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In this article, we derive the vacuum electric fields within specific cylindrically symmetric magnetically insulated transmission lines (MITLs) in the limit of an infinite speed of light for an arbitrary time-dependent current. We focus our attention on two types of MITLs: the radial MITL and a spherically curved MITL. We then simulate the motion of charged particles, such as electrons, present in these MITLs due to the vacuum fields. In general, the motion of charged particles due to the vacuum fields is highly nonlinear since the fields are nonlinear functions of spatial coordinates and depend on an arbitrary time-dependent current drive. Using guiding center theory, however, one can describe the gross particle kinetics using a combination of $\textbf {E} \times \textbf {B}$ and $\nabla B$ drifts. In addition, we compare our approximate inner MITL field models and particle kinetics with those from a fully electromagnetic simulation code. We find that the agreement between the approximate model and the electromagnetic simulations is excellent.

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.

A line VISAR (Velocity Interferometer System for Any Reflector) has been designed and commissioned at the Sandia National Laboratory’s Z-machine. The instrument consists of an F/2 collection system, beam transport, and an interferometer table that contains two Mach–Zehnder type interferometers and an eight channel Gated Optical Imaging (GOI) system. The VISAR probe laser operates at the 532 nm wavelength, and the GOI bandpass is 540–600 nm. The output of each interferometer is passed to an optical streak camera with four selectable sweep speeds. The system is designed with three interchangeable optics modules to select a full field of view of 1 mm, 2 mm, or 4 mm. The optical beam transport system connects the target image plane to the interferometers and the gated optical imagers. The target is integrated into a sacrificial final optics assembly that is integral to the transport beamline.

A challenge for the TW-class accelerators driving $Z$-pinch experiments, such as Sandia National Laboratories' $Z$ machine, is to efficiently couple power from multiple storage banks into a single multi-MA transmission line. The physical processes that lead to current loss are identified in new large-scale, multidimensional simulations of the $Z$ machine. Kinetic models follow the range of physics occurring during a pulse, from vacuum pulse propagation to charged-particle emission and magnetically-insulated current flow to electrode plasma expansion. Simulations demonstrate that current is diverted from the load through a combination of standard transport (uninsulated charged-particle flows) and anomalous transport. Standard transport occurs in regions where the electrode current density is a few $1{0}^{4}\ensuremath{-}{10}^{5}\text{ }\text{ }\mathrm{A}/{\mathrm{cm}}^{2}$ and current is diverted from the load via transport without magnetic insulation. In regions with electrode current density $g{10}^{6}\text{ }\text{ }\mathrm{A}/{\mathrm{cm}}^{2}$, electrode surface plasmas develop velocity-shear instabilities and a Hall-field-related transport which scales with electron density and may, therefore, lead to increased current loss.

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW “Z” pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22 MJ of energy stored in its capacitor banks into a current pulse that rises in 100 ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15 years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

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%.

We have developed a conceptual design of a next-generation pulsed-power accelerator that is optimized for advanced high-energy-density-physics experiments. The prime power source of the machine consists of 210 impedance-matched Marx generators (IMGs). Each IMG drives a 150-ns-long coaxial-transmission-line impedance transformer. The coaxial lines provide a minimum of 300 ns of transit-time isolation between each pair of IMGs. The lines in turn drive six radial-transmission-line impedance transformers, which transport the power generated by the IMGs to a six-level vacuum-insulator stack. The stack is connected to six conical outer magnetically insulated vacuum transmission lines (MITLs); these are joined in parallel at a 12-cm radius by a triple-post-hole vacuum convolute. The convolute sums the electrical currents at the outputs of the six outer MITLs, and delivers the combined current to a single short inner MITL. The inner MITL transmits the combined current to the accelerator's physics load. Since the accelerator would be the largest and most-powerful pulsed-power machine developed to date, we refer to it as Jupiter. The conceptual design of Jupiter is 72 m in diameter, stores 140 MJ of electrical energy, and generates 960 TW of peak electrical power at the output of the IMG system. The design delivers 2700 TW, 67 MA, and 9.2 MJ in a 110-ns pulse to a 0D magnetized-liner inertial-fusion (MagLIF) target. The principal goal of the design is to achieve high-yield thermonuclear fusion; i.e., a fusion yield that exceeds the energy initially stored by the accelerator's capacitors.

