Field-reversed configurations (FRCs) are often the plasma target of choice for magnetized target fusion (MTF) efforts of multi-microsecond timescale, which require closed-field lines. While Z is fast enough to operate in a hybrid inertial MTF regime (i.e. traditional MagLIF with open-field lines), compression of a high- energy-density (HED) FRC within a MagLIF-like liner may offer many advantages – including a greater flexibility in liner size and implosion time. This offers a world of possibilities in using the pulse-shaping and self-crowbar capabilities of Z for greater energy coupling.

Analytic estimates and 2D LASNEX simulations by Slutz et al. [1] suggest very interesting fusion gains (QDTsci~1) with FRC compression at the centimeter-sized, sub-microsecond hydrodynamic scale of Z. In an advantage over FRC liner compression efforts utilizing translation [2], it is proposed these FRCs be formed in- situ to the liner by using external bias coils in addition to a helical AutoMag-type liner [3].

To investigate this novel formation method, a high-field 𝜃-pinch and FRC formation platform was developed on the MAIZE LTD (1-MA, 100-ns) at UM. Fast-framing images and magnetic probe data reveal interesting dynamics to the plasma columns & annuli formed within deuterium-filled quartz discharge tubes, perhaps suggesting successful FRC production under the proper conditions. Effects of pre-ionization, bias field, and D2 fill pressure are explored and compared to expectations from the literature.

2D simulations in GORGON/Kraken of FRCs initialized with parameters relevant for MTF on Z predict anomalous trapped flux lifetimes consistent with theory and empirical scaling laws [4]. In fact resistive lifetimes are ample for compression; formation robustness and stability to tilt and rotational modes remain the primary concern at high-density. The effects of field gradients inherent to the AutoMag concept are explored, and it is shown that FRCs would be quite robust to axial ejection during the compression/burn. Synthetic images are generated from simulation data for comparison with experimental images.

In summary, prospects for HED FRC liner compression on Z are bright – but a great deal of work remains recommended, particularly in simulation. Optimization of energy coupling to a liner on Z with pulse- shaping remains an open question which may influence the desired FRC parameters. Once such parameters have been identified, the proper formation hardware should be designed and tested at-scale on a high- impedance 1-MA machine like the Mykonos LTD. If a proper FRC starting target can be produced and diagnosed on Mykonos, the path to the first HED FRC shot on Z should become clear.

[1] S. A. Slutz & M. R. Gomez, Phys. of Plasmas 28, 042707 (2021); https://doi.org/10.1063/5.0044919 [2] J. H. Degnan et al., Nucl. Fusion 53 093003 (2013); https://doi.org/10.1088/0029-5515/53/9/093003 [3] S. A. Slutz et al., Physics of Plasmas 24.1 (2017); https://doi.org/10.1063/1.4973551
[4] Alan L. Hoffman et al., Fusion Technology 23:2 (1993); https://doi.org/10.13182/FST93-A30147

This work was supported in part by the NNSA Laboratory Residency Graduate Fellowship program under DOE Contract No. DE-NA0003960, and by the NNSA Stewardship Sciences Academic Programs under DOE Cooperative Agreement DE-NA0003764. SNL is managed and operated by NTESS under DOE NNSA contract DE- NA0003525.

Nuclear fusion is a potential source of carbon-free electricity with many concepts in development. The Fusion Z-pinch Experiment (FuZE) is a sheared-flow stabilized Z-pinch device where the Portable and Adaptable Neutron Diagnostics for ARPA-E (PANDA) suite has been deployed since 2021 at the Zap Energy facility. The FuZE capacitor banks are discharged to ionize neutral deuterium gas and induce pinch currents that cause fusion in deuterium plasmas. Neutrons with mean energies of 2.45 MeV can be detected outside of the device chamber. There are two types of neutron detectors in PANDA: lanthanum bromide (LaBr₃) activation detectors and fast plastic scintillators. The activation detectors measure the integrated neutron yield for each shot, while the plastic scintillators record time resolved signals. The 16 gain matched plastic scintillators can be positioned along the Z-pinch device to measure the neutron source spatial and temporal characteristics. FuZE is designed to produce a long lived (few µs) fusing plasma in a column. Calculating the time resolved axial profile measured by the plastic scintillators shows where and when the plasma is hot and dense enough to produce neutrons.

This work is supported by a US DOE ARPA-E award 18/CJ000/05/05. Prepared by LLNL under Contract DE-AC52-07NA27344.

