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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.

Field-reversed configurations (FRCs) have become attractive targets for magneto-inertial fusion, a.k.a. magnetized target fusion (MTF), which may offer a more economical path to fusion gain greater than unity. Slutz et al 1 has simulated FRC formation and compression via a solid imploding liner on the Z-machine (20+ MA, 100 ns), located at Sandia National Labs. These FRC targets would be unique for an MTF campaign in that they would be formed with very strong fields (10-100 T), be centimeter-scale in size, and be formed in-situ (requiring no translation stage). With a 30 T bias axial field, LASNEX simulations suggest fusion yield from the compressed FRC could approach liner kinetic energies typically obtained in MagLIF 2 .

Magnetized Liner Inertial Fusion (MagLIF) is a magneto-inertial fusion (MIF) concept being studied on the Z-machine at Sandia National Laboratories. MagLIF relies on quasi-adiabatic heating of a gaseous deuterium (DD) fuel and flux compression of a background axially oriented magnetic field to achieve fusion relevant plasma conditions. The magnetic flux per fuel radial extent determines the confinement of charged fusion products and is thus of fundamental interest in understanding MagLIF performance. It was recently shown that secondary DT neutron spectra and yields are sensitive to the magnetic field conditions within the fuel, and thus provide a means by which to characterize the magnetic confinement properties of the fuel. 1 , 2 , 3 We utilize an artificial neural network to surrogate the physics model of Refs. [1] , [2] , enabling Bayesian inference of the magnetic confinement parameter for a series of MagLIF experiments that systematically vary the laser preheat energy deposited in the target. This constitutes the first ever systematic experimental study of the magnetic confinement properties as a function of fundamental inputs on any neutron-producing MIF platform. We demonstrate that the fuel magnetization decreases with deposited preheat energy in a fashion consistent with Nernst advection of the magnetic field out of the hot fuel and diffusion into the target liner.

Magnetized Liner Inertial Fusion (MagLIF) is a magneto-inertial fusion concept, which is presently being studied on the Z Pulsed Power Facility. The concept utilizes an axial magnetic field and laser heating to produce fusion-relevant conditions at stagnation despite a peak magnetically driven implosion velocity of less than 100 km/s. Initial mymargin experiments demonstrated the viability of the concept but left open questions about the amount of laser energy coupled to the fuel and the role that mix played in the stagnation conditions. In this paper, simple methodologies for estimating the laser energy coupled to the fuel and determining the stagnation pressure and mix are presented. These tools enabled comparisons across many experiments to establish performance trends, as well as allow comparisons with 2-D magnetohydrodynamics simulations. The initial experiments were affected by low laser energy coupling (0.2–0.6 kJ), which resulted in reduced neutron yields (1– $2\times 10^{12}$ ). In addition, all early experiments utilized mid-Z (aluminum) fuel-facing components. Mixing from these components had a significant impact on stagnation and increased with laser energy. Lower neutron yields (1– $3\times 10^{11}$ ) were measured with higher laser coupling (0.8–1.2 kJ), which significantly deviated from the predicted scaling. When all fuel-facing components were made from a low-Z material (beryllium), neutron production increased ( $3.2\times 10^{12}$ ) and scaled as expected with laser energy; experimental yields were approximately 40% of simulated yields. In addition, roughly I4 yield scaling was observed in experiments, where the load current was varied from 16–18 MA. These results represent the first step in experimental demonstration of stagnation performance scaling with input parameters in MagLIF.

We present an overview of the magneto-inertial fusion (MIF) concept Magnetized Liner Inertial Fusion (MagLIF) pursued at Sandia National Laboratories and review some of the most prominent results since the initial experiments in 2013. In MagLIF, a centimeter-scale beryllium tube or ‘liner’ is filled with a fusion fuel, axially pre-magnetized, laser pre-heated, and finally imploded using up to 20 MA from the Z machine. All of these elements are necessary to generate a thermonuclear plasma: laser preheating raises the initial temperature of the fuel, the electrical current implodes the liner and quasi-adiabatically compresses the fuel via the Lorentz force, and the axial magnetic field limits thermal conduction from the hot plasma to the cold liner walls during the implosion. MagLIF is the first MIF concept to demonstrate fusion relevant temperatures, significant fusion production (>1013 primary DD neutron yield), and magnetic trapping of charged fusion particles. On a 60 MA next-generation pulsed-power machine, two-dimensional simulations suggest that MagLIF has the potential to generate multi-MJ yields with significant self-heating, a long-term goal of the US Stockpile Stewardship Program. At currents exceeding 65 MA, the high gains required for fusion energy could be achievable.