Magnetized Liner Inertial Fusion is a magneto-inertial fusion concept in which a metal cylindrical shell containing deuterium gas is axially magnetized, the fuel is heated with a laser, and the metal cylinder is imploded by the current of the Z Machine. In previous experiments, the axial magnetic field was 9-10 T, the laser energy absorbed in the fuel was less than 1 kJ, and the peak current flowing through the target was about 17 MA. These experiments produced fusion-relevant temperatures and densities at stagnation, up to 3e12 primary DD neutrons, and a magnetic field in the fuel sufficient to trap a sizable fraction of the fusion-produced tritons.

High current pulsed-power generators efficiently store and deliver magnetic energy to z-pinch targets. We review applications of magnetically driven implosions (MDIs) to inertial confinement fusion. Previous research on MDIs of wire-array z-pinches for radiation-driven indirect-drive target designs is summarized. Indirect-drive designs are compared with new targets that are imploded by direct application of magnetic pressure produced by the pulsed-power current pulse. We describe target design elements such as larger absorbed energy, magnetized and pre-heated fuel, and cryogenic fuel layers that may relax fusion requirements. These elements are embodied in the magnetized liner inertial fusion (MagLIF) concept [Slutz “Pulsed-power-driven cylindrical liner implosions of laser pre-heated fuel magnetized with an axial field,” Phys. Plasmas, 17, 056303 (2010), and Stephen A. Slutz and Roger A. Vesey, “High-Gain Magnetized Inertial Fusion,” Phys. Rev. Lett., 108, 025003 (2012)]. MagLIF is in the class of magneto-inertial fusion targets. In MagLIF, the large drive currents produce an azimuthal magnetic field that compresses cylindrical liners containing pre-heated and axially pre-magnetized fusion fuel. Scientific breakeven may be achievable on the Z facility with this concept. Simulations of MagLIF with deuterium-tritium fuel indicate that the fusion energy yield can exceed the energy invested in heating the fuel at a peak drive current of about 27 MA. Scientific breakeven does not require alpha particle self-heating and is therefore not equivalent to ignition. Capabilities to perform these experiments will be developed on Z starting in 2013. These simulations and predictions must be validated against a series of experiments over the next five years. Near-term experiments are planned at drive currents of 16 MA with D2 fuel. MagLIF increases the efficiency of coupling energy (=target absorbed energy/driver stored energy) to targets by 10-150X relative to indirect-drive targets. MagLIF also increases the absolute energy absorbed by the target by 10-50X relative to indirect-drive targets. These increases could lead to higher fusion gains and yields. Single-shot high yields are of great utility to national security missions. Higher efficiency and higher gains may also translate into more compelling (lower cost and complexity) fusion reactor designs. We will discuss the broad goals of the emerging research on the MagLIF concept and identify some of the challenges. We will also summarize advances in pulsed-power technology and pulsed-power driver architectures that double the efficiency of the driver.

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...

A critical component of the magnetically driven implosion experiments at Sandia National Laboratories is the delivery of high-current, 10s of MA, from the Z pulsed power facility to a target. In order to assess the performance of the experiment, it is necessary to measure the current delivered to the target. Recent Magnetized Liner Inertial Fusion (MagLIF) experiments have included velocimetry diagnostics, such as PDV (Photonic Doppler Velocimetry) or Velocity Interferometer System for Any Reflector, in the final power feed section in order to infer the load current as a function of time. However, due to the nonlinear volumetrically distributed magnetic force within a velocimetry flyer, a complete time-dependent load current unfold is typically a time-intensive process and the uncertainties in the unfold can be difficult to assess. In this paper, we discuss how a PDV diagnostic can be simplified to obtain a peak current by sufficiently increasing the thickness of the flyer. This effectively keeps the magnetic force localized to the flyer surface, resulting in fast and highly accurate measurements of the peak load current. In addition, we show the results of experimental peak load current measurements from the PDV diagnostic in recent MagLIF experiments.

