In magnetized liner inertial fusion (MagLIF), a cylindrical liner filled with fusion fuel is imploded with the goal of producing a one-dimensional plasma column at thermonuclear conditions. However, structures attributed to three-dimensional effects are observed in self-emission x-ray images. Despite this, the impact of many experimental inputs on the column morphology has not been characterized. We demonstrate the use of a linear regression analysis to explore correlations between morphology and a wide variety of experimental inputs across 57 MagLIF experiments. Results indicate the possibility of several unexplored effects. For example, we demonstrate that increasing the initial magnetic field correlates with improved stability. Although intuitively expected, this has never been quantitatively assessed in integrated MagLIF experiments. We also demonstrate that azimuthal drive asymmetries resulting from the geometry of the “current return can” appear to measurably impact the morphology. In conjunction with several counterintuitive null results, we expect the observed correlations will encourage further experimental, theoretical, and simulation-based studies. Finally, we note that the method used in this work is general and may be applied to explore not only correlations between input conditions and morphology but also with other experimentally measured quantities.
For the cylindrically symmetric targets that are normally fielded on the Z machine, two dimensional axisymmetric MHD simulations provide the backbone of our target design capability. These simulations capture the essential operation of the target and allow for a wide range of physics to be addressed at a substantially lower computational cost than 3D simulations. This approach, however, makes some approximations that may impact its ability to accurately provide insight into target operation. As an example, in 2D simulations, targets are able to stagnate directly to the axis in a way that is not entirely physical, leading to uncertainty in the impact of the dynamical instabilities that are an important source of degradation for ICF concepts. In this report, we have performed a series of 3D calculations in order to assess the importance of this higher fidelity treatment on MagLIF target performance.
An x-ray imaging scheme using spherically bent crystals was implemented on the Z-machine to image x rays emitted by the hot, dense plasma generated by a Magnetized Liner Inertial Fusion (MagLIF) target. This diagnostic relies on a spherically bent crystal to capture x-ray emission over a narrow spectral range (<15 eV), which is established by a limiting aperture placed on the Rowland circle. The spherical crystal optic provides the necessary high-throughput and large field-of-view required to produce a bright image over the entire, one-cm length of the emitting column of a plasma. The average spatial resolution was measured and determined to be 18 µm for the highest resolution configuration. With this resolution, the radial size of the stagnation column can be accurately determined and radial structures, such as bifurcations in the column, are clearly resolved. The success of the spherical-crystal imager has motivated the implementation of a new, two-crystal configuration for identifying sources of spectral line emission using a differential imaging technique.
We report on progress implementing and testing cryogenically cooled platforms for Magnetized Liner Inertial Fusion (MagLIF) experiments. Two cryogenically cooled experimental platforms were developed: an integrated platform fielded on the Z pulsed power generator that combines magnetization, laser preheat, and pulsed-power-driven fuel compression and a laser-only platform in a separate chamber that enables measurements of the laser preheat energy using shadowgraphy measurements. The laser-only experiments suggest that ∼89% ± 10% of the incident energy is coupled to the fuel in cooled targets across the energy range tested, significantly higher than previous warm experiments that achieved at most 67% coupling and in line with simulation predictions. The laser preheat configuration was applied to a cryogenically cooled integrated experiment that used a novel cryostat configuration that cooled the MagLIF liner from both ends. The integrated experiment, z3576, coupled 2.32 ± 0.25 kJ preheat energy to the fuel, the highest to-date, demonstrated excellent temperature control and nominal current delivery, and produced one of the highest pressure stagnations as determined by a Bayesian analysis of the data.
In magneto-inertial fusion, the ratio of the characteristic fuel length perpendicular to the applied magnetic field R to the α-particle Larmor radius Q α 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 B R ∝ R / Q α 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.
