Zap Energy is a private fusion energy company developing the sheared-flow-stabilized (SFS) Z-pinch concept for commercial energy production. Spun out from the University of Washington, these experimental and computational efforts have resulted in devices with quasi-steady DD fusion yields above 109 per pulse. These devices support scaling toward energy breakeven on existing devices as well as beyond to commercially relevant engineering fusion gains. This article discusses the strategy behind Zap's development path, which is derived directly from the engineering and scientific elegance of the confinement method. Without need for external confinement or heating technologies, the SFS Z pinch relies on plasma self-organization. This compact magnetic confinement technology could, in turn, provide the basis for a cost-effective fusion power plant, vastly reduced in complexity from its competitors.
In the broad landscape of fusion confinement technologies,1 the Z pinch occupies special territory. Along with a very limited number of nearest neighbors (notably the field-reversed configuration and spheromak), the Z pinch is best characterized as self-organized, in the sense that plasma dynamics play a critical role in confinement. Axial current and resulting azimuthal magnetic field establish a simple radial force balance equilibrium that has been understood for nearly a century.2 In addition to the confinement, the plasma heating required to attain fusion-relevant plasma parameters is also provided by the plasma dynamics, primarily in the form of adiabatic compression. Thus, if one can address the notoriously difficult issue of stability for the Z pinch, what remains is arguably a more manageable combination of physics risks and engineering requirements relative to other confinement schemes.
Zap Energy is a fusion energy startup company developing a Z-pinch confinement concept for commercialization. As alluded to above, the limitation on Z-pinch performance has been plasma stability. Zap's particular approach utilizes plasma flow as a stabilization mechanism,3 allowing the generation of high-performance plasmas characterized by triple products similar to larger and more complex magnetic and inertial confinement fusion (MCF and ICF, respectively) devices.4
A critical fusion parameter that is often overlooked by plasma physicists who are naturally focused on plasma performance is future power plant capital cost. Bigger is better has been a dominant theme in fusion science until very recently, and for good reason—in toroidal fusion devices, fusion power scales with plasma volume, while losses scale with surface area. This trend toward large size can be somewhat mitigated for some MCF devices by the introduction of high-temperature superconducting (HTS) materials.5 However, the benefits of HTS may be offset by additional associated costs, risks, and lower technology readiness.
The engineering simplicity and low capital cost availed by a stabilized Z pinch is the central pillar of Zap's strategy. As confinement and heating are natural outcomes of the stable Z-pinch self-organization, the best features of the technology are the components that become unnecessary. Complex and costly systems found in common magnetic and inertial confinement schemes are absent. Not only are high-field magnets not required, but no external magnetic fields of any kind are needed. Equally, capital-intensive heating technologies, such as high-powered lasers (for ICF) and neutral beam injection and microwave heating (both for MCF), are avoided. Such simplifications lead not only to the obvious capital cost reductions, but also to operational efficiencies, higher technology readiness, rapid development iteration cycles, power plant footprint reductions, and, critically, to wall-plug efficiencies that will be manifested in favorable engineering gain (Qeng) and eventual cost of electricity.
The Zap Energy approach, characterized by the reliance on plasma self-organization and relaxation of technology requirements, results in a direct trade-off between taking on greater physics risk for the sake of a simpler, cheaper, more reliable, faster-to-market product.
Another critical parameter for fusion, commonly used to evaluate fusion performance in a plasma, is the triple product, , where n is the plasma density, T is the plasma temperature, and τE is the plasma energy confinement time.4 An interesting aspect of the parameter space occupied by Zap devices is that, unlike their extreme position on the self-organization axis, they occupy a relatively vacant middle ground between MCF and ICF machines. Steady-state MCF confinement aims to achieve elevated triple products with low n and high τE, 1020 m−3 and 1 s, respectively; ICF, on the other hand, relies on much higher n but for extremely short pulses: 1031 m−3 and 0.1 ns, respectively.6 The moderate middle ground for each of the parameters, however, is not only accessible but may be preferable, as it relaxes technology requirements on the associated mechanisms needed to get to extrema. As noted by Lindemuth and Siemon,7 “fusion might be possible at low cost by accessing the broad intermediate density range.” The expected approximate parameters for plant-relevant sheared-flow-stabilized (SFS) Z-pinch performance are n, T, and τE of 1026 m−3, 15 keV, and 10 μs, respectively. Particularly, in terms of density and confinement time, these are almost exactly halfway (logarithmically) between MCF and ICF parameters. One can think of this intermediate regime as a quasi-steady-state magneto-inertial confinement.
