Seeding the Electrothermal Instability through a Three-Dimensional, Nonlinear Perturbation

Electrothermal instability plays an important role in applications of current-driven metal, creating striations (which seed the magneto-Rayleigh-Taylor instability) and filaments (which provide a more rapid path to plasma formation). However, the initial formation of both structures is not well understood. Simulations show for the first time how a commonly occurring isolated defect transforms into the larger striation and filament, through a feedback loop connecting current and electrical conductivity. Simulations have been experimentally validated using defect-driven self-emission patterns.

Three-dimensional feedback processes in current-driven metal

Using three-dimensional (3D) magnetohydrodynamic simulations, we study how a pit on a metal surface evolves when driven by intense electrical current density j. Redistribution of j around the pit initiates a feedback loop: j both reacts to and alters the electrical conductivity σ, through Joule heating and hydrodynamic expansion, so that j and σ are constantly in flux. Thus, the pit transforms into larger striation and filament structures predicted by the electrothermal instability theory. Both structures are important in applications of current-driven metal: The striation constitutes a density perturbation that can seed the magneto-Rayleigh-Taylor instability, while the filament provides a more rapid path to plasma formation, through 3D j redistribution. Simulations predict distinctive self-emission patterns, thus allowing for experimental observation and comparison.

Harmonic Generation and Inverse Cascade in the z-Pinch Driven, Preseeded Multimode, Magneto-Rayleigh-Taylor Instability

The magneto-Rayleigh-Taylor instability (MRTI) plays an essential role in astrophysical systems and in magneto-inertial fusion, where it is known to be an important degradation mechanism of confinement and target performance. In this Letter, we show for the first time experimental evidence of mode mixing and the onset of an inverse-cascade process resulting from the nonlinear coupling of two discrete preseeded axial modes (400- and 550-μm wavelengths) on an Al liner that is magnetically imploded using the 20-MA, 100-ns rise-time Z Machine at Sandia National Laboratories. Four radiographs captured the temporal evolution of the MRTI. We introduce a novel unfold technique to analyze the experimental radiographs and compare the results to simulations and to a weakly nonlinear model. We find good quantitative agreement with simulations using the radiation magnetohydrodynamics code hydra. Spectral analysis of the MRTI time evolution obtained from the simulations shows evidence of harmonic generation, mode coupling, and the onset of an inverse-cascade process. The experiments provide a benchmark for future work on the MRTI and motivate the development of new analytical theories to better understand this instability.

Performance Scaling in Magnetized Liner Inertial Fusion Experiments

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 1.1×10^{13} (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.

A new time and space resolved transmission spectrometer for research in inertial confinement fusion and radiation source development

We describe the design and function of a new time and space resolved x-ray spectrometer for use in Z-pinch inertial confinement fusion and radiation source development experiments. The spectrometer is designed to measure x-rays in the range of 0.5-1.5 Å (8-25 keV) with a spectral resolution λ/Δλ ∼ 400. The purpose of this spectrometer is to measure the time- and one-dimensional space-dependent electron temperature and density during stagnation. These relatively high photon energies are required to escape the dense plasma created at stagnation and to obtain sensitivity to electron temperatures ≳3 keV. The spectrometer is of the Cauchois type, employing a large 30 × 36 mm², transmissive quartz optic for which a novel solid beryllium holder was designed. The performance of the crystal was verified using offline tests, and the integrated system was tested using experiments on the Z pulsed power accelerator.

Experimental Demonstration of the Stabilizing Effect of Dielectric Coatings on Magnetically Accelerated Imploding Metallic Liners

Enhanced implosion stability has been experimentally demonstrated for magnetically accelerated liners that are coated with 70  μm of dielectric. The dielectric tamps liner-mass redistribution from electrothermal instabilities and also buffers coupling of the drive magnetic field to the magneto-Rayleigh-Taylor instability. A dielectric-coated and axially premagnetized beryllium liner was radiographed at a convergence ratio [CR=Rin,0/Rin(z,t)] of 20, which is the highest CR ever directly observed for a strengthless magnetically driven liner. The inner-wall radius Rin(z,t) displayed unprecedented uniformity, varying from 95 to 130  μm over the 4.0 mm axial height captured by the radiograph.

