Quantifying electron temperature distributions from time-integrated x-ray emission spectra.

K-shell x-ray emission spectroscopy is a standard tool used to diagnose the plasma conditions created in high-energy-density physics experiments. In the simplest approach, the emissivity-weighted average temperature of the plasma can be extracted by fitting an emission spectrum to a single temperature condition. It is known, however, that a range of plasma conditions can contribute to the measured spectra due to a combination of the evolution of the sample and spatial gradients. In this work, we define a parameterized model of the temperature distribution and use Markov Chain Monte Carlo sampling of the input parameters, yielding uncertainties in the fit parameters to assess the uniqueness of the inferred temperature distribution. We present the analysis of time-integrated S and Fe x-ray spectroscopic data from the Orion laser facility and demonstrate that while fitting each spectral region to a single temperature yields two different temperatures, both spectra can be fit simultaneously with a single temperature distribution. We find that fitting both spectral regions together requires a maximum temperature of 1310-70 +90 eV with significant contributions from temperatures down to 200 eV.

Spectral sensor error analysis for measuring x-ray radiation drive using the DANTE diagnostic toward inertial confinement fusion experiments.

DANTE is a diagnostic used to measure the x-radiation drive produced by heating a high-Z cavity ("hohlraum") with high-powered laser beams. It records the spectrally and temporally resolved radiation flux at x-ray energies between 50 eV and 20 keV. Each sensor configuration on DANTE is composed of filters, mirrors, and x-ray diodes to define 18 different x-ray channels whose output is voltage as a function of time. The absolute flux is then determined from the photometric calibration of the sensor configuration and a spectral reconstructing algorithm. The reconstruction of the spectra vs time from the measured voltages and known response of each channel has presented challenges. We demonstrate a novel approach here for quantifying the error on the determined flux based on the channel sensor configuration and most commonly used reconstruction algorithm. In general, we find that the integrated spectral flux from a hohlraum can robustly be reconstructed (within ∼14%) using a traditional unfold approach with as few as ten channels due to the underlying assumption of a largely Planckian spectral intensity distribution.

DANTE as a primary temperature diagnostic for the NIF iron opacity campaign.

The Opacity Platform on the National Ignition Facility (NIF) has been developed to measure iron opacities at varying densities and temperatures relevant to the solar interior and to verify recent experimental results obtained at the Sandia Z-machine, that diverge from theory. The first set of NIF experiments collected iron opacity data at ∼150 eV to 160 eV and an electron density of ∼7 × 1021 cm-3, with a goal to study temperatures up to ∼210 eV, with electron densities of up to ∼3 × 1022 cm-3. Among several techniques used to infer the temperature of the heated Fe sample, the absolutely calibrated DANTE-2 filtered diode array routinely provides measurements of the hohlraum conditions near the sample. However, the DANTE-2 temperatures are consistently low compared to pre-shot LASNEX simulations for a range of laser drive energies. We have re-evaluated the estimated uncertainty in the reported DANTE-2 temperatures and also the error generated by varying channel participation in the data analysis. An uncertainty of ±5% or better can be achieved with appropriate spectral coverage, channel participation, and metrology of the viewing slot.

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.

A genetic algorithm approach for reconstructing spectral content from filtered x-ray diode array spectrometers.

Filtered diode array spectrometers are routinely employed to infer the temporal evolution of spectral power from x-ray sources, but uniquely extracting spectral content from a finite set of broad, spectrally overlapping channel spectral sensitivities is decidedly nontrivial in these under-determined systems. We present the use of genetic algorithms to reconstruct a probabilistic spectral intensity distribution and compare to the traditional approach most commonly found in the literature. Unlike many of the previously published models, spectral reconstructions from this approach are neither limited by basis functional forms nor do they require a priori spectral knowledge. While the original intent of such measurements was to diagnose the temporal evolution of spectral power from quasi-blackbody radiation sources-where the exact details of spectral content were not thought to be crucial-we demonstrate that this new technique can greatly enhance the utility of the diagnostic by providing more physical spectra and improved robustness to hardware configuration for even strongly non-Planckian distributions.