Here, quasi-steady-state implies that Zap Z-pinch devices are pulsed, but deploy relatively moderate pulsed-power current drivers compared with well known fast Z-pinch machines. Here, moderate means specifically slower rise time (10 μs), extended in duration (100 μs) and lower peak current (1 MA), which also come at a comparatively lower cost. To leverage this type of operation into an economic plant requires pulsed operation on the order of 10 Hz. While this Perspective focuses on development of high-performance Z-pinch plasmas in the single-shot context, Zap Energy also has a comprehensive system engineering effort under way to develop suitable repetitive pulsed power systems.8
In the remainder of the Introduction, we briefly review the private fusion industry landscape (Sec. I A) and the climate change context (Sec. I B) and discuss historical Z-pinch development leading to the establishment of Zap Energy (Sec. I C). Section II describes the core Zap technology, including sheared-flow-stabilization (SFS) and an outline of the associated fusion system concept. Section III is an overview of recent experimental and computational results supporting the scaling of these devices to commercial relevance. The path forward and research plans are discussed in Sec. IV. Finally, conclusions are drawn in Sec. V.
A. Status of the private fusion industry
While a handful of fusion companies have existed for a decade or more, the pace at which new startups are being formed has accelerated significantly since 2017.9 In the Fusion Industry Association10 alone, there are three dozen member companies pursuing the commercialization of fusion energy with very little overlap in their respective core technologies. As the number of private companies has grown, so also has the amount of private funding invested in fusion. As of mid-2022, publicly disclosed private funding for fusion development exceeded US$4.8B,9 and in the U.S., private funding support is starting to exceed the amount provided by the government.11 In strongly capitalized fusion startup companies, such as Zap Energy (>US$200M), many hundreds of people around the world now pursue fusion energy from within a private company. If one also counts ongoing large capital projects preparing new facilities and sites, that number tops well over a thousand jobs. Those numbers are just in direct support of the fusion companies. Outside of the companies pursuing fusion, there is also an ecosystem of affiliates rapidly growing such as suppliers of key components, materials, and services, information and advocacy groups, and energy/utility partners. Beyond the work advancing fusion energy science in national laboratories and universities, fusion is entering the mainstream and beginning to attract the diverse set of expertise and stakeholders that will be necessary for it to penetrate the commercial market.
Given the climate change context (discussed below), the rise of this industry is propelled by the need for an alternative to the field's largest fusion devices and their ever-increasing size and cost. The scientific accomplishments of such efforts—whether recent, e.g., NIF,12 or future, e.g., ITER13—are laudable, but these devices are likely to play only a limited role in actually commercializing fusion energy.
Even within the private fusion industry itself, we suggest that well founded concerns about size and cost have still not been adequately digested. Many private efforts are based on compelling science, but extremely complex and capital-intensive technologies. Fusion is an attractive energy source for many reasons (safety, sustainability, and power density), but electricity is a commodity for which ultimate success in the market is driven by cost considerations. While it is too soon to reliably forecast the market share that will be captured by fusion, we believe it is reasonable to conclude that eventually nothing will displace fusion from the market except cheaper fusion. To realize this vision, fusion will need to be scalable and highly deployable while offering compelling economics. This is the raison d'etre of Zap Energy.
