Researchers have demonstrated a sheared-flow Z pinch possesses enhanced m=1 kink stability characteristics compared to a static pinch [1], with some work speculating that the nature of this stability could be a kinetic effect [2,3], beyond the framework of magnetohydrodynamics (MHD). The goal of our work is to investigate specifically how the m=1 growth rate changes as the pinch properties vary from highly fluid to highly kinetic, using the ratio of a representative ion Larmor radius to pinch radius as our metric [4].

Experimental research efforts at Zap Energy advance development of sheared-flow-stabilized (SFS) Z-pinch fusion energy [Levitt et al., Phys. Plasmas 30, 9 (2023)]. This fusion energy concept requires quasi-steady sustainment of a high-pressure flowing pinch, stabilized by a radially sheared profile of axial velocity. Three research platforms, FuZE-3, FuZE-Q, and FuZE-A emphasize different aspects of the concept, facilitating continuous, parallel developments necessary to advance plasma triple product and ultimately fusion gain [Shumlak et al., Fusion Sci. Technol. 80, 1 (2024)]. Recent FuZE-Q results demonstrate extended periods of pinch stability concurrently with the presence of sheared-flow profiles in the deuteron fuel ions, as measured with collective Thomson scattering. The FuZE-3 device, commissioned in 2025, compresses flow pinches to high pressure and density states through direct magnetic flux injection into the pinch assembly region. This method provides independent control of the plasma acceleration and compression processes and has resulted in the highest plasma pressures recorded so far at Zap Energy, exceeding one gigapascal. The plasma sourcing, acceleration, and pinch assembly processes are studied in detail with the FuZE-A platform to promote control of fusion-grade pinch profiles and their sustainment. Plasmas in all three devices are characterized with a sophisticated suite of diagnostics, including Thomson scattering, Faraday polarimetry, interferometry, spectroscopy, and fusion product diagnostics. Recent advances in diagnostic techniques have resulted in novel and high-fidelity inferences of the pinch density, temperature, internal magnetic structure, current, and images of the fusion source. These developments demonstrate Zap Energy's progress in plasma performance and the development of Z-pinch fusion.

We present an experimental and simulation-based investigation of the temporal evolution of light emission from a thin, laser-ionized helium plasma source. We demonstrate an analytic model to calculate the approximate scaling of the time-integrated, on-axis light emission with the initial plasma density and temperature, supported by the experiment, which enhances the understanding of plasma light measurement for plasma wakefield accelerator (PWFA) plasma sources. Our model simulates the plasma density and temperature using a split-step Fourier code and a particle-in-cell code. A fluid simulation is then used to model the plasma and neutral density, and the electron temperature as a function of time and position. We then show the numerical results of the space-and-time-resolved light emission and that collisional excitation is the dominant source of light emission. We validate our model by measuring the light emitted by a laser-ionized plasma using a novel statistical method capable of resolving the nanosecond-scale temporal dynamics of the plasma light using a cost-effective camera with microsecond-scale timing jitter. This method is ideal for deployment in the high radiation environment of a particle accelerator that precludes the use of expensive nanosecond-gated cameras. Our results show that our models can effectively simulate the dynamics of a thin, laser-ionized plasma source. In addition, this work provides a detailed understanding of the plasma light measurement, which is one of the few diagnostic signals available for the direct measurement of PWFA plasma sources.

Zap Energy is pursuing a sheared-flow-stabilized Z-pinch as the core of a fusion reactor technology. Recent experimental efforts have demonstrated currents higher than 600 kA and electron temperatures higher than lkeV. Some of the open questions for this concept are how the neutron yield scales with current, how the power supply bank couples to the dynamic plasma load, and how the cathodes survive under repeated discharges of several hundred klloJoules, among other questions. To help answer these questions, the Zap Energy Theory and Modeling team is using the WARPXM code, a discontinuous Galerkin modeling framework developed at U. Washington. Using a two-dimensional MHD model coupled to a circuit solver, we show scaling of neutron yields as a power law with current for several different voltage configurations, and discuss the implications for cathode erosion. We also discuss coupling of WARPXM with PIC models, benchmarking of WARPXM with NIMROD, and acceleration of WARPXM with GPU.