At the Z Facility at Sandia National Laboratories, the magnetized liner inertial fusion (MagLIF) program aims to study the inertial confinement fusion in deuterium-filled gas cells by implementing a three-step process on the fuel: premagnetization, laser preheat, and Z-pinch compression. In the laser preheat stage, the Z-Beamlet laser focuses through a thin polyimide window to enter the gas cell and heat the fusion fuel. However, it is known that the presence of the few μm thick window reduces the amount of laser energy that enters the gas and causes window material to mix into the fuel. These effects are detrimental to achieving fusion; therefore, a windowless target is desired. The Lasergate concept is designed to accomplish this by “cutting” the window and allowing the interior gas pressure to push the window material out of the beam path just before the heating laser arrives. In this work, we present the proof-of-principle experiments to evaluate a laser-cutting approach to Lasergate and explore the subsequent window and gas dynamics. Further, an experimental comparison of gas preheat with and without Lasergate gives clear indications of an energy deposition advantage using the Lasergate concept, as well as other observed and hypothesized benefits. While Lasergate was conceived with MagLIF in mind, the method is applicable to any laser or diagnostic application requiring direct line of sight to the interior of gas cell targets.

Fuel magnetization in magneto-inertial fusion (MIF) experiments improves charged burn product confinement, reducing requirements on fuel areal density and pressure to achieve self-heating. By elongating the path length of 1.01 MeV tritons produced in a pure deuterium fusion plasma, magnetization enhances the probability for deuterium–tritium reactions producing 11.8−17.1 MeV neutrons. Nuclear diagnostics thus enable a sensitive probe of magnetization. Characterization of magnetization, including uncertainty quantification, is crucial for understanding the physics governing target performance in MIF platforms, such as magnetized liner inertial fusion (MagLIF) experiments conducted at Sandia National Laboratories, Z-facility. We demonstrate a deep-learned surrogate of a physics-based model of nuclear measurements. A single model evaluation is reduced from O(10–100) CPU hours on a high-performance computing cluster down to O(10) ms on a laptop. This enables a Bayesian inference of magnetization, rigorously accounting for uncertainties from surrogate modeling and noisy nuclear measurements. The approach is validated by testing on synthetic data and comparing with a previous study. We analyze a series of MagLIF experiments systematically varying preheat, resulting in the first ever systematic experimental study of magnetic confinement properties of the fuel plasma as a function of fundamental inputs on any neutron-producing MIF platform. We demonstrate that magnetization decreases from BR∼0.5 to BR∼0.2 MG cm as laser preheat energy deposited increases from Epreheat∼460 J to Epreheat∼1.4 kJ. This trend is consistent with 2D LASNEX simulations showing Nernst advection of the magnetic field out of the hot fuel and diffusion into the target liner.

MagLIF experiments [M.R. Gomez et al., Phys. Plasmas 22, 056306 (2015)] on Z have demonstrated the basic principles of Magneto-Inertial Fusion (MIF) for wall confined plasmas. Other MIF schemes have been proposed based on the liner implosion of closed field magnetically confined plasmas such as Field Reversed Configurations (FRCs) [T. P. Intrator et al., Phys. Plasmas 15, 042505 (2008)]. We present a semi-analytical model of liner driven FRC implosions that predicts the fusion gain of such systems. The model predicts a fusion gain near unity for an FRC imploded by a liner driven by the Z Machine. We show that FRCs could be formed and imploded at the Z facility using the AutoMag liner concept [S. A. Slutz et al., Phys. Plasmas 24, 012704 (2017)]. An initial bias magnetic field can be supplied by the external magnets used in MagLIF experiments. The reverse field is then supplied by an AutoMag liner, which has helical conducting paths imbedded in an insulating substance. Experiments [Shipley et al., Phys. Plasmas 26, 052705 (2019)] have demonstrated that AutoMag can generate magnetic fields greater than 30 Tesla inside of the liner. We have performed 2D Radiation MHD simulations of the formation and implosion of an FRC, which are in good agreement with the analytical model. The FRC formation process could be studied on small pulsed power machines delivering about 1 MA.

Recent computational work on Z-pinches has been made, using the open source adaptive mesh refinement (AMR) code FLASH. Here we present two-dimensional simulations of thick liner Z-pinches, where we have utilized user defined boundary conditions with a predefined magnetic drive. AMR may elucidate upon the suite of large-k instabilities' contribution to mix and other potentially deleterious effects in the process of turbulent motion's conversion to heat. Such phenomena include the magneto-Rayleigh-Taylor instability, and variations axially, if coupled with a hydrodynamic blast wave simulating a form of laser preheat in a magnetic liner inertial fusion (MagLIF)-like scenario. The implementation of AMR may determine to what extent instabilities are mitigated by magnetic fields for all k, and to what extent the coupling of additional fields, such as an axial magnetic field, suppress and eliminate mixing and turbulent motion.