B. Climate change context
The looming threat of anthropogenic climate change14 has motivated a global push to decarbonize the global energy economy. Renewable wind and solar energy, in spite of many years of increased installations and falling capital costs, do not by themselves form a complete solution to decarbonizing the electricity sector. Without a carbon-free source of on-demand electricity, full decarbonization is projected to increase electricity costs by up to 3× or more.15 In a study of over 1000 scenarios that address a variety of cases for carbon emissions limits, technology uncertainty, and geographic differences in renewable energy, Sepulveda et al.16 found that “firm low-carbon resources consistently lower decarbonized electricity system costs” and that “batteries and demand flexibility do not substitute for low-carbon resources.” The somewhat surprising takeaway is that, after a certain point, further increases in market capture by wind and solar dramatically amplify the value of on-demand resources such as fusion. While both fission and fusion can provide on-demand, carbon-free power, fusion holds promise for scaling more rapidly due to inherent differences in the associated hazards and risks. These differences are acknowledged by the U.S. Nuclear Regulatory Commission in their decision to pursue a risk-appropriate framework for licensing fusion plants that is outside the structure used for fission power plants.17 Fusion power has unique potential to be transformative in the sense that it can complete the transition from carbon by providing on-demand power at low cost with a modest environmental footprint.18
The private fusion energy sector is animated by the goal of providing a crucial contribution to averting the worst of climate change and shaping an environmentally friendly future for a flourishing human species. Whether fusion can form a sufficient part of the global energy mix quickly enough to mitigate the worst impacts of climate change in the short- to medium-term remains to be seen—speed is of the essence. The societal benefit of fusion is tantalizing and, combined the economic opportunity outlined above, has resonated with many investors that have been making growing financial commitments to fusion energy.
C. Historical context of SFS Z-pinch development
When humanity first recognized the energy contained in atomic nuclei, concerns about climate change had not yet emerged, and fossil fuels were available with no end in sight. During and after the Manhattan Project, speculation nevertheless began as to whether the enormous potential of fusion energy could be harnessed, and fusion science was born alongside commercial atomic energy.
The Z pinch was an early frontrunner among the possible configurations for MCF due to its conceptual simplicity.19–21 Experimental research with toroidal pinches began in the late 1940s,22 and problematic kink and sausage instabilities were immediately observed. Fast linear (“Z”) pinch programs, e.g., Columbus II at Los Alamos,23 were launched in the 1950s, aiming to rapidly heat plasma to thermonuclear conditions before such instabilities could disrupt the plasma. Flowing Z-pinch research began around the same time at Los Alamos with experiments based on the coaxial Marshall gun, which produced stable, long-lived Z pinches at up to 400 kA total current.24,25
Following the report and confirmation in 1969 of electron temperatures near 1 keV in the T-3 tokamak at the Kurchatov Laboratory,26,27 research in the USA and elsewhere was rapidly refocused on the tokamak. The flurry of activity related to flowing Z pinches was lost in the enthusiasm to pursue the tokamak. With the prospect of a successful fusion demonstration just around the corner, there was no perceived need to pursue a variety of confinement schemes. Over the coming decades, that viewpoint was proven shortsighted, as the tokamak research program encountered major unexpected difficulties ranging from plasma turbulence to runaway electrons, not to mention the need for superconducting magnets in a damaging neutron-saturated environment.28 Although some version of an advanced tokamak may yet be commercially feasible, the path to viability remains uncertain today. Minimally, it has become clear that the timelines for such developments were dramatically underestimated, eventually warranting a second look at alternatives. The flowing Z pinch was considered in the ensuing years in the USA and USSR,29,30 and the research basis of Zap Energy was established at the University of Washington starting in the late 1990s as discussed in Sec. II.
Fast Z pinches and dense plasma focus (DPF), which are plasma concepts closely related to the flowing Z pinch, are reviewed elsewhere.31,32 These approaches have interesting applications as neutron and x-ray sources, but do not have a clear path to commercially viable fusion energy production, primarily due to the unfavorable scaling of beam-target neutron production.33
Various methods have indeed proven effective in stabilizing Z-pinch equilibria. The m = 0 “sausage” instability can be tamed by simply limiting the pressure gradient below the stability threshold.34 Of course, this places limits on plasma performance and does not address the m = 1 “kink” instability. Introduction of an axial magnetic field35,36 is effective in stabilizing both m = 0 and m = 1, at the cost of adding engineering complexity (external magnets) as well as limiting achievable plasma beta. Finally, installing a close-fitting conducting boundary37 supports enhanced stability at the cost of greater plasma–material interaction. The commonality in each of these methodologies is that they pose severe constraints or challenges on either fusion plant design or plasma performance itself.
In this Perspective, we limit our attention to the sheared-flow-stabilized (SFS) Z pinch, which is the development focus of Zap Energy since it does not suffer any of the limitations discussed above.
