X-ray spectroscopic measurements of high densities and temperatures from indirectly driven inertial confinement fusion capsules

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.

Hot Spot Evolution Measured by High-Resolution X-Ray Spectroscopy at the National Ignition Facility

Evolution of the hot spot plasma conditions was measured using high-resolution x-ray spectroscopy at the National Ignition Facility. The capsules were filled with DD gas with trace levels of Kr and had either a high-density-carbon (HDC) ablator or a tungsten (W)-doped HDC ablator. Time-resolved measurement of the Kr Heβ spectra, absolutely calibrated by a simultaneous time-integrated measurement, allows inference of the electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. By matching the calculated hot spot emission using a collisional-radiative code to experimental observations, the hot spot size and areal density are determined. These advanced spectroscopy techniques further reveal the effect of W dopant in the ablator on the hot spot parameters for their improved implosion performance.

All-Order Full-Coulomb Quantum Spectral Line-Shape Calculations

Understanding how atoms interact with hot dense matter is essential for astrophysical and laboratory plasmas. Interactions in high-density plasmas broaden spectral lines, providing a rare window into interactions that govern, for example, radiation transport in stars. However, up to now, spectral line-shape theories employed at least one of three common approximations: second-order Taylor treatment of broadening operator, dipole-only interactions between atom and plasma, and classical treatment of perturbing electrons. In this Letter, we remove all three approximations simultaneously for the first time and test the importance for two applications: neutral hydrogen and highly ionized magnesium and oxygen. We found 15%-50% change in the spectral line widths, which are sufficient to impact applications including white-dwarf mass determination, stellar-opacity research, and laboratory plasma diagnostics.

Absolute throughput calibration of multiple spherical crystals for the Orion High-REsolution X-ray spectrometer (OHREX)

We present absolute throughput analysis of several crystals for the Orion High-REsolution X-ray (OHREX) imaging crystal spectrometer using ray tracing and experimental measurements. The OHREX spectrometer is a high-resolution x-ray spectrometer designed to measure spectral line shapes at the Orion laser facility. The spectrometer is fielded with up to two spherical crystals simultaneously covering two independent spectral ranges. Each crystal has a nominal radius of curvature of R = 67.2 cm and is fielded at a nominal Bragg angle of 51.3°. To cover different bands of interest, several different crystals are available, including Ge (111), KAP, and several cuts of quartz, whose resolving power λ/Δλ exceeds 10 000. The calibrated response of the available crystals has previously been reported from measurements at the EBIT-I electron beam ion trap at Lawrence Livermore National Laboratory. Here, we model the absolute throughput of each crystal using ray tracing and verify the results using experimental data for the quartz (101¯1) crystal.

Elliptically bent crystal x-ray spectrometer for time-resolved laser plasma experiments

Measuring time-resolved spectra is crucial in inertial confinement fusion and radiation source development experiments. An elliptically bent crystal spectrometer is designed to measure X-rays in the range of 2.5-11.0 keV, which was achieved using four different lattice spacings of 0.8512, 0.6687, 0.4246, and 0.2749 nm with spectral resolution E/δE of ∼500. The X-rays emitted from a source at one focus of the ellipse undergo Bragg reflection off a crystal and pass through the second focus of the ellipse to a streak camera slit with 18-mm length and 80-μm width to generate a time-resolved spectrum. An alignment method for the time-resolved spectrometer was developed with the straight line connecting the centers of the two small holes on the fabricated substrate being the axis of the ellipse, thus allowing the spacing between the source and the elliptical crystal to be tuned to couple with the streak camera. The time-resolved spectrometer's performance was experimentally tested at the Shenguang II laser facility. The results indicate that its performance is close to that predicted theoretically.

Calibration of the OHREX high-resolution imaging crystal spectrometer at the Livermore electron beam ion traps

We report the calibration of the Orion High-Resolution X-ray (OHREX) imaging crystal spectrometer at the EBIT-I electron beam ion trap at Livermore. Two such instruments, dubbed OHREX-1 and OHREX-2, are fielded for plasma diagnostics at the Orion laser facility in the United Kingdom. The OHREX spectrometer can simultaneously house two spherically bent crystals with a radius of curvature of r = 67.2 cm. The focusing properties of the spectrometer allow both for larger distance to the source due to the increase in collected light and for observation of extended sources. OHREX is designed to cover a 2.5°-3° spectral range at Bragg angles around 51.3°. The typically high resolving powers at these large Bragg angles are ideally suited for line shape diagnostics. For instance, the nominal resolving power of the instrument (>10 000) is much higher than the effective resolving power associated with the Doppler broadening due to the temperature of the trapped ions in EBIT-I. The effective resolving power is only around 3000 at typical EBIT-I conditions, which nevertheless is sufficient to set up and test the instrument's spectral characteristics. We have calibrated the spectral range for a number of crystals using well known reference lines in the first and second order and derived the ion temperatures from these lines. We have also made use of the 50 μm size of the EBIT-I source width to characterize the spatial focusing of the spectrometer.