Auto-magnetizing liners (AutoMag [1], [2]) are cylindrical tubes made of metallic helical conductors separated by electrically insulating material. In the first stage of AutoMag, helical current flows in the AutoMag liner and produces a strong internal axial field (20 to 100 T) during a 5 kA/ns current prepulse that lasts 100 to 300 ns. In the second stage, the rapidly-rising main current pulse (200 kA/ns) induces a strong electric field in the liner that causes the insulating material to undergo dielectric breakdown. Lastly, after breakdown, the liner current reorients to be primarily axial and the liner implodes radially via the Lorentz force. AutoMag is designed to eliminate the need for the external coil system [3] that is used to premagnetize fusion fuel in Magnetized Liner Inertial Fusion (MagLIF [4]) which impedes diagnostic access and necessitates use of a high inductance power feed that reduces current delivery to the liner. Experiments have been successfully executed on the Mykonos accelerator [5] to evaluate the magnetization and breakdown stages of AutoMag. Microscopic magnetic field probes (microBdots) measured magnetic field inside of the liner and an iCCD imager and fast photodiodes made spatially-resolved and temporally-resolved measurements, respectively, of optical plasma emission in the load region. Fields near 1 MG were measured in multiple experiments and plasma emission indicative of breakdown was observed for select liner designs. These experiments, the first of their kind, represent an advance in magneto-inertial fusion that will enable the design of a new class of MagLIF targets capable of reaching higher current delivered to the liner (better fuel compression) and higher magnetization fields inside of the fusion fuel (better thermal insulation). Success of the experiments on Mykonos has resulted in the design of Z Machine experiments (planned Spring 2018) to study the implosion stage of AutoMag.

We have developed a physics-based transmission-line-circuit model of the Z pulsed-power accelerator. The 33-m-diameter Z machine generates a peak electrical power as high as 85 TW, and delivers as much as 25 MA to a physics load. The circuit model is used to design and analyze experiments conducted on Z. The model consists of 36 networks of transmission-line-circuit elements and resistors that represent each of Zs 36 modules. The model of each module includes a Marx generator, intermediate-energy-storage capacitor, laser-triggered gas switch, pulse-forming line, self-break water switches, and tri-plate transmission lines. The circuit model also includes elements that represent Zs water convolute, vacuum insulator stack, four parallel outer magnetically insulated vacuum transmission lines (MITLs), double-post-hole vacuum convolute, inner vacuum MITL, and physics load. Within the vacuum-transmission-line system the model conducts analytic calculations of current loss. To calculate the loss, the model simulates the following processes: (i) electron emission from MITL cathode surfaces wherever an electric-field threshold has been exceeded; (ii) electron loss in the MITLs before magnetic insulation has been established; (iii) flow of electrons emitted by the outer-MITL cathodes after insulation has been established; (iv) closure of MITL anode-cathode (AK) gaps due to expansion of cathode plasma; (v) energy loss to MITL conductors operated at high lineal current densities; (vi) heating of MITL-anode surfaces due to conduction current and deposition of electron kinetic energy; (vii) negative-space-charge-enhanced ion emission from MITL anode surfaces wherever an anode-surface-temperature threshold has been exceeded; and (viii) closure of MITL AK gaps due to expansion of anode plasma. The circuit model is expected to be most accurate when the fractional current loss is small. We have performed circuit simulations of 52 Z experiments conducted with a variety of accelerator configurations and load-impedance time histories. For these experiments, the apparent fractional current loss varies from 0% to 20%. Results of the circuit simulations agree with data acquired on 52 shots to within 2%.

The Magnetized Liner Inertial Fusion concept (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010)] is being studied on the Z facility at Sandia National Laboratories. Neutron yields greater than 1012 have been achieved with a drive current in the range of 17–18 MA and pure deuterium fuel [Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]. We show that 2D simulated yields are about twice the best yields obtained on Z and that a likely cause of this difference is the mix of material into the fuel. Mitigation strategies are presented. Previous numerical studies indicate that much larger yields (10–1000 MJ) should be possible with pulsed power machines producing larger drive currents (45–60 MA) than can be produced by the Z machine [Slutz et al., Phys. Plasmas 23, 022702 (2016)]. To test the accuracy of these 2D simulations, we present modifications to MagLIF experiments using the existing Z facility, for which 2D simulations predict a 100-fold enhancement of MagLIF fusion yields and considerable increases in burn temperatures. Experimental verification of these predictions would increase the credibility of predictions at higher drive currents.The Magnetized Liner Inertial Fusion concept (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010)] is being studied on the Z facility at Sandia National Laboratories. Neutron yields greater than 1012 have been achieved with a drive current in the range of 17–18 MA and pure deuterium fuel [Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]. We show that 2D simulated yields are about twice the best yields obtained on Z and that a likely cause of this difference is the mix of material into the fuel. Mitigation strategies are presented. Previous numerical studies indicate that much larger yields (10–1000 MJ) should be possible with pulsed power machines producing larger drive currents (45–60 MA) than can be produced by the Z machine [Slutz et al., Phys. Plasmas 23, 022702 (2016)]. To test the accuracy of these 2D simulations, we present modifications to MagLIF experiments using the existing Z facility, for which 2D simulations predict a 100-fold enhancement of MagLIF fusion yields and considerable increase...

