High-yield inertial fusion offers a transformative path to affordable, clean, firm power and advanced defense capabilities. Recent milestones at large facilities, particularly the National Ignition Facility (NIF), have demonstrated the feasibility of ignition but highlight the need for approaches that can deliver large amounts of energy to fusion targets at much higher efficiency and lower cost. We propose that pulser-driven inertial fusion energy (IFE), which uses high-current pulsed-power technology to compress targets to thermonuclear conditions, can achieve this goal. In this paper, we detail the physics basis for pulser IFE, focusing on magnetized liner inertial fusion, where cylindrical metal liners compress DT fuel under strong magnetic fields and preheat. We discuss how the low implosion velocities, direct-drive efficiency, and scalable pulser architecture can achieve ignition-level conditions at low capital cost. Our multi-dimensional simulations, benchmarked against experiments at the Z facility, show that scaling from 20 to 50-60 MA of current enables net facility gain. We then introduce our Demonstration System (DS), a pulsed-power driver designed to deliver more than 60 MA and store approximately 80 MJ of energy. The DS is designed to achieve a 1000x increase in effective performance compared to the NIF, delivering approximately 100x greater facility-level energy gain-and importantly, achieving net facility gain, or Q(f)>1-at just 1/10 the capital cost. We also examine the engineering requirements for repetitive operation, target fabrication, and chamber maintenance, highlighting a practical roadmap to commercial power plants. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

FLASH is a widely available radiation magnetohydrodynamics code used for astrophysics, laboratory plasma science, high energy density physics, and inertial confinement fusion. Increasing interest in magnetically driven inertial confinement fusion (ICF), including Pacific Fusion's development of a 60 MA Demonstration System designed to achieve facility gain, motivates the improvement and validation of FLASH for modeling magnetically driven ICF concepts, such as MagLIF, at ignition scale. Here we present a collection of six validation benchmarks from experiments at the Z Pulsed Power Facility and theoretical and simulation studies of scaling MagLIF to high currents. The benchmarks range in complexity from focused experiments of linear hydrodynamic instabilities to fully integrated MagLIF fusion experiments. With the latest addition of physics capabilities, FLASH now obtains good agreement with the experimental data, theoretical results, and leading ICF target design simulation code results across all six benchmarks. These results establish confidence in FLASH as a useful tool for designing magnetically driven ICF targets on facilities like Z and Pacific Fusion's upcoming Demonstration System.

Magnetized liner inertial fusion (MagLIF) experiments have demonstrated fusion-relevant ion temperatures up to 3.1 keV and thermonuclear production of up to 1.1 × 1013 deuterium–deuterium neutrons. This performance was enabled through platform development that provided increases in applied magnetic field, coupled preheat energy, and drive current. Advanced coil designs with internal reinforcement enabled an increase from 10 to 20 T. An improved laser pulse shape, beam smoothing, and thinner laser entrance foils increased preheat energy coupling from less than 1 to 2.3 kJ. A redesign of the final transmission line and load region increased peak load current from 16 to 20 MA. The wider range of input parameters was leveraged to study target performance trends with preheat energy, applied magnetic field, and peak load current. Ion temperature and neutron yield generally followed trends in two-dimensional clean Lasnex calculations. Stagnation performance improved with peak load current when other input parameters were also increased such that convergence was maintained. This dataset suggests that reducing convergence to less than 30 would improve predictability of target performance. Lasnex was used to identify a simulation-optimized scaling path, which suggests 10+ kJ of fusion yield is possible on the Z facility with achievable input parameters. This path also indicates >10 MJ could be generated through volume burn on a future facility with a path to high yield (>200 MJ) using cryogenic dense fuel layers. The newly developed MagLIF platform enables exploration of both this simulation optimized scaling path and a recently developed similarity-scaling path.