Analysis and implementation of a space resolving spherical crystal spectrometer for x-ray Thomson scattering experiments

The application of a space-resolving spectrometer to X-ray Thomson Scattering (XRTS) experiments has the potential to advance the study of warm dense matter. This has motivated the design of a spherical crystal spectrometer, which is a doubly focusing geometry with an overall high sensitivity and the capability of providing high-resolution, space-resolved spectra. A detailed analysis of the image fluence and crystal throughput in this geometry is carried out and analytical estimates of these quantities are presented. This analysis informed the design of a new spectrometer intended for future XRTS experiments on the Z-machine. The new spectrometer collects 6 keV x-rays with a spherically bent Ge (422) crystal and focuses the collected x-rays onto the Rowland circle. The spectrometer was built and then tested with a foam target. The resulting high-quality spectra prove that a spherical spectrometer is a viable diagnostic for XRTS experiments.

Pulsed-coil magnet systems for applying uniform 10-30 T fields to centimeter-scale targets on Sandia's Z facility

Sandia has successfully integrated the capability to apply uniform, high magnetic fields (10-30 T) to high energy density experiments on the Z facility. This system uses an 8-mF, 15-kV capacitor bank to drive large-bore (5 cm diameter), high-inductance (1-3 mH) multi-turn, multi-layer electromagnets that slowly magnetize the conductive targets used on Z over several milliseconds (time to peak field of 2-7 ms). This system was commissioned in February 2013 and has been used successfully to magnetize more than 30 experiments up to 10 T that have produced exciting and surprising physics results. These experiments used split-magnet topologies to maintain diagnostic lines of sight to the target. We describe the design, integration, and operation of the pulsed coil system into the challenging and harsh environment of the Z Machine. We also describe our plans and designs for achieving fields up to 20 T with a reduced-gap split-magnet configuration, and up to 30 T with a solid magnet configuration in pursuit of the Magnetized Liner Inertial Fusion concept.

Understanding fuel magnetization and mix using secondary nuclear reactions in magneto-inertial fusion

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.

Experimental demonstration of fusion-relevant conditions in magnetized liner inertial fusion

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).

X-ray power and yield measurements at the refurbished Z machine

Advancements have been made in the diagnostic techniques to measure accurately the total radiated x-ray yield and power from z-pinch implosion experiments at the Z machine with high accuracy. The Z machine is capable of outputting 2 MJ and 330 TW of x-ray yield and power, and accurately measuring these quantities is imperative. We will describe work over the past several years which include the development of new diagnostics, improvements to existing diagnostics, and implementation of automated data analysis routines. A set of experiments on the Z machine were conducted in which the load and machine configuration were held constant. During this shot series, it was observed that the total z-pinch x-ray emission power determined from the two common techniques for inferring the x-ray power, a Kimfol filtered x-ray diode diagnostic and the total power and energy diagnostic, gave 449 TW and 323 TW, respectively. Our analysis shows the latter to be the more accurate interpretation. More broadly, the comparison demonstrates the necessity to consider spectral response and field of view when inferring x-ray powers from z-pinch sources.

Observations of modified three-dimensional instability structure for imploding z-pinch liners that are premagnetized with an axial field

Novel experimental data are reported that reveal helical instability formation on imploding z-pinch liners that are premagnetized with an axial field. Such instabilities differ dramatically from the mostly azimuthally symmetric instabilities that form on unmagnetized liners. The helical structure persists at nearly constant pitch as the liner implodes. This is surprising since, at the liner surface, the azimuthal drive field presumably dwarfs the axial field for all but the earliest stages of the experiment. These fundamentally 3D results provide a unique and challenging test for 3D-magnetohydrodynamics simulations.

Investigation of high-temperature bright plasma X-ray sources produced in 5-MA X-pinch experiments

Using solid, machined X-pinch targets driven by currents rising from 0 to 5-6 MA in 60 ns, we observed bright spots of 5-9-keV continuum radiation from 5±2-μm diameter regions. The >6-keV radiation is emitted in about 0.4 ns, and the bright spots are roughly 75 times brighter than the bright spots measured at 1 MA. A total x-ray power of 10 TW peak and yields of 165±20 kJ were emitted from a 3-mm height. The 3-5-keV continuum radiation had a 50-90-GW peak power and 0.15-0.35-kJ yield. The continuum is plausibly from a 1275±75-eV blackbody or alternatively from a 3500±500-eV bremsstrahlung source.