The sheared-flow-stabilized (SFS) Z-pinch concept is on a path to commercialization at Zap Energy. Recent experiments on the Fusion Z-pinch Experiment (FuZE) and newly commissioned FuZE-Q devices are advancing the state of the art in pinch current, stable plasma duration, and deuterium–deuterium fusion neutron production. The SFS Z-pinch configuration offers the promise of a compact fusion device owing to its simple geometry, unity beta, and absence of external magnetic field coils. In addition to a robust experimental program pushing plasma performance toward breakeven conditions, Zap Energy has parallel programs developing power handling systems suitable for future power plants. Technologies under development include high-repetition-rate pulsed power, high-duty-cycle electrodes, and liquid metal wall systems. The issue of electrode durability in future SFS Z-pinch power plants is elaborated on and compared with plasma material interaction regimes in other industrial processes and fusion energy systems.

The goal of this work is to investigate the behavior of alpha particles in a Z-pinch plasma configuration. A Z pinch is one of the oldest plasma fusion configurations, but Z pinches have always suffered from a series of instabilities that limit their performance. Recently, sheared flow stabilization has resulted in significant stability gains, with some pinches lasting up to 10 us (several thousand linear instability growth times). Zap Energy is currently operating a sheared-flow-stabilized Z pinch: the Fusion Z-pinch Experiment (FuZE). However, as these devices reach higher rates of fusion, the resulting fusion by-products may play a key role in the plasma energy balance.

This manuscript presents verification cases that are developed to study the electrothermal instability (ETI). Specific verification cases are included to ensure that the unit physics components necessary to model the ETI are accurate, providing a path for fluid-based codes to effectively simulate ETI in the linear and nonlinear growth regimes. Two software frameworks with different algorithmic approaches are compared for accuracy in their ability to simulate diffusion of a magnetic field, linear growth of the ETI, and a fully nonlinear ETI evolution. The nonlinear ETI simulations show early time agreement, with some differences emerging, as noted in the wavenumber spectrum, late into the nonlinear development of ETI. A sensitivity study explores the role of equation-of-state (EOS), vacuum density, and vacuum resistivity. EOS and vacuum resistivity are found to be the most critical factors in the modeling of nonlinear ETI development.

Currently, there is a lack of publicly available design specifications for Crossed-Field Amplifiers (CFAs), which severely impedes CFA research in the public domain. The L3-Harris CFA, L-4953, was commonly used for the Air Route Surveillance Radar (ARSR-1/2) since the 1970’s. This is a high power $\left( {P_{out}^{peak} \approx 5\;{\text{MW}},P_{out}^{avg} \approx 3.2\;{\text{kW}}} \right)$ , moderate gain (G=11.2 dB), pulsed ( t pulse = 1.8 µs), L-band (f = 1.28 to 1.35 GHz), reentrant, backward wave, thermionic cathode amplifier. Our group has been developing a particle-in-cell (PIC) model of the CFA to study power saturation and the effects of electron injection. Here, VSim is used to validate the model against CFA operation specifications, such as gain, bandwidth, and dispersion. Preliminary, non-optimized simulation results show as table 9 dB gain at in only 10 ns with a relatively coarse grid of 101×101×60 cells. The short time required to reach steady state and the low number of grid cells allows for short simulation times on the order of only a few hours for common multi-core processors. This makes this CFA design an ideal standard for simulation studies. Additional simulation studies are planned using ICEPIC. We will report the results of the simulations, comparison between the two different PIC codes, assessment with operating specifications, and studies of the electron injection models.

Many emerging applications of high-power microwave sources require operation at new and higher frequencies. Computer modeling is the main tool for the design and optimization of these sources, such as magnetrons. However, when designing a new source, the parameter space to scan can be too large to study with traditional techniques. We apply machine learning (ML) (supervised learning in particular) to search this parameter space automatically. We demonstrate this technique by optimizing the operation of a magnetron at 4 GHz, investigating selected parameters tradeoff and predicting operation space characteristics for the discovered device based on a limited amount of measurements. The combination of ML and optimization techniques that we demonstrate here has wide applicability for virtual prototyping and design of problems with sophisticated computer models and allows us to fundamentally reimagine the role of the human in the design workflow.

