribution, improving the confidence in the forward-fit method. Gamma backgrounds have been measured and the impact of these contributions on the isotropy results have been studied. Additionally, a time dependent measurement of the isotropy has been resolved for the first time, indicating increases to possible deuteron beam energies at late times. This suggests the possible growth of m = 0 instabilities at the end of the main radiation event but confirms that the majority of the neutron production exhibits isotropy consistent with thermonuclear origin.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Simulation Resource Team for Innovative Fusion Concepts
This project created a shared simulation resource for innovative fusion concepts at the University of Rochester, built around the FLASH, TriForce, OSIRIS, and OSHUN codes. Many promising fusion approaches are too complex to evaluate by experiment alone yet building a custom simulation capability from scratch for each new concept is expensive and slow. The BETHE Simulation Resource Team addressed this problem by developing and validating a flexible set of numerical tools, which were then applied across three major concept areas: plasma-jet-driven magneto-inertial fusion, staged Z pinches, and field-reversed configurations. The team assisted three concept teams and carried out independent analyses of all three concepts.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Addressing key physics problems in high-energy-density plasmas with a novel kinetic simulation capability
Many important physical processes in inertial confinement fusion (ICF) and dense Z-pinch (DZP) experiments require a kinetic (velocity-space-dependent) description. Conventional particle-in-cell (PIC) methods are poorly suited for high-energy-density (HED) plasmas, due to restrictive time-step constraints and the inability to conserve energy. In a previous LDRD (21-FS-048), we demonstrated that a fully implicit PIC formulation overcomes these limitations: it conserves energy even when coupled with Coulomb collision models and can be solved efficiently with large grid cells and large time steps. Thus, it is feasible to use this method to study kinetic effects in ICF and DZP plasmas on hydro-like time and spatial scales. In this follow-on LDRD, we advanced this methodology into a high-fidelity tool for production-scale simulations and used it to answer key questions relevant to ICF and DZP experiment.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Sensitivity of magnetohydrodynamic simulations of Joule-heated conductors to the vaporization curve in equations of state
Magnetohydrodynamic (MHD) simulations of electrically exploded aluminum and copper rods demonstrate a technique to validate equations of state (EOS) for rapidly Joule-heated conductors. The balance of internal and magnetic forces at the conductor-insulator interface drives the metal there along the vaporization phase boundary. Variations between critical points and vaporization curves in existing models predict differing densities and temperatures in MHD simulations for these models. Here, the inclusion of Maxwell constructs in the liquid-vapor biphase region of the EOS caused the rod surface to vaporize earlier in time than unmodified tables with van der Waals loops. Velocimetry of recent experiments is used to validate the location of the vaporization curve in existing EOS models and differentiate between the vapor dome treatments. Dielectric coatings applied to the metal surface restricted the conductor’s expansion and diverted the metal into the warm dense matter regime.
36 MATERIALS SCIENCE↗
$Z$-Pinch Interferometry Analysis With the Fourier-Based TNT Code
Here, we present the analysis of interferometry diagnostics with the user-friendly Talbot Numerical Tool (TNT), a Fourier-based postprocessing code that enables real-time assessment of plasma systems. TNT performance was explored with visible and infrared interferometry in pulsed-power-driven Z -pinch configurations to expand its capabilities beyond Talbot X-ray interferometry in the high-intensity laser environment. TNT enabled accurate electron density characterization of magnetically driven plasma flows and shocks through phase-retrieval methods that did not require data modification or masking. TNT demonstrated enhanced resolution, detecting below 4 % fringe shift, which corresponds to 8.7 × 10 15 cm –2 within 28 μ m, approaching the laser probing system limit. TNT was tested against a well-known interferometry analysis software, delivering an average resolving power nearly ten times better (~28 μ m versus ~ 210 μ m) when resolving plasma ablation features. TNT demonstrated higher sensitivity when probing sharp electron density gradients in supersonic shocks. A maximum electron areal density of 4.1 × 10 17 cm –2 was measured in the shocked plasma region, and a minimum electron density detection of ~ 1.0 × 10 15 cm –2 was achieved. When probing colliding plasma flows, the calculations of the effective adiabatic index and the associated errors were improved from γ* = 2.6 ± 1.6 – 1.4 ± 0.2 with TNT postprocessing, contributing valuable data for the interpretation of radiative transport. Additional applications of TNT in the characterization of pulsed-power plasmas and beyond are discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions
Implosions of magnetically driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the (A, M) parametric plane, where A is the in-flight aspect ratio and M is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of A ≫ 1, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters.