Laser propagation experiments using four beams of the National Ignition Facility to deliver up to 35 kJ of laser energy at 351 nm laser wavelength to heat magnetized liner inertial fusion-scale (1 cm-long), hydrocarbon-filled gas pipe targets to ∼keV electron temperatures have demonstrated energy coupling >20 kJ with essentially no backscatter in 15% critical electron density gas fills with 0-19 T applied axial magnetic fields. The energy coupling is also investigated for an electron density of 11.5% critical and for applied field strengths up to 24 T at both densities. This spans a range of Hall parameters 0 < ω c e τ e i ≲2, where a Hall parameter of 0.5 is expected to reduce electron thermal conduction across the field lines by a factor of 4-5 for the conditions of these experiments. At sufficiently high applied field strength (and therefore Hall parameter), the measured laser propagation speed through the targets increases in the measurements, consistent with reduced perpendicular electron thermal transport; this reduces the coupled energy to the target once the laser burns through the gas pipe. The results compare well with a 1D analytic propagation model for inverse Bremsstrahlung absorption.
Helium or neopentane can be used as surrogate gas fill for deuterium (D2) or deuterium-tritium (DT) in laser-plasma interaction studies. Surrogates are convenient to avoid flammability hazards or the integration of cryogenics in an experiment. To test the degree of equivalency between deuterium and helium, experiments were conducted in the Pecos target chamber at Sandia National Laboratories. Observables such as laser propagation and signatures of laser-plasma instabilities (LPI) were recorded for multiple laser and target configurations. It was found that some observables can differ significantly despite the apparent similarity of the gases with respect to molecular charge and weight. While a qualitative behaviour of the interaction may very well be studied by finding a suitable compromise of laser absorption, electron density, and LPI cross sections, a quantitative investigation of expected values for deuterium fills at high laser intensities is not likely to succeed with surrogate gases.
Here we present a new analysis methodology that allows for the self-consistent integration of multiple diagnostics including nuclear measurements, x-ray imaging, and x-ray power detectors to determine the primary stagnation parameters, such as temperature, pressure, stagnation volume, and mix fraction in magnetized liner inertial fusion (MagLIF) experiments. The analysis uses a simplified model of the stagnation plasma in conjunction with a Bayesian inference framework to determine the most probable configuration that describes the experimental observations while simultaneously revealing the principal uncertainties in the analysis. We validate the approach by using a range of tests including analytic and three-dimensional MHD models. An ensemble of MagLIF experiments is analyzed, and the generalized Lawson criterion χ is estimated for all experiments.
We present an overview of the magneto-inertial fusion (MIF) concept MagLIF (Magnetized Liner Inertial Fusion) 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 (>10^13 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.
We report on experimental measurements of how an externally imposed magnetic field affects plasma heating by kJ-class, nanosecond laser pulses. The experiments reported here took place in gas cells analogous to magnetized liner inertial fusion targets. We observed significant changes in laser propagation and energy deposition scale lengths when a 12T external magnetic field was imposed in the gas cell. We find evidence that the axial magnetic field reduces radial electron thermal transport, narrows the width of the heated plasma, and increases the axial plasma length. Reduced thermal conductivity increases radial thermal gradients. This enhances radial hydrodynamic expansion and subsequent thermal self-focusing. Our experiments and supporting 3D simulations in helium demonstrate that magnetization leads to higher thermal gradients, higher peak temperatures, more rapid blast wave development, and beam focusing with an applied field of 12T.
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 CPU hours on a high-performance computing cluster down to 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 B ∼0.5 to B MG cm as laser preheat energy deposited increases from preheat ∼460 J to E preheat ∼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.