Penetrating radiography of imploding and stagnating beryllium liners on the Z accelerator

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

Compact, rugged in-chamber transmission spectrometers (7-28 keV) for the Sandia Z facility

We describe a pair of time-integrated transmission spectrometers that are designed to survey 7-28 keV (1.9 to 0.43 Å) x-ray photons produced by experiments on the Sandia Z pulsed power facility. Each spectrometer uses a quartz 10-11 crystal in a Cauchois geometry with a slit to provide spatial resolution along one dimension. The spectrometers are located in the harsh environment of the Z vacuum chamber, which necessitates that their design be compact and rugged. Example data from calibration tests and Z experiments are shown that illustrate the utility of the instruments.

Measurements of magneto-Rayleigh-Taylor instability growth during the implosion of initially solid Al tubes driven by the 20-MA, 100-ns Z facility

The first controlled experiments measuring the growth of the magneto-Rayleigh-Taylor instability in fast (∼100  ns) Z-pinch plasmas are reported. Sinusoidal perturbations on the surface of an initially solid Al tube (liner) with wavelengths of 25-400  μm were used to seed the instability. Radiographs with 15  μm resolution captured the evolution of the outer liner surface. Comparisons with numerical radiation magnetohydrodynamic simulations show remarkably good agreement down to 50  μm wavelengths.

Effects of mass ablation on the scaling of X-ray power with current in wire-array Z pinches

X-ray production by imploding wire-array Z pinches is studied using radiation magnetohydrodynamics simulation. It is found that the density distribution created by ablating wire material influences both x-ray power production, and how the peak power scales with applied current. For a given array there is an optimum ablation rate that maximizes the peak x-ray power, and produces the strongest scaling of peak power with peak current. This work is consistent with trends in wire-array Z pinch x-ray power scaling experiments on the Z accelerator.

2-20 ns interframe time 2-frame 6.151 keV x-ray imaging on the recently upgraded Z Accelerator: a progress report

When used for the production of an x-ray imaging backlighter source on Sandia National Laboratories' recently upgraded 26 MA Z Accelerator, the terawatt-class, multikilojoule, 526.57 nm Z-Beamlet laser (ZBL) [P. K. Rambo et al., Appl. Opt. 44, 2421 (2005)], in conjunction with the 6.151 keV (1s(2)-1s2p triplet line of He-like Mn) curved-crystal imager [D. B. Sinars et al., Rev. Sci. Instrum. 75, 3672 (2004); G. R. Bennett et al., Rev. Sci. Instrum. 77, 10E322 (2006)], is capable of providing a high quality x radiograph per Z shot for inertial confinement fusion (ICF), complex hydrodynamics, and other high-energy-density physics experiments. For example, this diagnostic has recently afforded microgram-scale mass perturbation measurements on an imploding ignition-scale 1 mg ICF capsule [G. R. Bennett et al., Phys. Rev. Lett. 99, 205003 (2007)], where the perturbation was initiated by a surrogate deuterium-tritium (DT) fuel fill tube. Using an angle-time multiplexing technique, ZBL now has the capability to provide two spatially and temporally separated foci in the Z chamber, allowing "two-frame" imaging to be performed, with an interframe time range of 2-20 ns. This multiplexing technique allows the full area of the four-pass amplifiers to be used for the two pulses, rather than split the amplifiers effectively into two rectangular sections, with one leg delayed with respect to the other, which would otherwise double the power imposed onto the various optics thereby halving the damage threshold, for the same irradiance on target. The 6.151 keV two frame technique has recently been used to image imploding wire arrays, using a 7.3 ns interframe time. The diagnostic will soon be converted to operate with p-rather than s-polarized laser light for enhanced laser absorption in the Mn foil, plus other changes (e.g., operation at the possibly brighter 6.181 keV Mn 1s(2)-1s2p singlet line), to increase x-ray yields. Also, a highly sensitive inline multiframe ultrafast (1 ns gate time) digital x-ray camera is being developed [G. R. Bennett et al., Rev. Sci. Instrum. 77, 10E322 (2006)] to extend the system to "four-frame" and markedly improve the signal-to-noise ratio. [At present, time-integrating Fuji BAS-TR2025 image plate (scanned with a Fuji BAS-5000 device) forms the time-integrated image-plane detector.].