We report on the progress made to date for a Laboratory Directed Research and Development (LDRD) project aimed at diagnosing magnetic flux compression on the Z pulsed-power accelerator (0-20 MA in 100 ns). Each experiment consisted of an initially solid Be or Al liner (cylindrical tube), which was imploded using the Z accelerator's drive current (0-20 MA in 100 ns). The imploding liner compresses a 10-T axial seed field, B z ( 0 ) , supplied by an independently driven Helmholtz coil pair. Assuming perfect flux conservation, the axial field amplification should be well described by B z ( t ) = B z ( 0 ) x [ R ( 0 ) / R ( t )] 2 , where R is the liner's inner surface radius. With perfect flux conservation, B z ( t ) and dB z / dt values exceeding 10 4 T and 10 12 T/s, respectively, are expected. These large values, the diminishing liner volume, and the harsh environment on Z, make it particularly challenging to measure these fields. We report on our latest efforts to do so using three primary techniques: (1) micro B-dot probes to measure the fringe fields associated with fluxmore » compression, (2) streaked visible Zeeman absorption spectroscopy, and (3) fiber-based Faraday rotation. We also mention two new techniques that make use of the neutron diagnostics suite on Z. These techniques were not developed under this LDRD, but they could influence how we prioritize our efforts to diagnose magnetic flux compression on Z in the future. The first technique is based on the yield ratio of secondary DT to primary DD reactions. The second technique makes use of the secondary DT neutron time-of-flight energy spectra. Both of these techniques have been used successfully to infer the degree of magnetization at stagnation in fully integrated Magnetized Liner Inertial Fusion (MagLIF) experiments on Z [P. F. Schmit et al. , Phys. Rev. Lett. 113 , 155004 (2014); P. F. Knapp et al. , Phys. Plasmas, 22 , 056312 (2015)]. Finally, we present some recent developments for designing and fabricating novel micro B-dot probes to measure B z ( t ) inside of an imploding liner. In one approach, the micro B-dot loops were fabricated on a printed circuit board (PCB). The PCB was then soldered to off-the-shelf 0.020- inch-diameter semi-rigid coaxial cables, which were terminated with standard SMA connectors. These probes were recently tested using the COBRA pulsed power generator (0-1 MA in 100 ns) at Cornell University. In another approach, we are planning to use new multi-material 3D printing capabilities to fabricate novel micro B-dot packages. In the near future, we plan to 3D print these probes and then test them on the COBRA generator. With successful operation demonstrated at 1-MA, we will then make plans to use these probes on a 20-MA Z experiment.« less

The size, temporal and spatial shape, and energy content of a laser pulse for the pre-heat phase of magneto-inertial fusion affect the ability to penetrate the window of the laser-entrance-hole and to heat the fuel behind it. High laser intensities and dense targets are subject to laser-plasma-instabilities (LPI), which can lead to an effective loss of pre-heat energy or to pronounced heating of areas that should stay unexposed. While this problem has been the subject of many studies over the last decades, the investigated parameters were typically geared towards traditional laser driven Inertial Confinement Fusion (ICF) with densities either at 10% and above or at 1% and below the laser's critical density, electron temperatures of 3–5 keV, and laser powers near (or in excess of) 1 × 1015 W/cm2. In contrast, Magnetized Liner Inertial Fusion (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010) and Slutz and Vesey, Phys. Rev. Lett. 108, 025003 (2012)] currently operates at 5% of the laser's critical dens...

Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primary fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized alpha-particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated., Comment: Published in Physics of Plasmas [http://dx.doi.org/10.1063/1.4918953]

Fast ignition using pulsed-power drivers combines the efficient production of X-rays to drive fusion fuel assembly with precise ultraintense laser pulses for fuel ignition. Z-pinches convert electrical energy into thermal X-ray energy with high efficiency, which makes them attractive drivers for indirect-drive fuel assembly. Currently, experiments use the Z-pinch vacuum hohlraum, in which the Z-pinch heats a hohlraum that reemits thermal X-rays to drive the capsule. Surface-guided hemispherical capsule implosion experiments in Z-pinch vacuum hohlraums are in progress to study energetics, symmetry control, and pulse shaping. Simulations including radiation asymmetry and glide-plane physics have been performed to optimize the imploded fuel. Higher density capsule implosions at a given driver energy may be possible using the Z-pinch dynamic hohlraum, in which the Z-pinch plasma itself creates the hohlraum. Capsule and hohlraum designs for both vacuum and dynamic hohlraum sources are in progress, including liquid cryogenic fuel capsules. Analytic models for D-Tfuel heating and burn have been developed for scoping purposes and breakeven scaling. Implicit particle-in-cell modeling of the interaction of laser-produced energetic particles with calculated fuel configurations demonstrates that details of the entire fuel/glide material density profile significantly affect the calculated energy deposition and thus the ignition requirements.

Fast ignition fusion targets require a uniform cryogenic D-T fuel layer for efficient fuel assembly. Uniform beta layering of solid D-T fuel within a fast ignition capsule will be complicated by th...

Recyclable transmission lines (RTLs) are being studied as a means to repetitively drive Z pinches. Minimizing the mass of the RTL should also minimize the reprocessing costs. Low mass RTLs could also help reduce the cost of a single shot facility such as the proposed X-1 accelerator and make Z-pinch driven nuclear space propulsion feasible. Calculations are presented to determine the minimum electrode mass to provide sufficient inertia against the magnetic pressure produced by the large currents needed to drive the Z pinches. The results indicate an electrode thickness which is much smaller than the initial resistive skin depth. This suggests that the minimum electrode thickness may be not be solely determined by inertial effects, but also by the ability of the electrode to efficiently carry the current. A series of experiments have been performed to determine the ability of the electrodes to carry current as a function of the electrode thickness. The results indicate that electrodes much thinner than the...

The energy required to ignite compressed deuterium–tritium fuel decreases strongly with fuel density. Thermal radiation is an effective way of driving inertial fusion capsules to high density. The achievable fuel density increases with peak radiation temperature, since the ablation pressure depends strongly on the radiation temperature. Through a series of detailed numerical simulations, peak fuel densities have been calculated as a function of the peak radiation drive temperature. In these calculations, the time dependence of the radiation temperature has been optimized to obtain maximum density for each scaling point. These results are then used with the fast ignition scaling of Atzeni [S. Atzeni, Phys. Plasmas 6, 3316 (1999)] to obtain ignition energy as peak drive temperature.

This Letter presents results from the first fully integrated experiments testing the magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)], in which a cylinder of deuterium gas with a preimposed 10 Taxial magnetic field is heated by Z beamlet, a 2.5 kJ, 1 TW laser, and magnetically imploded by a 19 MA, 100 ns rise time current on the Z facility. Despite a predicted peak implosion velocity of only 70 km = s, the fuel reaches a stagnation temperature of approximately 3 keV, with T(e) ≈ T(i), and produces up to 2 x 10(12) thermonuclear deuterium-deuterium neutrons. X-ray emission indicates a hot fuel region with full width at half maximum ranging from 60 to 120 μm over a 6 mm height and lasting approximately 2 ns. Greater than 10(10) secondary deuterium-tritium neutrons were observed, indicating significant fuel magnetization given that the estimated radial areal density of the plasma is only 2 mg = cm(2).

A quasianalytic model of the dynamic hohlraum is presented. Results of the model are compared to both experiments and full numerical simulations with good agreement. The computational simplicity of the model allows one to find the behavior of the hohlraum radiation temperature as a function of the various parameters of the system and thus find optimum parameters as a function of the driving current. The model is used to investigate the benefits of ablative standoff and quasispherical Z pinches.

Peak x-ray powers as high as 280±40 TW have been generated from the implosion of tungsten wire arrays on the Z Accelerator at Sandia National Laboratories. The high x-ray powers radiated by these z-pinches provide an attractive new driver option for high yield inertial confinement fusion (ICF). The high x-ray powers appear to be a result of using a large number of wires in the array which decreases the perturbation seed to the magnetic Rayleigh-Taylor (MRT) instability and diminishes other 3-D effects. Simulations to confirm this hypothesis require a 3-D MHD code capability, and associated databases, to follow the evolution of the wires from cold solid through melt, vaporization, ionization, and finally to dense imploded plasma. Strong coupling plays a role in this process, the importance of which depends on the wire material and the current time history of the pulsed power driver. Strong coupling regimes are involved in the plasmas in the convolute and transmission line of the powerflow system. Strong coupling can also play a role in the physics of the z-pinch-driven high yield ICF targeL Finally, strong coupling can occur in certain z-pinch-driven application experiments.