Optimizing the performance of the Magnetized Liner Inertial Fusion (MagLIF) platform on the Z pulsed power facility requires coupling greater than 2 kJ of preheat energy to an underdense fuel in the presence of an applied axial magnetic field ranging from 10 to 30 T. Achieving the suggested optimal preheat energies has not been experimentally achieved so far. In this work, we explore the preheat design space for cryogenically cooled MagLIF targets, which represent a viable candidate for increasing preheat energies. Using 2D and 3D HYDRA MHD simulations, we first discuss the various physical effects that occur during laser preheat, such as laser energy deposition, self-focusing, and filamentation. After identifying the changes that different phase plates, gas-fill densities, and magnetic fields bring to the aforementioned physical effects, we, then, consider higher laser energies that are achievable with modest upgrades to the Z Beamlet laser. Lastly, with a 6.0-kJ upgraded laser, 3D calculations suggest that it is possible to deliver 4.25 kJ into the MagLIF fuel, resulting in an expected deuterium neutron yield of YDD ≃ 1.5 × 1014, or roughly 50 kJ of DT equivalent yield, at 20-MA current drive. This represents a 10-fold increase in the currently achieved yields for MagLIF.
The magnetized liner inertial fusion (MagLIF) scheme relies on coupling laser energy into an underdense fuel raising the fuel adiabat at the start of the implosion. To deposit energy into the fuel, the laser must first penetrate a laser entrance hole (LEH) foil which can be a significant energy sink and introduce mix. In this paper, we report on experiments investigating laser energy coupling into MagLIF-relevant gas cell targets with LEH foil thicknesses varying from 0.5 μm to 3 μm. Two-dimensional (2D) axisymmetric simulations match the experimental results well for 0.5 μm and 1 μm thick LEH foils but exhibit whole-beam self-focusing and excessive penetration of the laser into the gas for 2 μm and 3 μm thick LEH foils. Better agreement for the 2 μm-thick foil is found when using a different thermal conductivity model in 2D simulations, while only 3D Cartesian simulations come close to matching the 3 μm-thick foil experiments. The study suggests that simulations may over-predict the tendency for the laser to self-focus during MagLIF preheat when thicker LEH foils are used. This effect is pronounced with 2D simulations where the azimuthally symmetric density channel effectively self-focuses the rays that are forced to traverse the center of the plasma. The extra degree of freedom in 3D simulations significantly reduces this effect. The experiments and simulations also suggest that, in this study, the amount of energy coupled into the gas is highly correlated with the laser propagation length regardless of the LEH foil thickness.
We present experimental results from the first systematic study of performance scaling with drive parameters for a magnetoinertial fusion concept. In magnetized liner inertial fusion experiments, the burn-averaged ion temperature doubles to 3.1 keV and the primary deuterium-deuterium neutron yield increases by more than an order of magnitude to 1.1×1013 (2 kJ deuterium-tritium equivalent) through a simultaneous increase in the applied magnetic field (from 10.4 to 15.9 T), laser preheat energy (from 0.46 to 1.2 kJ), and current coupling (from 16 to 20 MA). Individual parametric scans of the initial magnetic field and laser preheat energy show the expected trends, demonstrating the importance of magnetic insulation and the impact of the Nernst effect for this concept. A drive-current scan shows that present experiments operate close to the point where implosion stability is a limiting factor in performance, demonstrating the need to raise fuel pressure as drive current is increased. Simulations that capture these experimental trends indicate that another order of magnitude increase in yield on the Z facility is possible with additional increases of input parameters.
We present two-dimensional temperature measurements of magnetized and unmagnetized plasma experiments performed at Z relevant to the preheat stage in magnetized liner inertial fusion. The deuterium gas fill was doped with a trace amount of argon for spectroscopy purposes, and time-integrated spatially resolved spectra and narrow-band images were collected in both experiments. The spectrum and image data were included in two separate multiobjective analysis methods to extract the electron temperature spatial distribution Te(r,z). The results indicate that the magnetic field increases Te, the axial extent of the laser heating, and the magnitude of the radial temperature gradients. Comparisons with simulations reveal that the simulations overpredict the extent of the laser heating and underpredict the temperature. Temperature gradient scale lengths extracted from the measurements also permit an assessment of the importance of nonlocal heat transport.