The Magneto Rayleigh-Taylor instability (MRTI) is a concern for magnetized, imploding z-pinch configurations such as the magnetized liner inertial fusion (MagLIF) concept being studied on the Z facility at Sandia National Laboratories [1]. In MagLIF, MRTI degrades the assembly and confinement of thermonuclear fuel. A key component to MagLIF experiments is the pre-embedded axial magnetic field, which reduces thermal conduction losses during the implosion and traps charged fusion products at stagnation to enhance the fusion yield in the fuel. This axial field modifies MRTI, generating helical plasma striations on the liner surface. The observed pitch angle of the helices is significantly larger than what was originally anticipated. It is hypothesized that the amplification of axial magnetic field, from flux compression occurring in a low-density plasma (LDP) surrounding the liner, could explain the large pitch angle [2]. The LDP is suspected to be generated from the high current densities in the transmission lines leading up to the liner.

To investigate this hypothesis, we are developing a platform to study axial flux compression in LDP on the University of Michigan’s MAIZE facility, a 1-MA class linear transformer driver. This platform uses MAIZE to implode a low-density gas-puff plasma onto a thin foil liner. The resulting MRTI structure, with and without a pre-applied axial magnetic field, will be observed with a 12-frame optical self-emission camera as well as laser-based diagnostics. The two laser diagnostics under development are a laser schlieren refractometer [3] and a laser interferometer system, both with a 532-nm probe beam from a Nd:YAG laser. Ongoing efforts and challenges will be presented.

Understanding the impact of hydrodynamic perturbations transmitted through thin, dense layers is important for inertial confinement fusion ignition schemes, particularly double- or multi-shell systems. Experiments to validate our understanding are challenging as they necessarily involve multiple interfaces, materials, transmitted and reflected shocks, etc. We present experimental data for a Z Machine platform at Sandia National Laboratories investigating the Richtmyer-Mehskov process and interfacial feedthrough, and a comparison to a similar laser-driven design fielded at the National Ignition Facility. The pulsed-power driven platform is a cylindrical liner filled with liquid deuterium and is magnetically imploded with >20 MA of current, driving a converging shock that propagates towards the central axis and generating a high plasma-beta system suitable for investigating HED hydrodynamical processes. These experiments test and validate aspects of transmitted instability theory and feedthrough, including the qualitative difference in behavior between long and short wavelength modes: the buckling of the layer by long modes into imprinted shapes, and the cumulative impact of short modes leading to mix. Recent improvements in analysis have demonstrated how, beyond integral measures such as dominant wavelength and mix width, higher-order metrics such as material variances may also be extracted from the diagnostics and compared with theory and simulation.

*This work conducted under the auspices of the U.S. DOE by Los Alamos National Laboratory under contract 89233218CNA000001 and by Sandia National Laboratories under contract DE-NA0003525

The Magnetized Liner Inertial Fusion (MagLIF) platform on Sandia’s Z-Machine consists of a beryllium liner filled with deuterium (D2) gas that is pre-ionized and heated by a short-pulse laser and magnetized by a set of high magnetic field coils before being directly-drive by the high-current pulse from the Z-machine. Recently, an idea to add tritium (T2) gas on the MagLIF is getting more attention because DT fusion signature can add valuable additional information on the nuclear phase of MagLIF. In this work, DT nuclear reaction history diagnostics previously developed for Inertial Confinement Fusion (ICF) experiments on the National Ignition Facility (NIF) are being extended to the MagLIF platform. The nuclear diagnostics planned to be fielded include the Gamma-Reaction History (GRH) diagnostic which consists of four independently thresholded gas Cherenkov detector cells which enables measurements of the 16-MeV gamma rays emitted from the D(T,.)5He reaction. Also in development were sets of Aerogel Cerenkov Detectors (ACDs) for measuring the 0.1 - 5 MeV gamma ray continuum from the 9Be(n,.)9mBe inelastic scattering reactions from the beryllium liner, enabling time-resolved liner areal density measurements at high temporal resolution. Also in development is a new proton-recoil telescope (PRT) which enable time-resolved neutron spectroscopy measurements for fuel areal density measurements. This suite of diagnostics will enable high temporal resolution measurements of the reaction history and liner dynamics which will enable constraints on the energy balance of theoretical models that were not previously accessible with DD implosions on MagLIF. In anticipation for future DT shots, forward modelling in MCNP6.3 was conducted to estimate the detector response functions for low tritium percentage implosions. The pulsed power environment poses a different set of challenges such as high-flux bremsstrahlung backgrounds that must be accounted for not present in laser-driven systems. Detector design will be presented along with the predicted response functions and anticipated challenges of diagnostic operation with the pulsed power environment.