The electric force that accelerates ions in a magnetically insulated diode is transferred to the electrodes by the magnetic field. This force, which appears as an ion pressure term in the pressure balance equation, causes a bending of the virtual-cathode and consequently a lensing effect. Analytic calculations of the shape of the virtual-cathode resulting from this ion pressure are presented and a simple formula for the effective focal length resulting from the bending of the virtual-cathode is given. The focussing is a function of the accelerating voltage and the injected beam kinetic energy and current density. Thus a relationship between these parameters must be maintained to keep the beam on target.

The MagLIF (Magnetized Liner Inertial Fusion) concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] has demonstrated fusion–relevant plasma conditions [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] on the Z accelerator with a peak drive current of about 18 MA. We present 2D numerical simulations of the scaling of MagLIF on Z as a function of drive current, preheat energy, and applied magnetic field. The results indicate that deuterium-tritium (DT) fusion yields greater than 100 kJ could be possible on Z when all of these parameters are at the optimum values: i.e., peak current = 25 MA, deposited preheat energy = 5 kJ, and Bz = 30 T. Much higher yields have been predicted [S. A. Slutz and R. A. Vesey, Phys. Rev. Lett. 108, 025003 (2012)] for MagLIF driven with larger peak currents. Two high performance pulsed-power accelerators (Z300 and Z800) based on linear-transformer-driver technology have been designed [W. A. Stygar et al., Phys. Rev. ST Accel. Beams 18, 110401 (2015)]. The Z300 design would provide 48 MA to a MagLIF load, while Z800 would provide 65 MA. Parameterized Thevenin-equivalent circuits were used to drive a series of 1D and 2D numerical MagLIF simulations with currents ranging from what Z can deliver now to what could be achieved by these conceptual future pulsed-power accelerators. 2D simulations of simple MagLIF targets containing just gaseous DT have yields of 18 MJ for Z300 and 440 MJ for Z800. The 2D simulated yield for Z800 is increased to 7 GJ by adding a layer of frozen DT ice to the inside of the liner.

In this paper, we explore magnetized liner inertial fusion (MagLIF) [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] using a semi-analytic model [R. D. McBride and S. A. Slutz, Phys. Plasmas 22, 052708 (2015)]. Specifically, we present simulation results from this model that: (a) illustrate the parameter space, energetics, and overall system efficiencies of MagLIF; (b) demonstrate the dependence of radiative loss rates on the radial fraction of the fuel that is preheated; (c) explore some of the recent experimental results of the MagLIF program at Sandia National Laboratories [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]; (d) highlight the experimental challenges presently facing the MagLIF program; and (e) demonstrate how increases to the preheat energy, fuel density, axial magnetic field, and drive current could affect future MagLIF performance., Comment: Published in Physics of Plasmas [http://dx.doi.org/10.1063/1.4939479]

The implosions of initially solid beryllium liners (tubes) have been imaged with penetrating radiography through to stagnation. These novel radiographic data reveal a high degree of azimuthal correlation in the evolving magneto-Rayleigh-Taylor structure at times just prior to (and during) stagnation, providing stringent constraints on the simulation tools used by the broader high energy density physics and inertial confinement fusion communities. To emphasize this point, comparisons to 2D and 3D radiation magnetohydrodynamics simulations are also presented. Both agreement and substantial disagreement have been found, depending on how the liner's initial outer surface finish was modeled. The various models tested, and the physical implications of these models are discussed. These comparisons exemplify the importance of the experimental data obtained.

A diffusive model of the radial transport of thermal radiation out of a cylindrical core of fissioning plasma is presented. The diffusion approximation is appropriate because the opacity of uranium is very high at the temperatures of interest (greater than 3000 K). We make one additional simplification of assuming constant opacity throughout the fuel. This allows the complete set of solutions to be expressed as a single function. This function is approximated analytically to facilitate parametric studies of the performance of a test module of the nuclear light bulb gas-core nuclear-rocket-engine concept, in the Annular Core Research Reactor at Sandia National Laboratories. Our findings indicate that radiation temperatures in range of 4000-6000 K are attainable, which is sufficient to test the high specific impulse potential (approximately 2000 s) of this concept. 15 refs.