II. ZAP ENERGY SFS Z-PINCH TECHNOLOGY
The SFS Z pinch has garnered less attention and study over the past 70 years than the more mainstream approaches. For example, the tokamak has undergone many decades of study. Dozens of major tokamak experiments across the world have mapped out high-performance operational spaces and identified engineering design points. In contrast, Zap Energy and our collaborators at the University of Washington have operated the only major research efforts on the SFS Z-pinch approach. As such, Zap Energy has a continuing focus on concept development, working to map out, and identify and optimize the operational parameter space for SFS Z pinches on an accelerated timeline. This section summarizes the concept and describes the related devices, from ZaP and ZaP-HD at the University of Washington, through the Zap Energy successors, fusion Z-pinch experiment (FuZE) and FuZE-Q.
Rather than applying an axial magnetic field “backbone,”35,36 the SFS Z pinch uses flow shear for stability, allowing a path to fusion-grade plasma confinement without the use of external magnets. The radial Z-pinch magnetohydrodynamic (MHD) equilibrium is unaffected by a purely axial flow with radial variation; in the steady ideal MHD momentum equation, with , the balance is reduced to the familiar . A sufficient radial shear in the axial flow can mitigate m = 0 and m = 1 instabilities, which plague static Z pinches.38–40 Since the azimuthal magnetic field rises rapidly away from the Z-pinch axis, viscous damping effects are small near the pinch radius such that the characteristic viscous damping length exceeds the pinch length.40 Under the assumptions of adiabatic scaling outlined in Sec. III C, as the SFS Z-pinch current increases, the pinch radius decreases, which extrapolates to a very compact fusion core design. These attributes make the SFS Z-pinch a compelling configuration for commercially competitive fusion energy. Adiabatic compressional heating results in the scaling of the relevant plasma parameters with pinch current, indicating that the triple product, , scales strongly with pinch current, for a fixed τE.41 Refer to Sec. III for a detailed discussion.
A. Overview of a SFS Z-pinch discharge
A schematic diagram of a standard SFS Z-pinch discharge is given in Fig. 1. Fuel gas is introduced into the coaxial acceleration region, and a capacitor bank is triggered to apply voltage between the inner and outer electrodes, thereby ionizing the gas and forming an annular plasma current sheet (a). The magnetic pressure upstream of the plasma accelerates the annular current sheet to the right, and dependence of the magnetic pressure exerts a stronger force near the inner electrode, stretching the current sheet (b). The plasma near the inner electrode assembles on axis in the assembly region (c), forming a Z pinch with embedded sheared flow (d). Neutral gas still in the upstream end of the acceleration region (e) is continually ionized, providing a “deflagration” plasma supply42–46 and sustaining the sheared flow.
The details of how to generate these discharges in practice and a description of the experimental devices are discussed in Sec. II B.
B. SFS Z-pinch devices
Recent advancement of SFS Z-pinch physics began at the University of Washington, from which Zap Energy was spun out in 2017. A brief description of the four devices that span the past 25 years of development follows:
The original ZaP experiment,47, Fig. 2(a), was designed in 1998 at UW, modeled after a “Marshall plasma gun” experiment conducted at LANL by Newton et al. in the 1960s, where long-lived plasma columns were observed.25 ZaP had an acceleration region geometry similar to the Newton experiment, but with the addition of a nosecone, an extended outer electrode (the “assembly region”), and an end wall.
ZaP was successfully operated from 1998 to 2010 and studied the physics of the SFS Z pinch under a variety of conditions: pinch “quiescent” periods thousands of times longer than MHD instability growth times ( – s);38 pinch lengths of 0.5, 1.0, and 1.26 m;40 stable pinches with 80% of the outer electrode wall removed from a 0.34 m long section;48 stability strongly correlated with the presence of sheared flows and current flow in the acceleration region;39 experiments with a larger inner electrode;49 and experimental scaling of quiescent period length with gas-fueling plenum pressure.39
ZaP was succeeded by the ZaP-HD (“High Density”) experiment, Fig. 2(b), where a third “middle” electrode was included between the inner and outer electrodes. The goal was to allow separate optimization of the acceleration region formation processes from the pinch compression processes, the so-called three-electrode configuration. This method introduces some machine and operational complexity, which were studied and developed on this device. After optimizing these operational issues, ZaP-HD performed well, producing ion temperatures up to 800 eV and pinch currents up to 150 kA.40 The device is still operating at UW, with a strong focus on the study of plasma material interactions.