Using L-shell x-ray spectra to determine conditions of non-local thermal dynamic equilibrium plasmas.

K-shell x-ray spectra of Li- to H-like ions have long been used to determine plasma conditions. The ratio of integrated line intensities is used to determine the temperature. At the density of non-local thermal dynamic equilibrium (NLTE) plasmas (n e ≈ 1021 cm-3), the K-shell spectrum is not very sensitive to density. We propose using the L-shell emission of open L-shell ions (C- to Li-like) as an alternative to determine both temperature and density of NLTE plasmas. First, the L-shell models of a mid-Z material need to be verified against the temperatures obtained using a K-shell spectrum of a low-Z material. A buried layer platform is being developed at the OMEGA laser to study the open L-shell spectra of NLTE plasmas of mid-Z materials. Studies have been done using a 250 µm diameter dot composed of a layer of 1200 Å thick Zn between two 600 Å thick layers of Ti, in the center of a 1000 µm diameter, 13 µm thick beryllium tamper. Lasers heat the target from both sides for up to 3 ns. The size of the emitting volume vs time was measured with x-ray imaging (face-on and side-on) to determine the density. The temperature was measured from the Ti K-shell spectra. The use of this platform for the verification of atomic L-shell models is discussed.

Developing an Experimental Basis for Understanding Transport in NIF Hohlraum Plasmas.

We report on the first multilocation electron temperature (T_{e}) and flow measurements in an ignition hohlraum at the National Ignition Facility using the novel technique of mid-Z spectroscopic tracer "dots." The measurements define a low resolution "map" of hohlraum plasma conditions and provide a basis for the first multilocation tests of particle and energy transport physics in a laser-driven x-ray cavity. The data set is consistent with classical heat flow near the capsule but reduced heat flow near the laser entrance hole. We evaluate the role of kinetic effects, self-generated magnetic fields, and instabilities in causing spatially dependent heat transport in the hohlraum.

Understanding reconstructed Dante spectra using high resolution spectroscopy.

The Dante is an 18 channel filtered diode array used at the National Ignition Facility (NIF) to measure the spectrally and temporally resolved radiation flux between 50 eV and 20 keV from various targets. The absolute flux is determined from the radiometric calibration of the x-ray diodes, filters, and mirrors and a reconstruction algorithm applied to the recorded voltages from each channel. The reconstructed spectra are very low resolution with features consistent with the instrument response and are not necessarily consistent with the spectral emission features from the plasma. Errors may exist between the reconstructed spectra and the actual emission features due to assumptions in the algorithm. Recently, a high resolution convex crystal spectrometer, VIRGIL, has been installed at NIF with the same line of sight as the Dante. Spectra from L-shell Ag and Xe have been recorded by both VIRGIL and Dante. Comparisons of these two spectroscopic measurements yield insights into the accuracy of the Dante reconstructions.

Use of a priori spectral information in the measurement of x-ray flux with filtered diode arrays.

Filtered x-ray diode (XRD) arrays are often used to measure x-ray spectra vs. time from spectrally continuous x-ray sources such as hohlraums. A priori models of the incident x-ray spectrum enable a more accurate unfolding of the x-ray flux as compared to the standard technique of modifying a thermal Planckian with spectral peaks or dips at the response energy of each filtered XRD channel. A model x-ray spectrum consisting of a thermal Planckian, a Gaussian at higher energy, and (in some cases) a high energy background provides an excellent fit to XRD-array measurements of x-ray emission from laser heated hohlraums. If high-resolution measurements of part of the x-ray emission spectrum are available, that information can be included in the a priori model. In cases where the x-ray emission spectrum is not Planckian, candidate x-ray spectra can be allowed or excluded by fitting them to measured XRD voltages. Examples are presented from the filtered XRD arrays, named Dante, at the National Ignition Facility and the Laboratory for Laser Energetics.