Radiation energetics of ICF-relevant wire-array Z pinches

Short-implosion-time 20-mm diameter, 300-wire tungsten arrays maintain high peak x-ray powers despite a reduction in peak current from 19 to 13 MA. The main radiation pulse on tests with a 1-mm on-axis rod may be explained by the observable j x B work done during the implosion, but bare-axis tests require sub-mm convergence of the magnetic field not seen except perhaps in >1 keV emission. The data include the first measurement of the imploding mass density profile of a wire-array Z pinch that further constrains simulation models.

Wide band focusing x-ray spectrograph with spatial resolution

A new, wide spectral bandwidth x-ray spectrograph, the wide-bandwidth focusing spectrograph with spatial resolution (WB-FSSR), based on spherically bent mica crystals, is described. The wide bandwidth is achieved by combining three crystals to form a large aperture dispersive element. Since the WB-FSSR covers a wide spectral band, it is very convenient for application as a routine diagnostic tool in experiments in which the desired spectral coverage is different from one test to the next. The WB-FSSR has been tested in imploding wire-array experiments on a 1 MA pulsed power machine, and x-ray spectra were recorded in the 1-20 A spectral band using different orders of mica crystal reflection. Using a two mirror-symmetrically placed WB-FSSR configuration, it was also possible to distinguish between a real spectral shift and a shift of recorded spectral lines caused by the spatial distribution of the radiating plasma. A spectral resolution of about 2000 was demonstrated and a spatial resolution of approximately 100 microm was achieved in the spectral band of 5-10 A in second order of mica reflection. A simple method of numerical analysis of spectrograph capability is proposed.

Fill-tube-induced mass perturbations on x-ray-driven, ignition-scale, inertial-confinement-fusion capsule shells and the implications for ignition experiments

On the first inertial-confinement-fusion ignition facility, the target capsule will be DT filled through a long, narrow tube inserted into the shell. microg-scale shell perturbations Delta m' arising from multiple, 10-50 microm-diameter, hollow SiO2 tubes on x-ray-driven, ignition-scale, 1-mg capsules have been measured on a subignition device. Simulations compare well with observation, whence it is corroborated that Delta m' arises from early x-ray shadowing by the tube rather than tube mass coupling to the shell, and inferred that 10-20 microm tubes will negligibly affect fusion yield on a full-ignition facility.

Demonstration of radiation pulse shaping with nested-tungsten-wire-array pinches for high-yield inertial confinement fusion

Nested wire-array pinches are shown to generate soft x-ray radiation pulse shapes required for three-shock isentropic compression and hot-spot ignition of high-yield inertial confinement fusion capsules. We demonstrate a reproducible and tunable foot pulse (first shock) produced by interaction of the outer and inner arrays. A first-step pulse (second shock) is produced by inner array collision with a central CH2 foam target. Stagnation of the inner array at the axis produces the third shock. Capsules optimized for several of these shapes produce 290-900 MJ fusion yields in 1D simulations.

Direct experimental evidence for current-transfer mode operation of nested tungsten wire arrays at 16-19 MA

Nested tungsten wire arrays (20-mm on 12-mm diam.) are shown for the first time to operate in a current-transfer mode at 16-19 MA, even for azimuthal interwire gaps of 0.2 mm that are the smallest typically used for any array experiment. After current transfer, the inner wire array shows discrete wire ablation and implosion characteristics identical to that of a single array, such as axially nonuniform ablation, delayed acceleration, and trailing mass and current. The presence of trailing mass from the outer and the inner arrays may play a role in determining nested array performance.

Characteristics and scaling of tungsten-wire-array z -pinch implosion dynamics at 20 MA