The fusion Z-pinch experiment (FuZE),50 Fig. 2(c), was initially designed in 2014–2015, before ZaP-HD three-electrode designs were completed; thus, the decision was made to design FuZE as a two-electrode SFS Z-pinch, with the possibility of studying the addition of a third electrode. FuZE studies concentrated on neutron production, measurement, and analyses at up to 400 kA pinch currents. The FuZE power banks support Z pinch lifetimes of several μs.
Following the incorporation of Zap Energy, the FuZE device was moved from UW to a Zap Energy facility in 2021, pushing operation up to 500 kA pinch currents and pursuing further advancements in plasma operation: Both ion and electron temperatures in the 1–3 keV range were recently measured, consistent with thermal equilibrium;51 the thermonuclear nature of the neutron generation was confirmed,52 with axial extent of 0.33 m;53 and D–D neutron yields of have been observed, limited by the FuZE bank stored energy.
FuZE-Q is the latest SFS Z-pinch device and was designed and built fully by Zap Energy engineers and scientists. The device, Fig. 2(d), is nearly identical in scale to its predecessors, but is both two- and three-electrode compatible. A maximally modular design allows for both of these operational configurations, as well as the ability to modify internal electrode components with ease. The device also allows more advanced gas injection configurations that are beyond the scope of this discussion.
The FuZE-Q device was commissioned in 2022 and is presently operating in a two-electrode configuration using a new capacitor bank with significantly larger stored energy ( MJ) than used for any previous SFS Z-pinch device. Zap Energy is currently focused on optimizing FuZE-Q plasma performance with the new bank and opening up new operating regimes, both in terms of peak power delivered as well as extending the duration of the plasma pulse to approximately 100 μs. These efforts are ongoing; progress has been made both in peak pinch current attained, above 600 kA, as well as D–D neutron yields above 109 at the time of publication. The FuZE-Q bank is able to deliver as much as 1.5 MA plasma current and is expected to enable operational regimes consistent with net fusion gain.
All of these two-electrode configurations produce axially extended and long-lived stable Z pinches. The two-electrode devices depend on a single power supply to drive both the acceleration process and the compression process. A key avenue for future development is the three-electrode configuration, which is discussed briefly in Sec. II C.
C. The three-electrode concept
In principle, an optimal blend of pinch current and sheared flow can be achieved by separately controlling the acceleration and compression current waveforms. The three-electrode configuration deploys distinct acceleration and compression power supplies to drive these currents, while preserving the aspect ratio of the coaxial acceleration region used in two-electrode devices. Experimental work has demonstrated high-performance plasma operation in the three-electrode mode.40
Novel three-electrode geometries have been designed to further optimize the SFS Z-pinch to improve both its operation and efficiency. These designs are ready for implementation in the FuZE-Q machine. The three-electrode design may prove crucial to scale the SFS Z-pinch concept to net-gain performance. The FuZE-Q device concept is readily compatible with both two- and three-electrode operation, enabling the study and optimization of each.
The compression and acceleration banks have been designed in a similar manner as those used on previous generations of SFS Z-pinch devices. High-voltage capacitors are switched through coaxial cables leading to connections at the “collector plates” at the device. Passive pulse-forming networks (PFNs), with multiple stages of inductively isolated capacitors, allow a wide range of current waveforms, typically with a fast rise and a long current flattop. Both electrical circuit (e.g., SPICE) and plasma physics (e.g., MHD) computational tools are used to design the banks, electrode shapes, and spacing. Both banks and the cable leads have been designed with the ability to be electrically isolated from ground. These power supplies are relatively simple compared to the complicated pulsed power used for fast Z pinches at Sandia, for example.54
D. SFS Z-pinch fusion core
The fusion-plant-relevant SFS Z-pinch concept8,55,56 shown in Fig. 3, makes for a compelling, cost-competitive energy system, as it does not require either magnetic field coils or auxiliary heating beyond the Z-pinch power banks. The SFS core module is compact (0.2 × 1.5 m2), surrounded by a liquid LiPb blanket that forms the end wall electrode and current return, functions as the heat transfer medium (absorbing nearly all particles and heat), provides tritium breeding, and serves as shielding for both personnel and surroundings. (Including this blanket, the core module dimensions are approximately 3 × 3 m2.) Deploying a “farm” of multiple low-cost modules would facilitate maintenance of individual modules, while the plant is still operating and provides economy of scale for the tritium handling and other balance of plant systems.