Development of a krypton-doped gas symmetry capsule platform for x-ray spectroscopy of implosion cores on the NIF

The electron temperature at stagnation of an ICF implosion can be measured from the emission spectrum of high-energy x-rays that pass through the cold material surrounding the hot stagnating core. Here we describe a platform developed on the National Ignition Facility where trace levels of a mid-Z dopant (krypton) are added to the fuel gas of a symcap (symmetry surrogate) implosion to allow for the use of x-ray spectroscopy of the krypton line emission.

Lineshape spectroscopy with a very high resolution, very high signal-to-noise crystal spectrometer

We have developed a high-resolution x-ray spectrometer for measuring the shapes of spectral lines produced from laser-irradiated targets on the Orion laser facility. The instrument utilizes a spherically bent crystal geometry to spatially focus and spectrally analyze photons from foil or microdot targets. The high photon collection efficiency resulting from its imaging properties allows the instrument to be mounted outside the Orion chamber, where it is far less sensitive to particles, hard x-rays, or electromagnetic pulses than instruments housed close to the target chamber center in ten-inch manipulators. Moreover, Bragg angles above 50° are possible, which provide greatly improved spectral resolution compared to radially viewing, near grazing-incidence crystal spectrometers. These properties make the new instrument an ideal lineshape diagnostic for determining plasma temperature and density. We describe its calibration on the Livermore electron beam ion trap facility and present spectral data of the K-shell emission from highly charged sulfur produced by long-pulse as well as short-pulse beams on the Orion laser in the United Kingdom.

Spectroscopic determination of temperature and density spatial profiles and mix in indirect-drive implosion cores

In the field of inertial confinement fusion (ICF), work has been consistently progressing in the past decade toward a more fundamental understanding of the plasma conditions in ICF implosion cores. The research presented here represents a substantial evolution in the ability to diagnose plasma temperatures and densities, along with characteristics of mixing between fuel and shell materials. Mixing is a vital property to study and quantify, since it can significantly affect implosion quality. We employ a number of new spectroscopic techniques that allow us to probe these important quantities. The first technique developed is an emissivity analysis, which uses the emissivity ratio of the optically thin Lybeta and Hebeta lines to spectroscopically extract temperature profiles, followed by the solution of emissivity equations to infer density profiles. The second technique, an intensity analysis, models the radiation transport through the implosion core. The nature of the intensity analysis allows us to use an optically thick line, the Lyalpha, to extract information on mixing near the core edge. With this work, it is now possible to extract directly from experimental data not only detailed temperature and density maps of the core, but also spatial mixing profiles.

Dopant radiative cooling effects in indirect-drive Ar-doped capsule implosion experiments

We present results from simulations performed to investigate the effects of dopant radiative cooling in inertial confinement fusion indirect-drive capsule implosion experiments. Using a one-dimensional radiation-hydrodynamics code that includes inline collisional-radiative modeling, we compute in detail the non-local thermodynamic equilibrium atomic kinetics and spectral characteristics for Ar-doped DD fuel. Specifically, we present results from a series of calculations in which the concentration of the Ar is varied, and examine the sensitivity of the fuel conditions (e.g., electron temperature) and neutron yield to the Ar dopant concentration. Simulation results are compared with data obtained in OMEGA indirect-drive experiments in which monochromatic imaging and spectral measurements of Ar Hebeta and Lybeta line emission were recorded. The incident radiation drive on the capsule is computed with a three-dimensional view factor code using the laser beam pointings and powers from the OMEGA experiments. We also examine the sensitivity of the calculated compressed core electron temperatures and neutron yields to the radiation drive on the capsule and to the radiation and atomic modeling in the simulations.

Hot dense capsule-implosion cores produced by Z-pinch dynamic Hohlraum radiation

Hot dense capsule implosions driven by Z-pinch x rays have been measured using a approximately 220 eV dynamic Hohlraum to implode 1.7-2.1 mm diameter gas-filled CH capsules. The capsules absorbed up to approximately 20 kJ of x rays. Argon tracer atom spectra were used to measure the T(e) approximately 1 keV electron temperature and the n(e) approximately 1-4 x 10(23) cm(-3) electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak emission values of T(e), n(e), and symmetry, indicating reasonable understanding of the Hohlraum and implosion physics.