Prior to implosion in Magnetized Liner Inertial Fusion (MagLIF), the fuel is heated to temperatures on the order of several hundred eV with a multi-kJ, multi-ns laser pulse. We present two laser heated plasma experiments, relevant to the MagLIF preheat stage, performed at Z with beryllium liners filled with deuterium and a trace amount of argon. In one experiment, there is no magnetic field and, in the other, the liner and fuel are magnetized with an 8.5 T axial magnetic field. The recorded time integrated, spatially resolved spectra of the Ar K-shell emission are sensitive to electron temperature Te. Individual analysis of the spatially resolved spectra produces electron temperature distributions Te(z) that are resolved along the axis of laser propagation. In the experiment with magnetic field, the plasma reaches higher temperatures and the heated region extends deeper within the liner than in the unmagnetized case. Radiation magnetohydrodynamics simulations of the experiments are presented and post-processed. A comparison of the results from experimental and simulated data reveals that the simulations underpredict Te in both cases but the differences are larger in the case with magnetic field.
A multi-frame shadowgraphy diagnostic has been developed and applied to laser preheat experiments relevant to the Magnetized Liner Inertial Fusion (MagLIF) concept. The diagnostic views the plasma created by laser preheat in MagLIF-relevant gas cells immediately after the laser deposits energy as well as the resulting blast wave evolution later in time. The expansion of the blast wave is modeled with 1D radiation-hydrodynamic simulations that relate the boundary of the blast wave at a given time to the energy deposited into the fuel. This technique is applied to four different preheat protocols that have been used in integrated MagLIF experiments to infer the amount of energy deposited by the laser into the fuel. The results of the integrated MagLIF experiments are compared with those of two-dimensional LASNEX simulations. The best performing shots returned neutron yields ∼40-55% of the simulated predictions for three different preheat protocols.
A series of Magnetized Liner Inertial Fusion (MagLIF) experiments have been conducted in order to investigate the mix introduced from various target surfaces during the laser preheat stage. The material mixing was measured spectroscopically for a variety of preheat protocols by employing mid-atomic number surface coatings applied to different regions of the MagLIF target. The data show that the material from the top cushion region of the target can be mixed into the fuel during preheat. For some preheat protocols, our experiments show that the laser-entrance-hole (LEH) foil used to contain the fuel can be transported into the fuel a significant fraction of the stagnation length and degrade the target performance. Preheat protocols using pulse shapes of a few-ns duration result in the observable LEH foil mix both with and without phase-plate beam smoothing. In order to reduce this material mixing, a new capability was developed to allow for a low energy (∼20 J) laser pre-pulse to be delivered early in time (-20 ns) before the main laser pulse (∼1.5 kJ). In experiments, this preheat protocol showed no indications of the LEH foil mix. The experimental results are broadly in agreement with pre-shot two-dimensional HYDRA simulations that helped motivate the development of the early pre-pulse capability.
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.
We recently developed a one-dimensional imager of neutrons on the Z facility. The instrument is designed for Magnetized Liner Inertial Fusion (MagLIF) experiments, which produce D-D neutrons yields of ∼3 × 1012. X-ray imaging indicates that the MagLIF stagnation region is a 10-mm long, ∼100-μm diameter column. The small radial extents and present yields precluded useful radial resolution, so a one-dimensional imager was developed. The imaging component is a 100-mm thick tungsten slit; a rolled-edge slit limits variations in the acceptance angle along the source. CR39 was chosen as a detector due to its negligible sensitivity to the bright x-ray environment in Z. A layer of high density poly-ethylene is used to enhance the sensitivity of CR39. We present data from fielding the instrument on Z, demonstrating reliable imaging and track densities consistent with diagnosed yields. For yields ∼3 × 1012, we obtain resolutions of ∼500 μm.