Magnetized inertial fusion (MIF) could substantially ease the difficulty of reaching plasma conditions required for significant fusion yields, but it has been widely accepted that the gain is not sufficient for fusion energy. Numerical simulations are presented showing that high-gain MIF is possible in cylindrical liner implosions based on the MagLIF concept [S. A. Slutz et al Phys. Plasmas 17, 056303 (2010)] with the addition of a cryogenic layer of deuterium-tritium (DT). These simulations show that a burn wave propagates radially from the magnetized hot spot into the surrounding much denser cold DT given sufficient hot-spot areal density. For a drive current of 60 MA the simulated gain exceeds 100, which is more than adequate for fusion energy applications. The simulated gain exceeds 1000 for a drive current of 70 MA.

The magneto-Rayleigh-Taylor (MRT) instability is ubiquitous to pinch plasmas compressed by magnetic pressure, and is an important factor in determining whether a cylindrical liner can reach the axis in a relatively intact form. While there are many RT characterization experiments, there are few well-characterized MRT experiments and none for fast (∼100 ns) z-pinch implosions in which the magnetic pressure typically quickly dominates over material strength. We will present data from our initial two campaigns to study the growth of MRT instabilities.

An approach is presented to design inertial-fusion capsules compensated for time-dependent radiation-drive asymmetries. This approach uses in depth variable doping of the capsule ablator, i.e., the addition of small amounts of material to tailor the opacity. Simulations show that an inertial-fusion capsule, using a beryllium ablator variably doped with gold, can be designed to compensate for a constant ${P}_{2}$ radiation asymmetry as high as 20% and still produce nominal yield (80% of a symmetrically driven capsule). In contrast, without variable doping the ${P}_{2}$ asymmetry must be less than 2% to obtain nominal yield. Similarly encouraging results are obtained for modes ${P}_{1}$, ${P}_{4}$, and ${P}_{6}$. Simulations also demonstrate that variable doping can compensate for nearly arbitrary time-dependent radiation-drive asymmetries by varying the polar dependence of the doping fraction with depth.

The magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)] utilizes a magnetic field and laser heating to relax the pressure requirements of inertial confinement fusion. The first experiments to test the concept [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] were conducted utilizing the 19 MA, 100 ns Z machine, the 2.5 kJ, 1 TW Z Beamlet laser, and the 10 T Applied B-field on Z system. Despite an estimated implosion velocity of only 70 km/s in these experiments, electron and ion temperatures at stagnation were as high as 3 keV, and thermonuclear deuterium-deuterium neutron yields up to 2 × 1012 have been produced. X-ray emission from the fuel at stagnation had widths ranging from 50 to 110 μm over a roughly 80% of the axial extent of the target (6–8 mm) and lasted approximately 2 ns. X-ray yields from these experiments are consistent with a stagnation density of the hot fuel equal to 0.2–0.4 g/cm3. In these experiments, up to 5 × 1010 secondary deuterium-...

Magnetized Liner Inertial Fusion experiments performed at Sandia's Z facility have demonstrated significant thermonuclear fusion neutron yields (∼1012 DD neutrons) from multi-keV deuterium plasmas inertially confined by slow (∼10 cm/μs), stable, cylindrical implosions. Effective magnetic confinement of charged fusion reactants and products is signaled by high secondary DT neutron yields above 1010. Analysis of extensive power, imaging, and spectroscopic x-ray measurements provides a detailed picture of ∼3 keV temperatures, 0.3 g/cm3 densities, gradients, and mix in the fuel and liner over the 1–2 ns stagnation duration.

By magnetizing the fusion fuel in inertial confinement fusion (ICF) systems, the required stagnation pressure and density can be relaxed dramatically. This happens because the magnetic field insulates the hot fuel from the cold pusher and traps the charged fusion burn products. This trapping allows the burn products to deposit their energy in the fuel, facilitating plasma self-heating. Here, we report on a comprehensive theory of this trapping in a cylindrical DD plasma magnetized with a purely axial magnetic field. Using this theory, we are able to show that the secondary fusion reactions can be used to infer the magnetic field-radius product, BR, during fusion burn. This parameter, not ρR, is the primary confinement parameter in magnetized ICF. Using this method, we analyze data from recent Magnetized Liner Inertial Fusion experiments conducted on the Z machine at Sandia National Laboratories. We show that in these experiments BR ≈ 0.34(+0.14/−0.06) MG · cm, a ∼ 14× increase in BR from the initial value, and confirming that the DD-fusion tritons are magnetized at stagnation. This is the first experimental verification of charged burn product magnetization facilitated by compression of an initial seed magnetic flux.