The vacuum vessel encapsulates the entire liquid LiPb structure, the surface of which forms the current return path. There are various current-return configurations that are topologically equivalent to the fusion module concept of Fig. 3, which can be realized on the FuZE-Q device. The process of optimizing fusion-core-relevant electrode geometries and current return paths is under way on the solid-metal FuZE-Q device before attempting to combine with the proposed liquid-metal topologies, which are being designed into a next-generation platform, FuZE-L (L for liquid).
To help match fluctuating grid power demands, the repetitively pulsed design of the SFS Z-pinch fusion system allows for operation at power levels below peak output capability by reducing the duty cycle and the coolant flow rate. Adding modest thermal storage to the fusion core is also under consideration; such thermal storage would potentially enable higher utilization of the fusion core, a faster ramp rate for some portion of the plant peak output power, restart capability from outages, service of industrial heat needs, etc. The modular nature of the Zap fusion core helps provide operational features tailored to the specific customer.
III. DEMONSTRATING ADIABATIC SCALING TOWARD Q = 1
A. 0D adiabatic scaling
A valuable high-level road map to achieving fusion gain ( ) has been established by considering the expected 0D adiabatic scaling of plasma parameters as a function of pinch current, Ip. Scalings of n, T, a, and are discussed above. As detailed in a recent publication,60 derivation of D–T equivalent scientific Q reveals that knowledge of n, T, and axial speed (vz) of the SFS Z-pinch plasma allows calculation of Q, given a starting point in the n – T space and the effective ionization state of the plasma ions ( ). The plasma operating contour map in Fig. 4 provides a compact representation of progress in gain as a function of n and T for a scenario with axial velocity chosen to be a fraction of the Alfvén speed, and with . The depicted adiabatic trajectory uses a particular set of initial conditions, which determine the conditions required for scientific breakeven. The chosen adiabat results in Q = 1 at 730 kA; other choices can give Q = 1 at currents as low as 650 kA and up to 1 MA or more. Heating by D–T alpha particles is not included in the results shown in Fig. 4. Although alpha heating has little effect for , in high-gain plasmas, Q can be dramatically enhanced.60 Experimental efforts are guided by seeking results that track with the expected scaling trajectory.
B. Experimental scaling
The total neutron yield per discharge offers a robust measurement that is integrated spatially over the entire plasma and over the entire duration. The yield is measured by a calibrated lanthanum bromide, LaBr3, activation detector, which is scaled by its distance and solid angle from the plasma. The yield is also corroborated by a spatial array of silicon detectors,53 which are relatively calibrated.
Recent measurements of total neutron yield vs total plasma current for FuZE-Q are shown in Fig. 5. [We use the total yield as a good proxy for the yield rate described by Eq. (1), as the duration of neutron emission does not significantly vary. We also use the total plasma current as measured by an external Rogowski coil as a proxy for the pinch current itself, which is a noisier measurement. We have found heuristically both in experimental data as well as modeling that plasma current is proportional to pinch current, with , and provides a useful metric for observing scaling.] The top and bottom panels display linear and log plots of these parameters, respectively. The log –log plot shows the best fit to the data in the high yield/high current regime of interest, in the upper-right corner. The regression is consistent with with . The overall dataset shows shot-to-shot scatter, particularly at lower performance, but observed scaling suggests that plasma heating rises at least as strongly as what would be expected from adiabatic compression.