Laser-driven magnetized liner inertial fusion (MagLIF) is being developed on the OMEGA Laser System to study scaling. MagLIF targets require a preheat laser entrance window that can hold the gas in the target yet allow sufficient laser energy to enter the gas. For OMEGA MagLIF targets, 1.8-μm-thick polyimide foils were found to be sufficient to hold a fuel pressure of up to 14 atm. Transmission and reflection of an OMEGA beam incident on such foils were measured with a calorimeter and time-resolved spectrometers for 2.5-ns square-shaped pulses, with energies from 60 to 200 J, focused to intensities from 0.65 to 2.2 × 1014 W/cm2. The laser energy transmitted in every case exceeded that required to achieve the goal of preheating the gas to 100 eV. The time-resolved measurements showed an initial period with very low, decreasing transmission, the duration of which decreased with increasing intensity, followed by a rapid transition to full transmission, accompanied by brief sidescattering of the transmitted light with a significant red shift. Reflection was always negligible. Two-dimensional radiation-hydrodynamic simulations, using 3-D ray tracing with inverse bremsstrahlung energy deposition, did not capture the rapid transition to full transmission, showing instead a slow increase in transmission, without significant sidescatter or red shift. We propose that full transmission is achieved by self-focusing followed by ponderomotive blowout of the plasma.
The MagLIF campaign operated by Sandia conducted a total of four shot days in FY17 (one on OMEGA and three on OMEGA-EP) aimed at characterizing the laser heating of underdense plasmas (D2, Ar) at parameters that are relevant to the Magnetized Liner Inertial Fusion (MagLIF) ICF scheme being pursued at Sandia National Laboratories [1] [2]. MagLIF combines fuel preheat, magnetization and pulsed power implosion to significantly relax the implosion velocity and pR required for self-heating. Effective fuel preheat requires coupling several kJ of laser energy into the 10 mm long, underdense (typically ne/nc<0.1) fusion fuel without introducing significant mix. Barriers to achieving this include the presence laser plasma instabilities (LPI) as laser energy is coupled to the initially cold fuel, and the presence of a thin, polyimide laser entrance hole (LEH) foil that the laser must pass through and that can be a significant perturbation.
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 density using much thicker windows (1.5-3.5 μm) than the sub-micron thick windows of traditional ICF hohlraum targets. This article describes the Pecos target area at Sandia National Laboratories using the Z-Beamlet Laser Facility [Rambo et al., Appl. Opt. 44(12), 2421 (2005)] as a platform to study laser induced pre-heat for magneto-inertial fusion targets, and the related progress for Sandia's MagLIF program. Forward and backward scattered light were measured and minimized at larger spatial scales with lower densities, temperatures, and powers compared to LPI studies available in literature.
Double-shell Ar gas puff implosions driven by 16.5±0.5 MA on the Z generator at Sandia National Laboratories are very effective emitters of Ar K-shell radiation (photon energy >3 keV), producing yields of 330 ± 9% kJ (B. Jones et al., Phys. Plasmas, 22, 020706, 2015). In addition, previous simulations and experiments have reported dramatic increases in K-shell yields when adding an on-axis jet to double shell gas puffs for some configurations.
Radiation-magnetohydrodynamic simulations using the non-local thermodynamic equilibrium Mach2-Tabular Collisional-Radiative Equilibrium code in (r, z) geometry are performed for two pairs of recent Ar gas-puff Z-pinch experiments on the refurbished Z generator with an 8 cm diameter nozzle. One pair of shots had an outer-to-inner shell mass ratio of 1:1.6 and a second pair had a ratio of 1:1. In each pair, one of the shots had a central jet. The experimental trends in the Ar K-shell yield and power are reproduced in the calculations. However, the K-shell yield and power are significantly lower than the other three shots for the case of a double-shell puff of 1:1 mass ratio and no central jet configuration. Further simulations of a hypothetical experiment with the same relative density profile of this configuration, but higher total mass, show that the coupled energy from the generator and the K-shell yield can be increased to levels achieved in the other three configurations, but not the K-shell power. Based on various measures of effective plasma radius, the compression in the 1:1 mass ratio and no central jet case is found to be less because the plasma inside the magnetic piston is hotter and of lower density. Because of the reduced density, and the reduced radiation cooling (which is proportional to the square of the density), the core plasma is hotter. Consequently, for the 1:1 outer-to-inner shell mass ratio, the load mass controls the yield and the center jet controls the power.