The Energetics and Other Physics of a Fusion-grade 20 MA Liner-on-Plasma Implosion without Preheating or Premagnetization, Irvin R. Lindemuth, retired, formerly Los Alamos National Laboratory—magnetically driven z-pinch implosions of cylindrical and quasi-spherical liners have a wide range of applications, including controlled fusion and creating high-energy-density environments for material studies. A priori a variety of phenomena might be expected in a liner-target configuration. The axial current can Ohmically heat the liner causing the liner to expand in a manner similar to an exploding wire. The magnetic forces generated by the current can implode the liner and the liner becomes a z-pinch, subject to all of the stability concerns of a classical z-pinch. An inward moving inner liner surface, whether generated by Ohmic heating or magnetic forces, can compress the target, i.e., the liner becomes a hydrodynamic piston. If the “jump-off” velocity of the liner is high enough and rises rapidly enough, shocks can be generated in the target. Depending upon the liner’s resistivity, the magnetic field can potentially diffuse through the liner and induce an axial current in the target. The current can Ohmically heat the target and, as with the liner, cause magnetic forces that can compress the fuel. If the magnetic forces on the target are strong enough, the inward moving fuel may separate from the liner, leaving a vacuum behind.¹ As with the liner, the magnetic field itself can become a piston that can potentially create shocks in the target. If the target separates from the liner, only the magnetic piston compresses the fuel; the fuel, too, becomes subject to all of the stability concerns of the classical z-pinch. In fusion applications, simultaneous heating mechanisms and cooling mechanisms compete to determine whether or not the fusion fuel can reach fusion temperatures. Radiation and thermal conduction can potentially be either cooling or heating mechanisms. This paper reports one-dimensional magnetohydrodynamic (MHD) computations that examine the energetics and other physical aspects of liner-on-plasma implosions. The MHD model includes the continuity equation, an equation of motion that includes the Lorentz force, and Faraday’s law using a simple Ohm’s law. The model also includes two energy equations with Ohmic heating, radiation, and diffusive radiation transport. The MagLIF concept uses laser-preheat the fuel and premagnetization to achieve significant fusion yield on a 20-MA-class machine, e.g., Z, because the implosion velocity is limited. In contrast, the so-called “staged z-pinch” (SZP) is claimed to be able to achieve fusion in the same velocity regime with a direct drive z-pinch without external fuel preheating and premagnetization, although published SZP calculations have been shown to be inaccurate.² However, we have identified a parameter space, not necessarily practical, where a simple 20-MA z-pinch liner-on-plasma can achieve fusion temperatures at possibly achievable convergence (e.g., 40-50). “Cold-start” (solid liner) calculations are reported. One interesting result is that the liner is essentially low-beta during its acceleration whereas the fusion fuel is high-beta.

¹I. Lindemuth, J. Comp. Phys. 25, 104 (1977).

²I. Lindemuth, M. Weis, W. Atchison, Phys. Plasmas 25, 102707 (2018).

Zap Energy is actively developing the sheared-flow-stabilized (SFS) Z-pinch concept for fusion energy applications with its currently operational FuZE and FuZE-Q devices. Sheared-flow stabilization offers a pathway toward long duration (~ 100 microseconds) Z-pinch plasmas that are stable to the m = 0 ‘sausage’ and m = 1 ‘kink’ MHD modes characteristic of static configurations. Sheared-flow stabilization provides for a more attractive trajectory towards a commercial Z-pinch fusion energy system by avoiding the need to embed an axial magnetic field with external coils or employ a close-fitting conducting wall around the plasma column. An experimental suite of diagnostics has been deployed on FuZE, and FuZE-Q, a next-generation SFS Z-pinch device designed to produce deuterium plasma conditions consistent with deuterium-tritium (DT) scientific breakeven Q = 1. These diagnostics include magnetic probes and current Rogowski coils, spectroscopic systems (e.g., Broadband visible, Ion Doppler, Extreme Ultraviolet (EUV)), optical Thomson scattering (OTS), 633 nm and digital holographic interferometry (DHI), high-speed cameras, neutronics (e.g. plastic scintillators and LaBr₃ activation detectors), X-ray detectors, among others. Experimental results from the recently commissioned and now operational FuZE-Q device will be provided from various diagnostic systems. The methodology for the calculation and measurement of scientific gain in a SFS Z-pinch with fielded diagnostics will be provided. Lastly, plans for potential additional diagnostics such as Faraday polarimetry, Zeeman spectroscopy, internal magnetic probes, X-ray crystal spectroscopy, and bolometry will be presented as well.