We report the results of the second charged-particle transport coefficient code comparison workshop, which was held in Livermore, California on 24–27 July 2023. This workshop gathered theoretical, computational, and experimental scientists to assess the state of computational and experimental techniques for understanding charged-particle transport coefficients relevant to high-energy-density plasma science. Data for electronic and ionic transport coefficients, namely, the direct current electrical conductivity, electron thermal conductivity, ion shear viscosity, and ion thermal conductivity were computed and compared for multiple plasma conditions. Additional comparisons were carried out for electron–ion properties such as the electron–ion equilibration time and alpha particle stopping power. Overall, 39 participants submitted calculated results from 18 independent approaches, spanning methods from parameterized semi-empirical models to time-dependent density functional theory. In the cases studied here, we find significant differences—several orders of magnitude—between approaches, particularly at lower temperatures, and smaller differences—roughly a factor of five—among first-principles models. We investigate the origins of these differences through comparisons of underlying predictions of ionic and electronic structure. The results of this workshop help to identify plasma conditions where computationally inexpensive approaches are accurate, where computationally expensive models are required, and where experimental measurements will have high impact.

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result.

Fusion is a potentially transformational energy technology, which promises limitless clean energy. Yet, it requires continued scientific and technological development to realize its potential. The conditions necessary for fusion energy gain in terms of the product of plasma pressure P and confinement time τ have been known for many decades. An underappreciated fact is that pulsed magnetic fusion has demonstrated P τ performance on par with laser-driven ICF and tokamaks despite receiving only a small fraction of investment relative to those concepts. In light of this demonstrated performance, well-established scaling relations, and opportunities for further innovations, here we advocate for pulsed magnetic fusion as the most attractive path towards commercialization of fusion energy.

X-ray imaging indicates magnetized liner inertial fusion (MagLIF) stagnation columns have a complicated quasi-helical structure with significant variations in x-ray brightness along the column. In this work, we describe MagLIF experiments aimed at controlling these stagnation structures by varying the initial liner geometry and composition. First, by varying the initial aspect ratio of the liner, we demonstrate a change in the stagnation structures that is consistent with helical magneto Rayleigh–Taylor (MRT) instabilities feedthrough from the outer-to-inner surfaces of the liner. Second, to minimize the seed for such instabilities, we incorporate a dielectric coating on the outer surface of the beryllium liner, which has previously been shown to reduce the growth of the electrothermal instability, a likely seed for MRT growth. Using this coating, we achieve a stagnation column with significantly reduced helical structure and axial variation in x-ray brightness. We discuss how this coating changes the evolution of structures through stagnation along with the spatial uniformity of neutron production. Finally, we show that these more uniform stagnations also result in improved reproducibility in stagnation temperatures and primary DD neutron yield.

In magnetized liner inertial fusion (MagLIF), a cylindrical liner filled with fusion fuel is imploded with the goal of producing a one-dimensional plasma column at thermonuclear conditions. However, structures attributed to three-dimensional effects are observed in self-emission x-ray images. Despite this, the impact of many experimental inputs on the column morphology has not been characterized. We demonstrate the use of a linear regression analysis to explore correlations between morphology and a wide variety of experimental inputs across 57 MagLIF experiments. Results indicate the possibility of several unexplored effects. For example, we demonstrate that increasing the initial magnetic field correlates with improved stability. Although intuitively expected, this has never been quantitatively assessed in integrated MagLIF experiments. We also demonstrate that azimuthal drive asymmetries resulting from the geometry of the “current return can” appear to measurably impact the morphology. In conjunction with several counterintuitive null results, we expect the observed correlations will encourage further experimental, theoretical, and simulation-based studies. Finally, we note that the method used in this work is general and may be applied to explore not only correlations between input conditions and morphology but also with other experimentally measured quantities.

We report on a series of Magnetized Liner Inertial Fusion (MagLIF) experiments conducted on the Z pulsed power facility that utilized high aspect ratio (ratio of outer radius to wall thickness) liners with dielectric coatings and low-mix laser preheat configurations. The liners consisted of an aspect ratio of 10.6 beryllium tube coated with 75 μm of epoxy on the outside that have been shown to maintain a better implosion stability than uncoated beryllium and have demonstrated consistent stagnation performances in previous experiments [Ampleford et al., Phys. Plasmas 31, 022703 (2024)]. Two-dimensional HYDRA simulations were used to design three different “co-injection” laser configurations, whereby a second laser is used to provide an early prepulse before the main pulse, to reduce LEH foil mix while increasing the fuel density and coupled energy. The laser preheat energy for each configuration was constrained using dedicated laser experiments before being applied to the integrated MagLIF experiments on Z. The DD neutron yield for experiments using co-injection preheat configurations is found to increase with the specific preheat energy in line with simulations. The highest neutron yield achieved in this study of 1.1 × 1013 matches the highest reported in a MagLIF experiment to date and is a factor 3.5 times higher than similar experiments using preheat with no phase plate smoothing. We attempt to assess the effects of mix and morphology to explain the improved performance; however, neither factor is found to be conclusive within the uncertainty of the measurements.

