A generalized approach to x-ray data modeling for high-energy-density plasma experiments.

Accurate understanding of x-ray diagnostics is crucial for both interpreting high-energy-density experiments and testing simulations through quantitative comparisons. X-ray diagnostic models are complex. Past treatments of individual x-ray diagnostics on a case-by-case basis have hindered universal diagnostic understanding. Here, we derive a general formula for modeling the absolute response of non-focusing x-ray diagnostics, such as x-ray imagers, one-dimensional space-resolved spectrometers, and x-ray power diagnostics. The present model is useful for both data modeling and data processing. It naturally accounts for the x-ray crystal broadening. The new model verifies that standard approaches for a crystal response can be good approximations, but they can underestimate the total reflectivity and overestimate spectral resolving power by more than a factor of 2 in some cases near reflectivity edge features. We also find that a frequently used, simplified-crystal-response approximation for processing spectral data can introduce an absolute error of more than an order of magnitude and the relative spectral radiance error of a factor of 3. The present model is derived with straightforward geometric arguments. It is more general and is recommended for developing a unified picture and providing consistent treatment over multiple x-ray diagnostics. Such consistency is crucial for reliable multi-objective data analyses.

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.

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).

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.

Compact hohlraum configuration with parallel planar-wire-array x-ray sources at the 1.7-MA Zebra generator.

A compact Z-pinch x-ray hohlraum design with parallel-driven x-ray sources is experimentally demonstrated in a configuration with a central target and tailored shine shields at a 1.7-MA Zebra generator. Driving in parallel two magnetically decoupled compact double-planar-wire Z pinches has demonstrated the generation of synchronized x-ray bursts that correlated well in time with x-ray emission from a central reemission target. Good agreement between simulated and measured hohlraum radiation temperature of the central target is shown. The advantages of compact hohlraum design applications for multi-MA facilities are discussed.

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.

Planar wire-array Z-pinch implosion dynamics and X-ray scaling at multiple-MA drive currents for a compact multisource hohlraum configuration.

An indirect drive configuration is proposed wherein multiple compact Z-pinch x-ray sources surround a secondary hohlraum. Planar compact wire arrays allow reduced primary hohlraum surface area compared to cylindrical loads. Implosions of planar arrays are studied at up to 15 TW x-ray power on Saturn with radiated yields exceeding the calculated kinetic energy, suggesting other heating paths. X-ray power and yield scaling studied from 1-6 MA motivates viewfactor modeling of four 6-MA planar arrays producing 90 eV radiation temperature in a secondary hohlraum.

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.

Compensation for time-dependent radiation-drive asymmetries in inertial-fusion capsules.

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

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.

Theoretical z -pinch scaling relations for thermonuclear-fusion experiments.

We have developed wire-array z -pinch scaling relations for plasma-physics and inertial-confinement-fusion (ICF) experiments. The relations can be applied to the design of z -pinch accelerators for high-fusion-yield (approximately 0.4 GJ/shot) and inertial-fusion-energy (approximately 3 GJ/shot) research. We find that (delta(a)/delta(RT)) proportional (m/l)1/4 (Rgamma)(-1/2), where delta(a) is the imploding-sheath thickness of a wire-ablation-dominated pinch, delta(RT) is the sheath thickness of a Rayleigh-Taylor-dominated pinch, m is the total wire-array mass, l is the axial length of the array, R is the initial array radius, and gamma is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product Rgamma is held constant the sheath thickness is, at sufficiently large values of m/l, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power P(r) proportional (I/tau(i))(3/2)Rlphigamma, where I is the peak pinch current, tau(i) is the pinch implosion time, and phi is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when 13 MA < or = I < or = 20 MA, 93 ns < or = tau(i) < or = 169 ns, 10 mm < or = R < or = 20 mm, 10 mm < or = l < or = 20 mm, and 2.0 mg/cm < or = m/l < or = 7.3 mg/cm. Assuming an ablation-dominated pinch and that Rlphigamma is held constant, we find that the x-ray-power efficiency eta(x) congruent to P(r)/P(a) of a coupled pinch-accelerator system is proportional to (tau(i)P(r)(7/9 ))(-1), where P(a) is the peak accelerator power. The pinch current and accelerator power required to achieve a given value of P(r) are proportional to tau(i), and the requisite accelerator energy E(a) is proportional to tau2(i). These results suggest that the performance of an ablation-dominated pinch, and the efficiency of a coupled pinch-accelerator system, can be improved substantially by decreasing the implosion time tau(i). For an accelerator coupled to a double-pinch-driven hohlraum that drives the implosion of an ICF fuel capsule, we find that the accelerator power and energy required to achieve high-yield fusion scale as tau(i)0.36 and tau(i)1.36, respectively. Thus the accelerator requirements decrease as the implosion time is decreased. However, the x-ray-power and thermonuclear-yield efficiencies of such a coupled system increase with tau(i). We also find that increasing the anode-cathode gap of the pinch from 2 to 4 mm increases the requisite values of P(a) and E(a) by as much as a factor of 2.

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.

X-ray emission from z pinches at 10 7 A: current scaling, gap closure, and shot-to-shot fluctuations.