The MAGnetized Liner Inertial Fusion (MagLIF) scheme has achieved thermonuclear fusion yields on the Z Facility by imploding a cylindrical liner filled with D2 fuel that is preheated with a multi-kJ laser and pre-magnetized with an axial Bz=10 T magnetic field. Preheating (Te = 100-200 eV) and pre-magnetizing (10-30 T) the fuel serves to reduce the implosion velocity required to achieve multi-keV fusion-relevant temperatures at stagnation with a modest radial convergence. The challenge of fuel preheat in MagLIF is to deposit multiple-kJ of energy into the underdense (ne/nc<0.1) fuel over ~10 mm target length efficiently and without introducing contaminants. Once the fuel is heated the applied axial magnetic field (ωceτe ~ 10) needs to suppress electron thermal conduction sufficiently to prevent unacceptable heat losses to the liner walls. In this LDRD we investigated laser energy deposition at two facilities: The OMEGA-EP laser at the Laboratory for Laser Energetics and the Z-beamlet laser at Sandia National Labs utilizing the PECOS chamber. Multiple experiments were carried out investigating laser transmission through LEH foils, laser heating of underdense gasses and the effects of magnetization on laser preheat. The studies find that magneto-hydrodynamic simulations are able to reproduce energy deposition at MagLIF-like conditions but that at the intensities currently used to preheat MagLIF significant laser plasma instabilities (LPI) occur which partly explain the inability of codes to reproduce previous MagLIF preheat studies. The experiments find that reducing the intensity and smoothing the beam dramatically reduces the amount of stimulated Brillouin backscatter and produces deposition profiles more similar to those produced in simulations. The experiments have provided a large and varied dataset that can be compared to simulations. As part of the LDRD new experimental capabilities have also been developed that will be used to design future MagLIF integrated experiments and investigate fuel magnetization.
Multi-keV X-ray radiation sources have a wide range of applications, from biomedical studies and research on thermonuclear fusion to materials science and astrophysics. The refurbished Z pulsed power machine at the Sandia National Laboratories produces intense multi-keV X-rays from argon Z-pinches, but for a krypton Z-pinch, the yield decreases much faster with atomic number ZA than similar sources on the National Ignition Facility (NIF) laser at the Lawrence Livermore National Laboratory. To investigate whether fundamental energy deposition differences between pulsed power and lasers could account for the yield differences, we consider the Kr plasma on the two machines. The analysis assumes the plasma not in local thermodynamic equilibrium, with a detailed coupling between the hydrodynamics, the radiation field, and the ionization physics. While for the plasma parameters of interest the details of krypton's M-shell are not crucial, both the L-shell and the K-shell must be modeled in reasonable detail, including the state-specific dielectronic recombination processes that significantly affect Kr's ionization balance and the resulting X-ray spectrum. We present a detailed description of the atomic model, provide synthetic K- and L-shell spectra, and compare these with the available experimental data from the Z-machine and from NIF to show that the K-shell yield behavior versus ZA is indeed related to the energy input characteristics. This work aims at understanding the probable causes that might explain the differences in the X-ray conversion efficiencies of several radiation sources on Z and NIF.
Several magnetized liner inertial fusion (MagLIF) experiments have been conducted on the Z accelerator at Sandia National Laboratories since late 2013. Measurements of the primary DD (2.45 MeV) neutrons for these experiments suggest that the neutron production is thermonuclear. Primary DD yields up to 3e12 with ion temperatures ∼2-3 keV have been achieved. Measurements of the secondary DT (14 MeV) neutrons indicate that the fuel is significantly magnetized. Measurements of down-scattered neutrons from the beryllium liner suggest ρRliner∼1g/cm2. Neutron bang times, estimated from neutron time-of-flight (nTOF) measurements, coincide with peak x-ray production. Plans to improve and expand the Z neutron diagnostic suite include neutron burn-history diagnostics, increased sensitivity and higher precision nTOF detectors, and neutron recoil-based yield and spectral measurements.