We present observations for 20-MA wire-array z pinches of an extended wire ablation period of 57%+/-3% of the stagnation time of the array and non-thin-shell implosion trajectories. These experiments were performed with 20-mm-diam wire arrays used for the double- z -pinch inertial confinement fusion experiments [M. E. Cuneo, Phys. Rev. Lett. 88, 215004 (2002)] on the Z accelerator [R. B. Spielman, Phys. Plasmas 5, 2105 (1998)]. This array has the smallest wire-wire gaps typically used at 20 MA (209 microm ). The extended ablation period for this array indicates that two-dimensional (r-z) thin-shell implosion models that implicitly assume wire ablation and wire-to-wire merger into a shell on a rapid time scale compared to wire acceleration are fundamentally incorrect or incomplete for high-wire-number, massive (>2 mg/cm) , single, tungsten wire arrays. In contrast to earlier work where the wire array accelerated from its initial position at approximately 80% of the stagnation time, our results show that very late acceleration is not a universal aspect of wire array implosions. We also varied the ablation period between 46%+/-2% and 71%+/-3% of the stagnation time, for the first time, by scaling the array diameter between 40 mm (at a wire-wire gap of 524 mum ) and 12 mm (at a wire-wire gap of 209 microm ), at a constant stagnation time of 100+/-6 ns . The deviation of the wire-array trajectory from that of a thin shell scales inversely with the ablation rate per unit mass: f(m) proportional[dm(ablate)/dt]/m(array). The convergence ratio of the effective position of the current at peak x-ray power is approximately 3.6+/-0.6:1 , much less than the > or = 10:1 typically inferred from x-ray pinhole camera measurements of the brightest emitting regions on axis, at peak x-ray power. The trailing mass at the array edge early in the implosion appears to produce wings on the pinch mass profile at stagnation that reduces the rate of compression of the pinch. The observation of precursor pinch formation, trailing mass, and trailing current indicates that all the mass and current do not assemble simultaneously on axis. Precursor and trailing implosions appear to impact the efficiency of the conversion of current (driver energy) to x rays. An instability with the character of an m = 0 sausage grows rapidly on axis at stagnation, during the rise time of pinch power. Just after peak power, a mild m = 1 kink instability of the pinch occurs which is correlated with the higher compression ratio of the pinch after peak power and the decrease of the power pulse. Understanding these three-dimensional, discrete-wire implosion characteristics is critical in order to efficiently scale wire arrays to higher currents and powers for fusion applications.

Mass-profile and instability-growth measurements for 300-wire Z-pinch implosions driven by 14-18 MA

We present the first comprehensive study of high wire-number, wire-array Z-pinch dynamics at 14-18 MA using x-ray backlighting and optical shadowgraphy diagnostics. The cylindrical arrays retain slowly expanding, dense wire cores at the initial position up to 60% of the total implosion time. Azimuthally correlated instabilities at the array edge appear during this stage which continue to grow in amplitude and wavelength after the start of bulk motion, resulting in measurable trailing mass that does not arrive on axis before peak x-ray emission.

Analysis of L -shell line spectra with 50-ps time resolution from Mo X -pinch plasmas

Mo wire X pinches typically emit several x-ray bursts from a bright spot near the crossing of the X -pinch wires. Streak camera images of L -shell line emission from Mo wire X pinches have been analyzed using a non-local thermodynamic equilibrium (NLTE) collisional-radiative atomic kinetics model, providing temperature and density profiles with approximately 50 ps time resolution over the approximately 350 ps x-ray bursts. In conjunction with nonspectroscopic measurements, the analysis is used to propose a picture of the dynamic evolution of the X -pinch plasma. The L -shell spectra from the first x-ray burst indicate an electron density near 10(22) cm(-3) and an electron temperature near 1 keV; subsequent x-ray bursts have L -shell spectra that indicate electron temperatures slightly above 1 keV and electron densities near 10(20) and 10(21) cm(-3). The size of the L -shell line-emitting region is estimated to be near 10 microm for the first x-ray burst and much larger for the later bursts. It is proposed that inner-shell excitation of low ionization stages of Mo in a microm -scale plasma region contributes to the observed radiation from the first micropinch, which typically emits a short burst of >3 keV radiation and has L -shell spectra characterized by broad spectral lines overlaying an intense continuum.

High energy density z-pinch plasma conditions with picosecond time resolution

Using an X-pinch configuration, we have determined that micropinches produced by exploding-wire z pinches can have densities approaching solid density and temperatures of 0.5-1.8 keV, depending upon the wire material used. These plasma parameters, determined from x-ray spectra recorded using an x-ray streak camera, vary drastically on time scales ranging from <10 to 100 ps. Computer simulations require radiation loss to reproduce the observed plasma implosion, suggesting that a radiative-collapse hypothesis for micropinch plasma formation may be correct.