Many high power electronic devices operate in a regime where the current they draw is limited by the self-fields of the particles. This space charge limited current poses particular challenges for numerical modeling where common techniques like over-emission or Gauss' Law are computationally inefficient or produce nonphysical effects. In this paper, we show an algorithm using the value of the electric field in front of the surface instead of attempting to zero the field at the surface, making the algorithm particularly well suited to both electromagnetic and parallel implementations of the particle-in-cell algorithm. We show how the algorithm is self-consistent within the framework of finite difference (for both electrostatics and electromagnetics). We show several 1D and 2D benchmarks against both theory and previous computational results. Finally, we show the application in 3D to high power microwave generation in a 13GHz magnetically insulated line oscillator.

In particle-in-cell simulation, generating a space-charge limited electron source presents challenges due to the steep gradients in electron density and electric field infinitesimally close to such an emitting surface. Simulating accurate emission current densities is essential for modeling complex microwave device geometries such as that of the magnetron. These simulations are complicated by the device geometry, which is resolved using cut-cells on a Cartesian grid. We will discuss modeling strategies for space-charge limited emission on planar cut-cell boundaries, and present convergence studies to evaluate their accuracy in both simple and complex geometries. As applications, we show simulation of explosive emission in a magnetron and magnetically insulated line oscillator (MILO). For the MILO, we show that this new emission algorithm results in the appearance of harmonics of the main frequency in the absorbed current.

Charged particle acceleration has been investigated in a dense plasma focus (DPF) driven by the Hawk pulsed-power generator at the Naval Research Laboratory. Neutron yields of over $5.0\times 10^{10}$ have been measured at a peak current of $\mathrm{I}=670\text{kA}$ ) significantly above the yield expected at this current based on purely I 4.4 scaling from conventional DPFs. The high inductance (607 nH) and associated high voltage (640 kV) and fast rise time $(1.2 \mu \mathrm{s})$ of Hawk are unusual for a DPF driver, as is the initialization of the DPF using local injection of neutral gas and plasma into a vacuum chamber, rather than a conventional neutral gas fill. This method of initialization allows for the selection of an extensive array of initial conditions. A subset of those initial conditions has been explored in conjunction with multi-dimensional MHD simulations to affect the energy of the accelerated ions, as measured by an ion multi-pinhole camera, the neutron yield, as measured by rhodium-foil activation counters, and the end point energy of the emitted neutrons, as measured by neutron time-of-flight detectors.

Novel plasma devices, including capillary discharge plasmas and laser-ionized plasma columns, show promise for application across a range of essential beamline components, including acceleration stages, focusing, energy compensators, and non-destructive beam diagnostics. These systems could enable fundamental advances in high quality electron and positron beams and support TeV-class high luminosity lepton collider concepts. However, modeling these systems with high fidelity requires integrated multi-physics capabilities at computational scales which exceed those of traditional electromagnetic simulation tools. This letter outlines the prospective applications and corresponding modeling efforts currently being undertaken in the community, alongside promising approaches to capturing the essential dynamics of these systems, such as hydrodynamic, magnetohydrodynamic, and Vlasov models. These tools are complementary to existing simulation codes, and address the intermediary dynamics required for integrated, end-to-end accelerator modeling suites. ∗ncook@radiasoft.net

Recent results 1 indicate that electrothermal effects (including electrothermal instabilities, ETI) could be a main source of unwanted perturbations in metal liners planned as drivers for magneto-inertial fusion concepts like MagLIF 2 . Traditionally, one simulates these types of systems with a magneto-hydrodynamics (MHD) approach. However, in order to include electrothermal effects in simulation, one needs a code with several advanced features: the code needs to include non-ideal MHD effects, like resistivity, and the code needs to handle realistic equations of state and resistivities, typically through tables. Additionally, for research at universities, the code ideally should be openly available to all researchers. We discuss the USim code and our application of it to ETI studies. In particular, we compare linear growth rates of ETI for realistic liner conditions in 2D (aluminum liner, $\text{rho}=2.7 \mathrm{g}/\text{cc}, \mathrm{I}=10$ MA) with tabular EOS and resistivities. We also show comparison with other well-established non-ideal MHD codes for evolution of ETI into the non-linear regime in 2D. Finally, we show initial 3D results of the non-linear regime.