We present a newly developed x-ray spectrometer known as the Multi-Optic Novel Spherical Spectrometer with Time Resolution, or MONSSTR. The MONSSTR relies on two spherically-bent crystal optics to image the spectra onto an hCMOS-based Ultra-Fast X-ray Imaging camera known as Icarus [1]. With a minimum gate time of 2 ns per frame and a maximum of 8 frames, 16 ns of continuous temporal coverage is achieved. MONSSTR was designed to detect trace dopants (e.g., Fe and Co) that are added or naturally occurring in the Magnetized Liner Inertial Fusion (MagLIF) experiments. To enable a high-collection efficiency, large aperture (36 mm wide) crystals were deployed. By changing the crystal plane (e.g., Quartz (203) vs. Ge (220)), the spectral range can easily be modified to accommodate a large variety of experiments. Good performance at x-ray energies as high as 13 keV have been demonstrated. Ray tracing models from SHADOW3 and initial data from Z-experiments will be presented.

[1] Q. Looker et. al, Rev. Sci. Instrum. 91, 043502 (2020); doi: 10.1063/5.0004711

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. This work was performed under the auspices of the U.S. Department of Energy by LLNL under Contract DE-AC52-07NA27344.

An open question important to a next generation pulsed power (NGPP) facility is the formation of plasma in the anode cathode (AK) gap of the power feed. Understanding this plasma formation and evolution is important as it can lead to current losses across the AK gap, which will affect a larger surface area on a NGPP facility. To help understand this plasma formation, it is important to measure the density of the plasma. We present the design and initial results of a photonic Doppler velocimetry (PDV) system that will enable the measurement of the electron density at 4 different points across 1 mm of the AK gap. PDV records the rate of change of the refractive index as a change in beat frequency and is capable of measuring densities down to 10¹⁶ cm^-3 over a 1 mm path. This diagnostic was deployed on the Mykonos pulsed power machine at Sandia, which has a peak current of 680 kA. It was tested on two different loads designed to study and diagnose plasmas in the AK region in planar and parallel plate loads. The current density on these platforms can reach values that are equivalent to 1.6 cm radius in the Z machine’s inner magnetically-insulated transmission line (MITL) making them useful platforms for studying power flow in high-stress inner MITLs. We present initial results from measurements with a single fiber probe, which shows the density rising about halfway to peak current. We will also discuss the challenges and steps for extending this measurement to 4 points.

This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

The one-dimensional imager of neutrons (ODIN) has been used to image neutrons emitted from the source of Magnetized Liner Inertial Fusion (MagLIF) experiments on the Z facility. These experiments produce DD-neutrons which pass through a 100-mm thick tungsten rolled edge slit to then be imaged on CR-39 detectors. A piece of high-density polyethylene is used as a neutron to proton convertor to improve the CR-39 detection efficiency. The latent tracks within the CR-39 are exposed using a chemical etching process and recorded using an optical scanning system. The data, consisting of track diameter, eccentricity, position, and contrast, is down selected for primary DD-neutrons expected to have traveled directly from the through the slit assemble to the detector. The selected data is binned and integrated along the resolving axis to produce an axial detector response. A mathematical model of the instrument response function has been developed which is used with existing ODIN data to perform neutron source profile recovery via a modified generalized expectation maximization algorithm. The modification uses basis functions to remove a background of intrinsic noise from the CR-39.

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Analyzing radiographs of pulsed-power experiments is key to understanding target behavior in ICF and HED platforms. In these platforms, the radiograph quality is heavily influenced by the Magneto Raleigh-Taylor (MRT) instability which may partially or completely obscure key features like spike growth and target density. By using machine learning postprocessing techniques on these radiography images, we aim to lessen and possibly eliminate the impacts of these obscured regions.

Here, we develop a method by which MRT darkened regions in radiography images are removed from radiographs of experiments on the Z-Machine of Sandia National Laboratories. This is achieved using a convolution neural network (CNN) that leverages existing segmentation functions^1,2 with CUDA³ additions. We employ a six-layer CNN to suppress the darkened regions by 1) treating the darkened regions as noise via a mixed loss function and 2) using end-to-end frameworks that minimize noise in each subsequent layer while maintaining sharpness. With the limited number of experimental data, training is done using synthetic target radiography supplied by 3D magnetohydrodynamics simulations at different perturbation modes, that is supplemented with experimental Z-Target data. The sparse datasets are further enlarged through transformation routines.