While this dataset provides solid evidence supporting the expected scaling, it does not give a direct measure of the associated efficiency of the process, as yield is plotted as a function of the total plasma current rather than the pinch current itself. (Note further that taking into account the heuristic scaling described above with respect to plasma vs pinch currents, that the expected maximum pinch current associated with this plot would be 600 kA.) Thus, this plot does not make a statement on Q. Quantitative assessment of progress toward fusion breakeven will be based on measurement of local plasma temperature, density, and flow speed, with the measured yield rate providing corroborating data.60
C. Computational scaling
Whole-device MHD modeling using the WARPXM code61 has been performed, using an approach similar to previous modeling with Mach2.41 WARPXM has several advantages relative to Mach 2 for whole-device modeling. Because it is designed for modern parallel processing, faster and higher-resolution calculations are possible. Also, it is a flexible modeling framework, allowing implementation of a variety of features and deployment of plasma physics models that are unavailable in Mach 2. As elaborated in Sec. IV, within the WARPXM framework, a two-fluid plasma model, and eventually continuum kinetic modeling, may replace the single-fluid (MHD) approach in WARPXM. The modeling approach initializes a plasma slug in the middle of the coaxial acceleration region and specifies a time-dependent magnetic field at the inlet boundary of the coaxial region, dictating the current driven through the plasma. The inner and outer electrode surfaces are treated as perfectly electrically conducting and thermally insulating. Representative results are shown in Fig. 6 for a case similar to the FuZE device, using a sinusoidal current waveform with a quarter-cycle time of 10.5 μs. Figure 7 shows results from a set of simulations in which peak plasma current and slug mass are varied. Strong scaling of neutron production rate with current is observed, near I11, as shown. These results are encouraging and corroborate the observed experimental scaling discussed in Sec. III B.
Experimental and modeling observations of strong scaling of neutron yield with plasma current are critical in that they give evidence these compact devices can scale to high fusion performance at modest levels of pulsed power. Given our observations of (1) the continued stabilization by sheared flow, (2) the associated fusion production resulting from thermal fusion, and (3) the strong scaling driven by adiabatic compression and heating, one can reasonably conclude that the Zap Energy devices show promise for achieving scalable and economical fusion power systems. All three of the above characteristics are observed in FuZE and FuZE-Q performance and in MHD whole-device modeling.
IV. THE PATH FORWARD
With the FuZE-Q device and its first power supply fully commissioned, Zap Energy is focused on scaling performance of the SFS Z-pinch concept toward commercially relevant fusion gain. This process is an industrial-speed iteration cycle. Our devices are small and modular, allowing for flexibility and accelerated feedback between theory, experiment, analysis, and machine modification. Several examples of iteration are discussed above, including three-electrode architectures, electrode materials and geometry testing, and power supply modification to match the pulsed-power delivery to the dynamic load impedance. These activities and more are simultaneously under way as a part of high-speed parallel development, enabled by having multiple on-line fusion devices (FuZE and FuZE-Q) as well as multiple capacitor power banks. The new FuZE-Q 1 MJ class power bank, for example, was designed, built, assembled, commissioned, and generated first plasma, all within eight months.
An extensive suite of advanced diagnostics is deployed on the Zap Energy devices and provides scientific rigor to complement our industrialized research strategy. Measurements of the pulsed millimeter-scale Z pinches pose specific challenges, so a major part of the experimental team is dedicated to instrumentation providing high-fidelity data. Zap has also benefited greatly from external collaborations, which allow it to make rapid scientific progress by leveraging outside expertise (e.g., Thomson scattering,62 neutronics,52,53 and spectroscopy63). Future progress requires continued scaling of diagnostic system capabilities to be compatible with ever-improving plasma performance.
As an example of the above, the determination of scientific Q, as discussed in Sec. III B as well as in previous work,60 can currently be made with a combination of Thomson scattering and ion Doppler spectroscopy methodologies. However, a more self-consistent method would be enabled by measuring the Ion Acoustic Wave (IAW) Thomson scattering feature from a collective measurement, rather than the Electron Plasma Wave (EPW) feature.64 We are working toward achieving this more difficult measurement, which would allow resolving ion temperature, density, and velocity in a single volume and at a single time, which are all of the inputs required for the Q determination.