Ruiz, D. E. [Sandia National Laboratories (SNL-NM)↗
Thermonuclear Fusion Verification of Staged Z-Pinch Fusion on a 0.5 MA LTD Pulsed Power Generator (Final Report)
LLNL fielded neutron detectors at UCSD’s CESZAR facility during the experimental campaigns investigating the staged Z-pinch concept. This concept uses high current to compress a cylindrical plasma composed a high atomic number gas, such as argon, surrounding fusion fuel. LLNL analyzed data from the diagnostics and improved the diagnostic setup specific to the experiment. This work helps to advance the mission creating a fusion energy source, which is a benefit to the economy and for energy security.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Energetic particle physics: Chapter 7 of the special issue: on the path to tokamak burning plasma operation
We review the physics of energetic particles (EPs) in magnetically confined burning fusion plasmas with focus on advances since the last update of the ITER Physics Basis (Fasoli et al 2007 Nucl. Fusion 47 S264). Topics include basic EP physics, EP generation, diagnostics of EPs and instabilities, the interaction of EPs and thermal plasma instabilities, EP-driven instabilities, energetic particle modes (EPMs), and turbulence, linear and nonlinear stability and simulation of EP-driven instabilities and EPMs, 3D effects, scenario optimization strategies based on EP phase-space control, EPs in reduced field scenarios in ITER before DT, and the physics of runaway electrons. We describe the simulation and modeling of EPs in fusion plasmas, including instability drive and damping as well as EP transport, with a range of approaches from first-principles to reduced models, including gyrokinetic simulations, kinetic-MHD models, gyrofluid models, reduced models, and semi-analytical approaches.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Fast ion relaxation in ITER mediated by Alfvén instabilities
Abstract We address the critical issue for future burning plasmas of whether high-energy fusion products or auxiliary heating-beam ions will be confined for a sufficiently long time to compensate for thermal plasma energy losses. This issue can be mitigated by one of the most deleterious collective phenomena—the instability of low, sub-cyclotron frequency Alfvén eigenmodes (AEs), such as toroidicity-induced AEs and reversed-shear AEs in the ITER steady-state scenario. Using a revised quasi-linear (QL) theory applied to energetic particle (EP) relaxation in the presence of AEs, we find that the AE instabilities can affect both neutral beam ions and alpha particles, although the resulting fast ion transport is expected to be modest if classical particle slowing down is assumed. On the other hand, the QL theory predicts that the AE amplitudes will be enhanced by the background microturbulence, although this topic remains outside our scope due to the significant numerical effort required to evaluate these effects. We report our results for EP relaxation dynamics obtained utilizing several tools: (i) a comprehensive linear stability study of the sub-cyclotron Alfvénic spectrum as computed by ideal magnetohydrodynamic NOVA simulations for the AE eigenproblem, (ii) drift kinetic NOVA-C calculations for wave–particle interaction and AE growth/damping rates, and (iii) predictive QL modeling coupled with the global transport code TRANSP to assess the EP relaxation on the equilibrium timescale.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A hybrid-kinetic simulation tool for non-thermal warm x-ray z-pinch sources, with gas-puff and wire array exemplars
Increasing the fluence of z-pinch x-ray radiation sources above ∼ 10 keV has been a long-standing goal for scientists at Sandia National Laboratories’ Z Machine. Optimizing sources for non-thermal “cold Kα” emission in higher atomic-number materials appears to be a promising path to increase warm x-ray yield. However, this emission is generated by supra-thermal electrons, which are not treated in the magnetohydrodynamic (MHD) codes that are typically used in z-pinch source development. MHD codes do not allow for charge separation or space-charge-generated electric fields, and constrain particle kinematics to Maxwellian distributions. The kinetic codes which do accommodate discrete, non-thermal energy distributions are computationally prohibitive when modeling plasmas near solid density and when modeling/tracking higher ionization states. Thus, modeling non-thermal z-pinch sources requires a new simulation tool. In this report, we present a new hybrid modeling capability that uses the fast features of MHD-type particles to the greatest extent possible, then transitions to the slower but more complete kinetic particle treatment to correctly capture the particle energy spectra that generate non-thermal emission. This capability is founded on the fully-relativistic particle-in-cell code Chicago, which already includes fluid particle treatments. The governing equations and hybrid methodology presented here are applied in simulations of an argon gas-puff and a molybdenum wire-array to provide preliminary code validation. The argon simulation is compared to measured implosion times and yields from Jones et al., Phys. Plasmas 22, 020706 (2015). The simulated x-ray yield is within 25% of measurements and the implosion times agree within a few percent. The molybdenum wire array simulation captures the implosion timing reported in Hansen et al., Phys. Plasmas 21, 031202 (2014), but work is needed to verify the available EOS table. These exemplar simulations represents the type of non-thermal sources that will be developed using the hybrid code capability going forward.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