¹ M. Gusarev, R. Kuleev, A. Khan, A. Ramirez Rivera and A. M. Khattak, "Deep learning models for bone suppression in chest radiographs," 2017 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB), Manchester, UK, 2017, pp. 1-7, doi: 10.1109/CIBCB.2017.8058543.

² H. Zhao, O. Gallo, I. Frosio and J. Kautz, "Loss Functions for Image Restoration With Neural Networks," in IEEE Transactions on Computational Imaging, vol. 3, no. 1, pp. 47-57, March 2017, doi: 10.1109/TCI.2016.2644865.

³ NVIDIA, Vingelmann, P., & Fitzek, F. H. P. (2020). CUDA, release: 10.2.89. Retrieved from https://developer.nvidia.com/cuda-toolkit

Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

a) Swcorda@sandia.gov

Modern experiments in inertial confinement fusion (ICF) are often susceptible to contamination of the hotspot region by high-Z material during compression that impedes thermonuclear burn. Hotspot mix can be quantified using the ion temperature distribution of the implosion given the predicted deviation between the plasma and contaminant [1], but current neutron time-of-flight (nToF) diagnostics can only measure the spatially integrated temperature. This project probes the feasibility of using time multiplexed optical fibers to record nToF spectra from segmented thin scintillators, which could be used to collect a spatially resolved temperature measurement on a single photomultiplier tube (PMT). A prototype detector was constructed in which 20 optical fibers of increasing length were coupled to an EJ-262 plastic scintillator at one end and a Photek PMT210 at the other. The detector was tested on the OMEGA laser and an nToF pulse was successfully measured through all 20 channels at the expected time separations. Design methodology, material selection, experimental results, and preliminary data analysis are discussed. Next steps will evaluate the feasibility of this technique for 2D ion temperature imaging based on previous work [2,3], as well as potential diagnostic development using the Michigan Accelerator for Inductive Z-Pinch Experiments (MAIZE), which could be useful to magnetically driven fusion experiments on the Z-machine.

The PuFF (Pulsed Fission Fusion) project aims to revolutionize space travel through nuclear propulsion. PuFF will produce both high specific impulse (Isp 5,000-10,000 sec) and high thrust (10-100 kN), enabling quick (~1 month) transit times to Mars, the outer planets and exiting the solar system (~5 years).

PuFF creates thrust by imploding a fission-fusion target using a Z-pinch. The process involves using the Lorentz (j×B) force to create gigapascal to terapascal pressures. Liquid lithium is injected in both a cylinder and cone. When the two connect, a circuit with a network of capacitors (referred to here as the pulser) is completed, and a 10-25 MA pulse flows down the lithium. The Z-pinch slams the lithium onto a fission-fusion target. The resulting compression (5-10 by volume) reaches super-criticality and explodes. The expanding plasma is then directed out of the back of the engine by a magnetic nozzle.

The current concept endeavors to fit the PuFF engine into a single Space Launch System (SLS) launch, with the expected 8-m fairing. This nacelle would contain all the propulsive elements for a mission. A second SLS or other launcher would lift the required propellant and payload for a variety of missions in deep space.

Development of the PuFF propulsion system has focused on the implosion process. Data on the actual compression of a nuclear target is not discussed here; however in addition to the vehicle design we discuss the implosion process, connecting the lithium medium to a Linear Transformer Driver (LTD) system. Also discussed is a regenerative magnetic nozzle and recharge system to enable pulse rates of about 1 Hz.

A dense plasma focus (DPF) is a co-axial plasma railgun whose discharge ends in a z-pinch phase. The MegaJOuLe Neutron Imaging Radiography (MJOLNIR) DPF is an LLNL experiment to demonstrate feasibility of flash neutron radiography using the DPF as a neutron source and a neutron camera to record an image. The MJOLNIR team is in the process of commissioning the DPF to full stored energy and current, 2 MJ/4.5 MA, with 1.3 MJ stored energy and 3.7 MA peak currents achieved as of spring 2023. A recent redesign/rebuild of the MJOLNIR DPF has enabled robust operations, supporting >450 high voltage/plasma shots on a single hardware setup over the course of 6 months. Neutron yields in excess of 1×10¹² have been achieved on the highest current shots with deuterium gas fill. Successful high current operation requires interleaving of high current shots with lower current (~2.8 MA peak) shots. Neutron spot sizes have been measured as a function of voltage, pressure, anode implosion radius, and gas dopant levels. An overview of the MJOLNIR redesign and high-current experimental results will be presented. This work was prepared by LLNL under Contract DE-AC52-07NA27344.