Recyclable transmission lines (RTL)s are being studied as a means to repetitively drive z pinches to generate fusion energy. We have shown previously that the RTL mass can be quite modest. Minimizing the RTL mass reduces recycling costs and the impulse delivered to the first wall of a fusion chamber. Despite this reduction in mass, a few seconds will be needed to reload an RTL after each subsequent shot. This is in comparison to other inertial fusion approaches that expect to fire up to ten capsules per second. Thus a larger fusion yield is needed to compensate for the slower repetition rate in a z-pinch driven fusion reactor. We present preliminary designs of z-pinch driven fusion capsules that provide an adequate yield of 1-4 GJ. We also present numerical simulations of the effect of these fairly large fusion yields on the RTL and the first wall of the reactor chamber. These simulations were performed with and without a neutron absorbing blanket surrounding the fusion explosion. We find that the RTL will be fully vaporized out to a radius of about 3 meters assuming normal incidence. However, at large enough radius the RTL will remain in either the liquid or solidmore » state and this portion of the RTL could fragment and become shrapnel. We show that a dynamic fragmentation theory can be used to estimate the size of these fragmented particles. We discuss how proper design of the RTL can allow this shrapnel to be directed away from the sensitive mechanical parts of the reactor chamber.« less

Recyclable transmission lines (RTL) are studied as a means of repetitively driving z pinches. The lowest reprocessing costs should be obtained by minimizing the mass of the RTL. Low mass transmission lines (LMTL) could also help reduce the cost of a single shot facility such as the proposed X-1 accelerator and make z-pinch driven space propulsion feasible. We present calculations to determine the minimum LMTL electrode mass to provide sufficient inertia against the magnetic pressure produced by the large currents needed to drive the z pinches. The results indicate an electrode thickness which is much smaller than the resistive skin depth. We have performed experiments to determine if such thin electrodes can efficiently carry the required current. The tests were performed with various thickness of materials. The results indicate that LMTLs should efficiently carry the large z-pinch currents needed for inertial fusion. We also use our results to estimate of the performance of pulsed power driven pulsed nuclear rockets.

The United States Department of Energy, Nuclear Energy Research Initiative (NERI) Direct Energy Conversion project has as its goal the development of direct energy conversion (DEC) processes suitable for commercial development. DEC is defined as any fission process that returns usable energy with no intermediate thermal process. This project includes the study of the fission electric cell (FEC). In the FEC, fission fragments exit the fuel element cathode and are collected by the cell anode. Previous work [1] has shown the potential of FECs, with theoretical efficiencies up to 60%. Inspection of this work indicates the need for additional system modeling prior to any conclusions regarding the final FEC reactor configuration. This paper builds on the previous work and outlines the development of models to facilitate design decisions. The models address criticality, design life, reactor configuration, and current-voltage characteristics. In addition, this paper proposes future work to complete the design model.Copyright © 2002 by ASME

A recent publication [K. J. Peterson et al., Phys. Plasmas 19, 092701 (2012)] describes simulations and experiments of electrothermal instability growth on well characterized initially solid aluminum and copper rods driven with a 20 MA, 100 ns rise time current pulse on Sandia National Laboratories Z accelerator. Quantitative analysis of the high precision radiography data obtained in the experiments showed excellent agreement with simulations and demonstrated levels of instability growth in dense matter that could not be explained by magneto-Rayleigh-Taylor instabilities alone. This paper extends the previous one by examining the nature of the instability growth in 2D simulations in much greater detail. The initial instability growth in the simulations is shown via several considerations to be predominantly electrothermal in nature and provides a seed for subsequent magneto-Rayleigh-Taylor growth.

The Nuclear Light Bulb (NLB) concept is an advanced closed cycle space propulsion rocket engine design that offers unprecidented performance characteristics in terms of specific impulse (≳1800 s) and thrust (≳445 kN). The NLB is a gas‐core nuclear reactor making use of thermal radiation from a high temperature U‐plasma core to heat the hydrogen propellant to very high temperatures (∼4000 K). The following paper describes analyses performed in support of the design of in‐reactor tests that are planned to be performed in the Annular Core Research Reactor (ACRR) at Sandia National Laboratories in order to demonstrate the technical feasibility of this advanced concept. The tests will examine the stability of a hydrodynamically confined fissioning U‐plasma under steady and transient conditions. Testing will also involve study of propellant heating by thermal radiation from the plasma and materials performance in the nuclear environment of the NLB. The analyses presented here include neutronic performance studies and U‐plasma radiation heat‐transport studies of small vortex‐confined fissioning U‐plasma experiments that are irradiated in the ACRR. These analyses indicate that high U‐plasma temperatures (4000 to 9000 K) can be sustained in the ACRR for periods of time on the order of 5 to 20 s. These testing conditions are well suited to examine the stability and performance requirements necessary to demonstrate the feasibility of this concept.