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

Gravitational confinement is clearly very effective but what can we do on Earth? Magnetic confinement has been studied since around 1950. Inertial confinement has been associated with lasers for over 50 years. We have made steady progress in both MCF and ICF over the last half-century.

A variety of spherical crystal x-ray imager (SCXI) diagnostics have been developed and fielded on Magnetized Liner Inertial Fusion (MagLIF) experiments at the Sandia National Laboratories Z-facility. These different imaging modalities provide detailed insight into different physical phenomena such as mix of liner material into the hot fuel, cold liner emission, or reduce impact of liner opacity. However, several practical considerations ranging from the lack of a consistent spatial fiducial for registration to different point-spread-functions and tuning crystals or using filters to highlight specific spectral regions make it difficult to develop broadly applicable metrics to compare experiments across our stagnation image database without making significant unverified assumptions. We leverage experimental data for a model-free assessment of sensitivities to instrumentation-based features for any specified image metric. In particular, we utilize a database of historical and recent MagLIF data including $N_{\text{scans}} = 139$ image plate scans gathered across $N_{\text{exp}} = 67$ different experiments to assess the impact of a variety of features in the experimental observations arising from uncertainties in registration as well as discrepancies in signal-to-noise ratio and instrument resolution. We choose a wavelet-based image metric known as the Mallat Scattering Transform for the study and highlight how alternate metric choices could also be studied. In particular, we demonstrate a capability to understand and mitigate the impact of signal-to-noise, image registration, and resolution difference between images. This is achieved by utilizing multiple scans of the same image plate, sampling random translations and rotations, and applying instrument specific point-spread-functions found by ray tracing to high-resolution datasets, augmenting our data in an effectively model-free fashion.

Pulsed power generators create high-energy-density conditions by rapidly delivering an immense pulse of electrical current to a compact imploding load. Accurately measuring the shape and amplitude of this load current pulse is essential to understanding the behavior of all pulsed power experiments. At the Z Pulsed Power Facility, the closest-in load current measurements are provided by velocimetry techniques such as VISAR (velocity interferometer system for any reflector) and PDV (photonic Doppler velocimetry). Here, fiber-coupled interferometers measure the velocity history of an exploding metallic flyer plate that is embedded in the vertical walls of the current return can. The flyer plate is driven outward by the magnetic pressure from the load current such that magnetohydrodynamic modeling can be used to determine the load current waveform from the measured velocity history. In this paper, we present the first load current velocimetry measurements to be made from the horizontal top flyer plate that carries current radially inward from the return can to the load. These spatially resolved measurements, which span R = 5- 9 mm, are enabled by a transformative new velocimetry diagnostic-a line-imaging velocity interferometer called Z Line VISAR (ZLV)-whose optical performance overcomes the measurement challenges presented by the steep velocity gradients encountered on the top flyer plate. To validate ZLV's capabilities, a 14-MA, 100-ns experiment was conducted to losslessly couple current up the return can and radially inward across the top flyer plate. Comparisons between the ZLV data obtained from this experiment and two-dimensional magnetohydrodynamic simulations driven with the current measured on the return can indicate that the current delivery across the top flyer plate is indeed lossless to within the few-percent uncertainty of the ZLV data. Given that the current coupling is lossless, the experimental results are used to demonstrate that one-dimensional current unfold techniques can be applied to generate a radially resolved load current map from the ZLV velocity data. This analysis provides a template for how to use the ZLV diagnostic to determine the efficacy of current delivery in future experiments where losses may occur in close proximity to the load.