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

Presently the Self Magnetic Pinch (SMP) diode is successfully utilized for flash radiography with pulsed power drivers. However, it is not capable of more than one pulse. Multi-pulse single-axis radiography is most preferred since it provides images of time-evolving dynamic targets. In an SMP diode, because the anode cathode (A-K) gap is very small (∼1–2 cm), the debris from the anode converter target arrives soon after the first pulse and completely destroy the cathode electron emitter, and thus the diode cannot produce a second pulse. We propose a feasibility study to scientifically evaluate the idea of decoupling the anode converter from the cathode electron emitter. This work will be based on two successful previous works we have accomplished: first, making a very small pencil-like beam in a magnetically immersed foilless diode (M.G. Mazarakis et al., Applied Physics Letters, 7, pp. 832 (1996)); and second, successfully demonstrating the two-pulse operation of a foilless diode with the RIIM accelerator (M. G. Mazarakis et al., Applied Physics 64 part I pp. 4815, (1988) Our approach will combine the above experimentally demonstrated successful work. The generated beam of 40–50 kA will be propagated in the same diode magnetic solenoid for a sufficient distance before striking the converter target. This way the diode could be multi-pulsed before the target debris reaches the cathode. Although the above describes the option of a foilless diode and a solenoidal transport system, a similar design could be made for a non-immersed low emittance 10 kA velvet emitter foilless diode.

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 paper is to elucidate a new method for quickly and reliably unfolding VISAR data.

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).

Magnetizing the fuel in inertial confinement fusion relaxes ignition requirements by reducing thermal conductivity and changing the physics of burn product confinement. Diagnosing the level of fuel magnetization during burn is critical to understanding target performance in magneto-inertial fusion (MIF) implosions. In pure deuterium fusion plasma, 1.01 MeV tritons are emitted during deuterium-deuterium fusion and can undergo secondary deuterium-tritium reactions before exiting the fuel. Increasing the fuel magnetization elongates the path lengths through the fuel of some of the tritons, enhancing their probability of reaction. Based on this feature, a method to diagnose fuel magnetization using the ratio of overall deuterium-tritium to deuterium-deuterium neutron yields is developed. Analysis of anisotropies in the secondary neutron energy spectra further constrain the measurement. Secondary reactions also are shown to provide an upper bound for the volumetric fuel-pusher mix in MIF. The analysis is applied to recent MIF experiments [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] on the Z Pulsed Power Facility, indicating that significant magnetic confinement of charged burn products was achieved and suggesting a relatively low-mix environment. Both of these are essential features of future ignition-scale MIF designs.

This paper analyzes the effects of an axial magnetic field on the magneto-Rayleigh-Taylor instability (MRT) of an imploding cylindrical liner. In recent MagLIF experiments with a premagnetized axial magnetic field [1], helical perturbations on the outer surface of the liner were found to persist despite the severe winding up of the magnetic field streamline. The inner surface of the liner exhibited improved integrity as a result of the premagnetized axial magnetic field. Here, we propose that the helical structure is the signature of the azimuthal m = 1 eigenmode with axial wavenumber k, so that the pitch angle of the helix, phi = arctan(m/kr) ∼ 1/kr. Here, r is the outer radius of the imploding liner at which the helical perturbations were observed [1]. This simple scaling shows that phi increases as the convergence ratio (CR) increases, i.e., as r decreases. It also qualitatively explains the evolution of phi in both the low CR and high CR shot data that were tabulated in [1]. We have extended our MRT theory for the slab geometry [2] to a cylindrical geometry, so as to include the coupling between MRT, the sausage mode (m = 0) and the kink mode (m = 1). The effect of feedthrough suppression by the strong axial magnetic field is noted. Instantaneous equilibrium profiles obtained from 1-D HYDRA runs have been applied to the aforementioned formulation.

