X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an ill-conditioned inverse problem, requiring regularization to obtain satisfactory results. Recently, deep learning has been adopted for tomographic reconstruction. Unlike iterative algorithms which require a distribution that is known a priori , deep reconstruction networks can learn a prior distribution through sampling the training distributions. In this work, we develop a Physics-assisted Generative Adversarial Network (PGAN), a two-step algorithm for tomographic reconstruction. In contrast to previous efforts, our PGAN utilizes maximum-likelihood estimates derived from the measurements to regularize the reconstruction with both known physics and the learned prior. Compared with methods with less physics assisting in training, PGAN can reduce the photon requirement with limited projection angles to achieve a given error rate. The advantages of using a physics-assisted learned prior in X-ray tomography may further enable low-photon nanoscale imaging.
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 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.
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.
The morphology of the stagnated plasma resulting from Magnetized Liner Inertial Fusion (MagLIF) is measured by imaging the self-emission x-rays coming from the multi-keV plasma, and the evolution of the imploding liner is measured by radiographs. Equivalent diagnostic response can be derived from integrated rad-MHD simulations from programs such as Hydra and Gorgon. There have been only limited quantitative ways to compare the image mor- phology, that is the texture, of simulations and experiments. We have developed a metric of image morphology based on the Mallat Scattering Transformation (MST), a transformation that has proved to be effective at distinguishing textures, sounds, and written characters. This metric has demonstrated excellent performance in classifying ensembles of synthetic stagnation images. We use this metric to quantitatively compare simulations to experimen- tal images, cross experimental images, and to estimate the parameters of the images with uncertainty via a linear regression of the synthetic images to the parameter used to generate them. This coordinate space has proved very adept at doing a sophisticated relative back- ground subtraction in the MST space. This was needed to compare the experimental self emission images to the rad-MHD simulation images. We have also developed theory that connects the transformation to the causal dynamics of physical systems. This has been done from the classical kinetic perspective and from the field theory perspective, where the MST is the generalized Green's function, or S-matrix of the field theory in the scale basis. From both perspectives the first order MST is the current state of the system, and the second order MST are the transition rates from one state to another. . An efficient, GPU accelerated, Python implementation of the MST was developed. Future applications are discussed.
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.
The formation of zonal flows from inhomogeneous drift-wave (DW) turbulence is often described using statistical theories derived within the quasilinear approximation. However, this approximation neglects wave-wave collisions. Hence, some important effects such as the Batchelor-Kraichnan inverse-energy cascade are not captured within this approach. Here we derive a wave kinetic equation that includes a DW collision operator in the presence of zonal flows. Our derivation makes use of the Weyl calculus, the quasinormal statistical closure and the geometrical-optics approximation. The obtained model conserves both the total enstrophy and energy of the system. The derived DW collision operator breaks down at the Rayleigh-Kuo threshold. This threshold is missed by homogeneous-turbulence theory but expected from a full-wave quasilinear analysis. In the future, this theory might help better understand the interactions between drift waves and zonal flows, including the validity domain of the quasilinear approximation that is commonly used in the literature.
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.
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.