We present a general method for optimizing the configuration of an experimental diagnostic to minimize uncertainty and bias in inferred quantities from experimental data. The method relies on Bayesian inference to sample the posterior using a physical model of the experiment and instrument. The mean squared error (MSE) of posterior samples relative to true values obtained from a high fidelity model (HFM) across multiple configurations is used as the optimization metric. The method is demonstrated on a common problem in dense plasma research, the use of radiation detectors to estimate physical properties of the plasma. We optimize a set of filtered photoconducting diamond detectors to minimize the MSE in the inferred X-ray spectrum, from which we can derive quantities like the electron temperature. In the optimization we self-consistently account for uncertainties in the instrument response with appropriate prior probabilities. We also develop a penalty term, acting as a soft constraint on the optimization, to produce results that avoid negative instrumental effects. We show results of the optimization and compare with two other reference instrument configurations to demonstrate the improvement. The MSE with respect to the total inferred X-ray spectrum is reduced by more than an order of magnitude using our optimized configuration compared with the two reference cases. We also extract multiple other quantities from the inference and compare with the HFM, showing an overall improvement in multiple inferred quantities like the electron temperature, the peak in the X-ray spectrum and the total radiated energy.

An x-ray imaging scheme using spherically bent crystals was implemented on the Z-machine to image x rays emitted by the hot, dense plasma generated by a Magnetized Liner Inertial Fusion (MagLIF) target. This diagnostic relies on a spherically bent crystal to capture x-ray emission over a narrow spectral range (<15 eV), which is established by a limiting aperture placed on the Rowland circle. The spherical crystal optic provides the necessary high-throughput and large field-of-view required to produce a bright image over the entire, one-cm length of the emitting column of a plasma. The average spatial resolution was measured and determined to be 18 µm for the highest resolution configuration. With this resolution, the radial size of the stagnation column can be accurately determined and radial structures, such as bifurcations in the column, are clearly resolved. The success of the spherical-crystal imager has motivated the implementation of a new, two-crystal configuration for identifying sources of spectral line emission using a differential imaging technique.

Accurate understanding of x-ray diagnostics is crucial for both interpreting high-energy-density experiments and testing simulations through quantitative comparisons. X-ray diagnostic models are complex. Past treatments of individual x-ray diagnostics on a case-by-case basis have hindered universal diagnostic understanding. Here, we derive a general formula for modeling the absolute response of non-focusing x-ray diagnostics, such as x-ray imagers, one-dimensional space-resolved spectrometers, and x-ray power diagnostics. The present model is useful for both data modeling and data processing. It naturally accounts for the x-ray crystal broadening. The new model verifies that standard approaches for a crystal response can be good approximations, but they can underestimate the total reflectivity and overestimate spectral resolving power by more than a factor of 2 in some cases near reflectivity edge features. We also find that a frequently used, simplified-crystal-response approximation for processing spectral data can introduce an absolute error of more than an order of magnitude and the relative spectral radiance error of a factor of 3. The present model is derived with straightforward geometric arguments. It is more general and is recommended for developing a unified picture and providing consistent treatment over multiple x-ray diagnostics. Such consistency is crucial for reliable multi-objective data analyses.

In magneto-inertial fusion, the ratio of the characteristic fuel length perpendicular to the applied magnetic field R to the α-particle Larmor radius ϱα is a critical parameter setting the scale of electron thermal-conduction loss and charged burn-product confinement. Using a previously developed deep-learning-based Bayesian inference tool, we obtain the magnetic-field fuel-radius product BR∝R/ϱα from an ensemble of 16 magnetized liner inertial fusion (MagLIF) experiments. Observations of the trends in BR are consistent with relative trade-offs between compression and flux loss as well as the impact of mix from 1D resistive radiation magneto-hydrodynamics simulations in all but two experiments, for which 3D effects are hypothesized to play a significant role. Finally, we explain the relationship between BR and the generalized Lawson parameter χ. Our results indicate the ability to improve performance in MagLIF through careful tuning of experimental inputs, while also highlighting key risks from mix and 3D effects that must be mitigated in scaling MagLIF to higher currents with a next-generation driver.