We have measured the x-ray power and energy radiated by a tungsten-wire-array z pinch as a function of the peak pinch current and the width of the anode-cathode gap at the base of the pinch. The measurements were performed at 13- and 19-MA currents and 1-, 2-, 3-, and 4-mm gaps. The wire material, number of wires, wire-array diameter, wire-array length, wire-array-electrode design, normalized-pinch-current time history, implosion time, and diagnostic package were held constant for the experiments. To keep the implosion time constant, the mass of the array was increased as I2 (i.e., the diameter of each wire was increased as I), where I is the peak pinch current. At 19 MA, the mass of the 300-wire 20-mm-diam 10-mm-length array was 5.9 mg. For the configuration studied, we find that to eliminate the effects of gap closure on the radiated energy, the width of the gap must be increased approximately as I. For shots unaffected by gap closure, we find that the peak radiated x-ray power P(r) proportional to I1.24+/-0.18, the total radiated x-ray energy E(r) proportional to I1.73+/-0.18, the x-ray-power rise time tau(r) proportional to I0.39+/-0.34, and the x-ray-power pulse width tau(w) proportional to demonstrate that the internal energy and radiative opacity of the pinch are not responsible for the observed subquadratic power scaling. Heuristic wire-ablation arguments suggest that quadratic power scaling will be achieved if the implosion time tau(i) is scaled as I(-1/3). The measured 1sigma shot-to-shot fluctuations in P(r), E(r), tau(r), tau(w), and tau(i) are approximately 12%, 9%, 26%, 9%, and 2%, respectively, assuming that the fluctuations are independent of I. These variations are for one-half of the pinch. If the half observed radiates in a manner that is statistically independent of the other half, the variations are a factor of 2(1/2) less for the entire pinch. We calculate the effect that shot-to-shot fluctuations of a single pinch would have on the shot-success probability of the double-pinch inertial-confinement-fusion driver proposed by Hammer et al. [Phys. Plasmas 6, 2129 (1999)]. We find that on a given shot, the probability that two independent pinches would radiate the same peak power to within a factor of 1+/-alpha (where 0< or =alpha<<1) is equal to erf(alpha/2sigma), where sigma is the 1sigma fractional variation of the peak power radiated by a single pinch. Assuming alpha must be < or =7% to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, sigma must be <3% for the shot-success probability to be > or =90%. The observed (12/2(1/2))%=8.5% fluctuation in P(r) would provide adequate symmetry on 44% of the shots. We propose that three-dimensional radiative-magnetohydrodynamic simulations be performed to quantify the sensitivity of the x-ray emission to various initial conditions, and to determine whether an imploding z pinch is a spatiotemporal chaotic system.

Demonstration of radiation symmetry control for inertial confinement fusion in double Z-pinch hohlraums.

Simulations of a double Z-pinch hohlraum, relevant to the high-yield inertial-confinement-fusion concept, predict that through geometry design the time-integrated P2 Legendre mode drive asymmetry can be systematically controlled from positive to negative coefficient values. Studying capsule elongation, recent experiments on Z confirm such control by varying the secondary hohlraum length. Since the experimental trend and optimum length are correctly modeled, confidence is gained in the simulation tools; the same tools predict capsule drive uniformity sufficient for high-yield fusion ignition.

Symmetric inertial-confinement-fusion-capsule implosions in a double-z-pinch-driven hohlraum.

An inertial-confinement-fusion (ICF) concept using two 60-MA Z pinches to drive a cylindrical hohlraum to 220 eV has been recently proposed. The first capsule implosions relevant to this concept have been performed at the same physical scale with a lower 20-MA current, yielding a 70+/-5 eV capsule drive. The capsule shell shape implies a polar radiation symmetry, the first high-accuracy measurement of this type in a pulsed-power-driven ICF configuration, within a factor of 1.6-4 of that required for scaling to ignition. The convergence ratio of 14-21 is to date the highest in any pulsed-power ICF system.

X-ray imaging measurements of capsule implosions driven by a Z-pinch dynamic hohlraum.

The radiation and shock generated by impact of an annular tungsten Z-pinch plasma on a 10-mm diam 5-mg/cc CH(2) foam are diagnosed with x-ray imaging and power measurements. The radiative shock was virtually unaffected by Z-pinch plasma instabilities. The 5-ns-duration approximately 135-eV radiation field imploded a 2.1-mm-diam CH capsule. The measured radiation temperature, shock radius, and capsule radius agreed well with computer simulations, indicating understanding of the main features of a Z-pinch dynamic-hohlraum-driven capsule implosion.

Double Z-pinch hohlraum drive with excellent temperature balance for symmetric inertial confinement fusion capsule implosions.

A double Z pinch driving a cylindrical secondary hohlraum from each end has been developed which can indirectly drive intertial confinement fusion capsule implosions with time-averaged radiation fields uniform to 2%-4%. 2D time-dependent view factor and 2D radiation hydrodynamic simulations using the measured primary hohlraum temperatures show that capsule convergence ratios of at least 10 with average distortions from sphericity of /r200 MJ.