The success of the Magnetized Liner Inertial Fusion (MagLIF) campaign requires successful mitigation of the Magneto-Rayleigh-Taylor instability (MRT). Initially, the exterior of the liner is MRT unstable; as the accelerated liner compresses a fill gas, it is eventually decelerated by the back pressure of the fill gas causing the inner surface to become MRT unstable. It is thought that feedthrough of MRT from the outer to inner surface can provide a seed for disruptive growth in the deceleration phase. A common method of studying MRT is by machining sinusoidal ripples on the exterior of metal targets (Al, Be in particular). This seeding provides a known wavelength for MRT whose growth can then be compared with linear theory. For the exterior of Al liners, linear MRT theory works quite well [1] and thus, feedthrough theory should apply equally well to the inner surface for an unshocked seeded liner. However, in most shots on the Z-machine a shock is driven through the liner. 2D HYDRA simulations show the shock is rippled with the seeded wavelength and imprints this ripple on the inner surface as it breaks-out. The amplitude of this ripple could be much larger than what would be expected from the feedthrough of MRT theory [2]. Thus, to study feedthrough directly either isentropic compression is required, or we must include the effect of the shock on feedthrough. We propose a simple model to determine the imprinted ripple amplitude from a shock and then calculate the evolution of the inner surface ripple using traditional MRT [2] and Richtmyer-Meshkov theory and then compare to 2D HYDRA results. This model allows for simultaneous study of outer/inner surface growth from an exterior seeded perturbation and includes the effect of feedthrough. We also examine the impact of axial magnetic fields and fill gases (cool and pre-heated) on feedthrough and shock imprinting by applying our model and compare with 2D simulations.

Summary form only given. This paper concentrates on the effects of cylindrical geometry on the magneto-Rayleigh-Taylor instability (MRT), a major concern in the magnetized liner inertial fusion concept (MagLIF) [1]. Several issues are being studied, such as the Bell-Plesset effect [2], the effects of magnetic shear and feedthrough [3], and the nonzero MRT growth rate that remains (but was hardly noticed) in the k = m = 0 limit in Harris' seminal paper on a cylindrical liner [4], where k and m are respectively the azimuthal and axial wavenumber. In liner implosions, such as those for MagLIF, significant magnetic shear can be present and feedthrough of MRT during compression can introduce unwanted fuel mix. We shall use recent simulation and experimental results [5] to compare with direct integration of the eigenvalue equation to investigate the importance of the cylindrical geometry in liner implosions. These analytic results may provide a parametric design in optimizing such parameters as the liner aspect ratio and magnetic field configuration.

Recent Magnetized Liner Inertial Fusion experiments at the Sandia National Laboratories Z pulsed power facility have featured a PDV (Photonic Doppler Velocimetry) diagnostic in the final power feed section for measuring load current. In this paper, we report on an anomalous pressure that is detected on this PDV diagnostic very early in time during the current ramp. Early time load currents that are greater than both B-dot upstream current measurements and existing Z machine circuit models by at least 1 MA would be necessary to describe the measured early time velocity of the PDV flyer. This leads us to infer that the pressure producing the early time PDV flyer motion cannot be attributed to the magnetic pressure of the load current but rather to an anomalous pressure. Using the MHD code ALEGRA, we are able to compute a time-dependent anomalous pressure function, which when added to the magnetic pressure of the load current, yields simulated flyer velocities that are in excellent agreement with the PDV mea...

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. Furthermore, 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.

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.

This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m = 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m = 0 sausage-MRT mode dominates at the main part of implosion. This analysis also sheds light on a puzzling feature in Harris' classic paper of MRT [E. G. Harris, Phys. Fluids 5, 1057 (1962)]. An attempt is made to interpret the persistence of the observed helical structures [Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] in terms of non-axisymmetric eigenmode.

Using the ideal magnetohydrodynamic model, we calculate the temporal evolution of initial ripples on the boundaries of a planar plasma slab that is subjected to the magneto-Rayleigh-Taylor instability. The plasma slab consists of three regions. We assume that in each region the plasma density is constant with an arbitrary value and the magnetic field is also constant with an arbitrary magnitude and an arbitrary direction parallel to the interfaces. Thus, the instability may be driven by a combination of magnetic pressure and kinetic pressure. The general dispersion relation is derived, together with the feedthrough factor between the two interfaces. The temporal evolution is constructed from the superposition of the eigenmodes. Previously established results are recovered in the various limits. Numerical examples are given on the temporal evolution of ripples on the interfaces of the finite plasma slab.