Sandia National Laboratories is pursuing a variation of Magneto-Inertial Fusion called Magnetized Liner Inertial Fusion, or MagLIF. The MagLIF approach requires magnetization of the deuterium fuel, which is accomplished by an initial external B-Field and laser-driven pre-heat. Although magnetization is crucial to the concept, it is challenging to couple sufficient energy to the fuel, since laser-plasma instabilities exist, and a compromise between laser spot size, laser entrance window thickness, and fuel density must be found. Ultimately, nonlinear processes in laser plasma interaction, or laser-plasma instabilities (LPI), complicate the deposition of laser energy by enhanced absorption, backscatter, filamentation and beam-spray. We determine and discuss key LPI processes and mitigation methods. Results with and without improvement measures are presented.
We report experimental results and simulations showing efficient laser energy coupling into plasmas at conditions relevant to the magnetized liner inertial fusion (MagLIF) concept. In MagLIF, to limit convergence and increase the hydrodynamic stability of the implosion, the fuel must be efficiently preheated. To determine the efficiency and physics of preheating by a laser, an Ar plasma with ne/ncrit∼0.04 is irradiated by a multi-ns, multi-kJ, 0.35-μm, phase-plate-smoothed laser at spot-averaged intensities ranging from 1.0×1014 to 2.5×1014W/cm2 and pulse widths from 2 to 10 ns. Time-resolved x-ray images of the laser-heated plasma are compared to two-dimensional radiation-hydrodynamic simulations that show agreement with the propagating emission front, a comparison that constrains laser energy deposition to the plasma. The experiments show that long-pulse, modest-intensity (I=1.5×1014W/cm2) beams can efficiently couple energy (∼82% of the incident energy) to MagLIF-relevant long-length (9.5 mm) underdense plasmas. The demonstrated heating efficiency is significantly higher than is thought to have been achieved in early integrated MagLIF experiments [A. B. Sefkow, Phys. Plasmas 21, 072711 (2014)10.1063/1.4890298].
In this study, 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.
We present a platform on the OMEGA EP Laser Facility that creates and diagnoses the conditions present during the preheat stage of the MAGnetized Liner Inertial Fusion (MagLIF) concept. Experiments were conducted using 9 kJ of 3ω (355 nm) light to heat an underdense deuterium gas (electron density: 2.5×1020 cm-3=0.025 of critical density) magnetized with a 10 T axial field. Results show that the deuterium plasma reached a peak electron temperature of 670 ± 140 eV, diagnosed using streaked spectroscopy of an argon dopant. The results demonstrate that plasmas relevant to the preheat stage of MagLIF can be produced at multiple laser facilities, thereby enabling more rapid progress in understanding magnetized preheat. Results are compared with magneto-radiation-hydrodynamics simulations, and plans for future experiments are described.
Velocity Interferometer System for Any Reflector (VISAR) [Barker and Hollenbach, J. Appl. Phys. 43, 4669 (1972)] is a well-known diagnostic that is employed on many shock physics and pulsed-power experiments. With the VISAR diagnostic, the velocity on the surface of any metal flyer can be found. For most experiments employing VISAR, either a kinetic pressure [Grady, Mech. Mater. 29, 181 (1998)] or a magnetic pressure [Lemke et al., Intl J. Impact Eng. 38, 480 (2011)] drives the motion of the flyer. Moreover, reliable prediction of the time-dependent pressure is often a critical component to understanding the physics of these experiments. Although VISAR can provide a precise measurement of a flyer’s surface velocity, the real challenge of this diagnostic implementation is using this velocity to unfold the time-dependent pressure. The purpose of this study is to elucidate a new method for quickly and reliably unfolding VISAR data.