As highlighted above by the whole-device modeling scaling study shown in Figs. 6 and 7, the theory and modeling effort at Zap Energy is tightly coupled to the experimental program, both in speed and scope, providing insight into experimental observations and guiding future experimental campaigns and designs. In addition to the scaling studies, detailed validation work is under way, driven by comparison of synthetic diagnostics that match the experimental diagnostic suite. For example, synthetic magnetic probe signals match the extensive experimental probe array and allow comparison of magnetic field data as a function of time and position. Also, synthetic chord-integrated spectroscopy is available to support direct comparison with experimental spectroscopic signals. Careful comparison of simulated and experimental results stimulates continuous improvement of modeling. For example, circuit modeling capability has been developed and applied. Multi-fluid and related radiation modeling is also under development to capture neutral and impurity species behavior (including recycling and erosion) by adapting the techniques developed for the tokamak edge.65,66
As mentioned in the Introduction, the SFS Z-pinch concept is relatively underexplored compared to mainline tokamak or stellarator concepts. Zap is actively working to refine important aspects of foundational SFS Z-pinch physics. There is work yet to be done to fully understand and exploit the sheared-flow mechanism for stabilizing m = 0 and m = 1 macroscopic modes. On the m = 0 front, PIC kinetic modeling67 and two-fluid modeling68 have clarified linear and nonlinear stabilization of m = 0. To address m = 1, full 3D two-fluid modeling is under way; initial results show nonlinear relaxation to quasi-stable equilibria, as depicted in Fig. 8. Hybrid kinetic69 and gyrokinetic70 modeling has been applied to m = 0 stability, showing that large ion Larmor orbits can play an important role. However, linear and nonlinear kinetic modeling of m = 1 behavior has not yet been achieved. At Zap, we are aiming to explore that uncharted territory via GPU-accelerated continuum kinetic modeling. Powerful kinetic modeling tools can also be applied to unanswered questions about the contribution of microturbulence to effective resistivity in the Z pinch.31 Moreover, as the understanding of these fundamental processes matures and is validated by experimental measurements, whole-device modeling will be upgraded. One possibility for harnessing fine-grained physics in the whole-device scenario is to apply composite fluid-kinetic modeling,71,72 in which fluid methods are applied in most of the domain, while continuum kinetic methods are deployed selectively where higher physics fidelity is required.
Zap Energy has brought together an exceptional combination of physics and engineering expertise, including plasma experimentalists and theorists, pulsed-power engineers, vacuum mechanical engineers, and the many other technical competencies required to develop fusion energy. In addition, fusion commercialization specialists at Zap bring expertise in government affairs, cost modeling, and market interface, which are necessary for the success of Zap Energy and fusion in general. Finally, we have a top supporting team to handle the necessary acquisition, financing, and human resource management to undertake the substantial task of realizing SFS Z-pinch fusion technology.
We have made major strides in building our human resources, developing the required infrastructure and, critically, building multiple experimental platforms in very short development cycles. Scientifically, we have successfully pushed these devices to fusion conditions and triple products competitive with much larger and more costly devices. The underlying adiabatic scaling mechanism has been demonstrated experimentally and computationally, and we are developing a modeling-based understanding of SFS Z-pinch physics. This progress is made possible because of the unique research environment combining excellence in engineering and plasma physics. The diagnostic output from Z-pinch experimental results is fed into an ongoing effort to validate and improve our modeling understanding and establish the predictive capability needed to rise to the next challenges.
Indeed, major challenges remain. Seventy years of history have proven that leveraging fusion science for practical purpose is exceedingly difficult. A compelling and simple concept, significant funding resources, and a unified, talented team provide the tools required to address these challenges. Zap Energy is determined to apply its industrialized scientific methods to resolve these challenges and commercialize fusion energy on a timescale relevant for our global concerns.
The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy (DOE) under Award Nos. DE-AR-0000571, DE-AR-0001010, and DE-AR-0001260, and by the Air Force Office of Scientific Research under Grant No. FA9550-15-1-0271. Our computational modeling research has used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231.
Conflict of Interest
The authors have no conflicts to disclose.
Benjamin Levitt: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Eric Meier: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Ryan Umstattd: Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Johnathon R. Barhydt: Data curation (supporting); Formal analysis (supporting); Visualization (supporting). Iman Anwar Michael Datta: Formal analysis (supporting); Methodology (supporting); Visualization (supporting). Chelsea Liekhus-Schmaltz: Data curation (supporting); Formal analysis (supporting); Visualization (supporting). Derek A. Sutherland: Formal analysis (supporting); Methodology (supporting); Visualization (supporting). Brian A. Nelson: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – review & editing (equal).
The data that support the findings of this study are available within the article.