New benchmarks from tokamak experiments for theoretical calculations of the dielectronic satellite spectra of heliumlike ions

Dielectronic satellite spectra of heliumlike argon, recorded with a high-resolution x-ray crystal spectrometer at the National Spherical Torus Experiment, were found to be inconsistent with existing predictions resulting in unacceptable values for the power balance and suggesting the unlikely existence of non-Maxwellian electron energy distributions. These problems were resolved with calculations from a new atomic code. It is now possible to perform reliable electron-temperature measurements and to eliminate the uncertainties associated with determinations of non-Maxwellian distributions.

X-ray-line diagnostic of magnetic field strength for high-temperature plasmas

An x-ray line diagnostic for use in magnetic field measurements in high-temperature plasmas has been identified. The intensity of the otherwise strictly forbidden 1s(2)2s(2)2p(1/2)2p(4)(3/2)3s(1/2) 3P0-->1s(2)2s(2)2p(6) 1S0 transition in neonlike ions is shown to depend on the magnetic field strength. The field dependence is illustrated between one and 3 T in the Ar8+ spectrum. The line is well resolved, bright, and close to reference lines, making it an experimentally simple to use diagnostic.

Shell mix in the compressed core of spherical implosions

The Rayleigh-Taylor instability in its highly nonlinear, turbulent stage causes atomic-scale mixing of the shell material with the fuel in the compressed core of inertial-confinement fusion targets. The density of shell material mixed into the outer core of direct-drive plastic-shell spherical-target implosions on the 60-beam, OMEGA laser system is estimated to be 3.4(+/-1.2) g/cm(3) from time-resolved x-ray spectroscopy, charged-particle spectroscopy, and core x-ray images. The estimated fuel density, 3.6(+/-1) g/cm(3), accounts for only approximately 50% of the neutron-burn-averaged electron density, n(e)=2.2(+/-0.4)x10(24) cm(-3).

Population kinetics on K alpha lines of partially ionized Cl atoms

A population kinetics code was developed to analyze K alpha emission from partially ionized chlorine atoms in hydrocarbon plasmas. Atomic processes are solved under collisional-radiative equilibrium for two-temperature plasmas. It is shown that the fast electrons dominantly contribute to ionize the K-shell bound electrons (i.e., inner-shell ionization) and the cold electrons to the outer-shell bound ones. Ratios of K alpha lines of partially ionized atoms are presented as a function of cold-electron temperature. The model was validated by observation of the K alpha lines from a chlorinated plastic target irradiated with 1 TW Ti:sapphire laser pulses at 1.5 x 10(17) W/cm(2), inferring a plasma temperature of about 100 eV on the target surface.

Spectroscopic determination of dynamic plasma gradients in implosion cores

The time-dependent gradient structure of a laser-compressed, high-energy-density plasma has been determined using a method based on the simultaneous analysis of time-resolved x-ray monochromatic images and x-ray line spectra from Ar-doped D2 implosion cores. The analysis self-consistently determines the temperature and density gradients that yield the best fits to the spatial-emissivity profiles and spectral line shapes. This measurement is important for understanding the spectra formation and plasma dynamics associated with the implosion process. In addition, since the results are independent of hydrodynamic simulations, they are also important for comparison with fluid-dynamic models.

Ionization balance in inertial confinement fusion hohlraums

We present the first x-ray spectroscopic measurements of the ionization balance in inertial confinement fusion hohlraums supported by 4omega Thomson scattering diagnostics. The experimental data show agreement with non-LTE radiation-hydrodynamic calculations of the averaged Au charge state and electron temperatures. These findings are consistent with the successful integrated modeling of the hohlraum radiation fields. Comparisons with detailed synthetic spectra calculations show that the experimental ionization distribution is slightly shifted indicating nonsteady state kinetics.

Accuracy of K-shell spectra modeling in high-density plasmas

We present spectroscopic measurements of the helium-like and lithium-like argon emission supported by Thomson scattering diagnostics on gas bag targets. These data provide critical tests of plasma spectroscopic K-shell models. In particular, we have measured the line radiation in the wavelength region of the He-like Ar 1s(2)-1s3l transition (He-beta) that is of interest for density and temperature measurements of plasmas from gas-filled targets (n(e)</=10(21) cm(-3)), laser ablation targets (n(e)</=10(22) cm(-3)), and inertial confinement fusion capsule implosions (n(e)>/=10(24) cm(-3)). The spectra show lithium-like dielectronic satellites on the red wing of the He-beta line that are temperature sensitive and are known to influence the shape of the Stark-broadened line profiles observed from implosions. To examine the kinetics modeling of this complex, i.e., the He-beta and its associated satellites, we have performed experiments in gas bag plasmas at densities of (0.6-1.1)x10(21) cm(-3) where we independently determine the electron temperature with ultraviolet Thomson scattering. The comparison of the satellite intensities with kinetics modeling shows good agreement for satellites whose upper states are populated by dielectronic capture, but shows discrepancies for inner-shell collisional excited transitions.