Large diameter multi-shell gas puffs rapidly imploded by high current (~20 MA, ~100 ns) on the Z generator of Sandia National Laboratories are able to produce high-intensity Krypton K-shell emission at ~13 keV. Efficiently radiating at these high photon energies is a significant challenge which requires the careful design and optimization of the gas distribution. To facilitate this, we hydrodynamically model the gas flow out of the nozzle and then model its implosion using a 3-dimensional resistive, radiative MHD code (GORGON). This approach enables us to iterate between modeling the implosion and gas flow from the nozzle to optimize radiative output from this combined system. Furthermore, guided by our implosion calculations, we have designed gas profiles that help mitigate disruption from Magneto-Rayleigh–Taylor implosion instabilities, while preserving sufficient kinetic energy to thermalize to the high temperatures required for K-shell emission.
In magnetizing the fusion fuel in inertial confinement fusion (ICF) systems, we found that 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 InertialFusion experiments conducted on the Z machine at Sandia National Laboratories. Furthermore, 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. Lastly, this is the first experimental verification of charged burn product magnetization facilitated by compression of an initial seed magnetic flux.
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.
In this study, the magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas17, 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-tritium neutrons were produced. Given that the areal density of the plasma was approximately 1–2 mg/cm2, this indicates the stagnation plasma was significantly magnetized, which is consistent with the anisotropy observed in the deuterium-tritium neutron spectra. Control experiments where the laser and/or magnetic field were not utilized failed to produce stagnation temperatures greater than 1 keV and primary deuterium-deuterium yields greater than 1010. An additional control experiment where the fuel contained a sufficient dopant fraction to substantially increase radiative losses also failed to produce a relevant stagnation temperature. The results of these experiments are consistent with a thermonuclear neutron source.
The standard approaches to inertial confinement fusion (ICF) rely on implosion velocities greater than 300 km/s and spherical convergence to achieve the high fuel temperatures (T > 4 keV) and areal densities (ρr > 0.3 g/cm2) required for ignition1. Such high velocities are achieved by heating the outside surface of a spherical capsuleeither directly with a large number of laser beams (Direct Drive) or with x-rays generated within a hohlraum (Indirect Drive). A much more energetically efficient approach is to use the magnetic pressure generated by a pulsed power machine to directly drive an implosion. In this approach 5-10% of the stored energy can be converted to the implosion of a metal tube generally referred to as a “liner”. However, the implosion velocity is not very high 70-100 km/s and the convergence is cylindrical (rather than spherical) making it more difficult to achieve the high temperatures and areal densities needed for ignition.
Argon gas puffs have produced 330kJ ± 9% of x-ray radiation above 3keV photon energy in fast z-pinch implosions, with remarkably reproducible K-shell spectra and power pulses. This reproducibility in x-ray production is particularly significant in light of the variations in instability evolution observed between experiments. Soft x-ray power measurements and K-shell line ratios from a time-resolved spectrum at peak x-ray power suggest that plasma gradients in these high-mass pinches may limit the K-shell radiating mass, K-shell power, and K-shell yield from high-current gas puffs.
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 axial magnetic field of 10 T is heated by Z beamlet, a 2.5 kJ, 1 TW laser, and magnetically imploded by a 19 MA current with 100 ns rise time 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 Te ≈ Ti, and produces up to 2e12 thermonuclear DD neutrons. In this study, 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. The number of secondary deuterium-tritium neutrons observed was greater than 1010, indicating significant fuel magnetization given that the estimated radial areal density of the plasma is only 2 mg/cm2.
Radiation magnetohydrodynamic r-z simulations are performed of recent Ar shots on the refurbished Z generator to examine the effective ion temperature as determined from the observed line width of the He-γ line. While many global radiation properties can be matched to experimental results, the Doppler shifts due to velocity gradients at stagnation cannot reproduce the large experimentally determined width corresponding to an effective ion temperature of 50 keV. Ion viscous heating or magnetic bubbles are considered, but understanding the width remains an unsolved challenge.