High-resolution grazing-incidence grating spectrometer for temperature measurements of low-Z ions emitting in the 100-300 Å spectral band.

We have constructed a high-resolution grazing-incidence spectrometer designed for measuring the ion temperature of low-Z elements, such as Li(+) or Li(2 +), which radiate near 199 Å and 135 Å, respectively. Based on measurements at the Livermore Electron Beam Ion Trap we have shown that the instrumental resolution is better than 48 mÅ at the 200 Å setting and better than 40 mÅ for the 135-Å range. Such a high spectral resolution corresponds to an instrumental limit for line-width based temperature measurements of about 45 eV for the 199 Å Li(+) and 65 eV for the 135 Å Li(2 +) lines. Recently obtained survey spectra from the Lithium Tokamak Experiment at the Princeton Plasma Physics Laboratory show the presence of these lithium emission lines and the expected core ion temperature of approximately 70 eV is sufficiently high to demonstrate the feasibility of utilizing our high-resolution spectrometer as an ion-temperature diagnostic.

Extended-range grazing-incidence spectrometer for high-resolution extreme ultraviolet measurements on an electron beam ion trap.

A high-resolution grazing-incidence grating spectrometer has been implemented on the Livermore electron beam ion traps for performing very high-resolution measurements in the soft x-ray and extreme ultraviolet region spanning from below 10 Å to above 300 Å. The instrument operates without an entrance slit and focuses the light emitted by highly charged ions located in the roughly 50 µm wide electron beam onto a cryogenically cooled back-illuminated charge-coupled device detector. The measured line widths are below 0.025 Å above 100 Å, and the resolving power appears to be limited by the source size and Doppler broadening of the trapped ions. Comparisons with spectra obtained with existing grating spectrometers show an order of magnitude improvement in spectral resolution.

Reduced instability growth with high-adiabat high-foot implosions at the National Ignition Facility.

Hydrodynamic instabilities are a major obstacle in the quest to achieve ignition as they cause preexisting capsule defects to grow and ultimately quench the fusion burn in experiments at the National Ignition Facility. Unstable growth at the ablation front has been dramatically reduced in implosions with "high-foot" drives as measured using x-ray radiography of modulations at the most dangerous wavelengths (Legendre mode numbers of 30-90). These growth reductions have helped to improve the performance of layered DT implosions reported by O. A. Hurricane et al. [Nature (London) 506, 343 (2014)], when compared to previous "low-foot" experiments, demonstrating the value of stabilizing ablation-front growth and providing directions for future ignition designs.

Observation of a reflected shock in an indirectly driven spherical implosion at the national ignition facility.

A 200 µm radius hot spot at more than 2 keV temperature, 1 g/cm^{3} density has been achieved on the National Ignition Facility using a near vacuum hohlraum. The implosion exhibits ideal one-dimensional behavior and 99% laser-to-hohlraum coupling. The low opacity of the remaining shell at bang time allows for a measurement of the x-ray emission of the reflected central shock in a deuterium plasma. Comparison with 1D hydrodynamic simulations puts constraints on electron-ion collisions and heat conduction. Results are consistent with classical (Spitzer-Harm) heat flux.

First measurements of hydrodynamic instability growth in indirectly driven implosions at ignition-relevant conditions on the National Ignition Facility.

Ignition experiments have shown an anomalous susceptibility to hydrodynamic instability growth. To help understand these results, the first hydrodynamic instability growth measurements in indirectly driven implosions on the National Ignition Facility were performed at ignition conditions with peak radiation temperatures up to ∼300 eV. Plastic capsules with two-dimensional preimposed, sinusoidal outer surface modulations of initial wavelengths of 240 (corresponding to a Legendre mode number of 30), 120 (mode 60), and 80 µm (mode 90) were imploded by using actual low-adiabat ignition laser pulses. The measured growth was in excellent agreement, validating 2D hydra simulations for the most dangerous modes in the acceleration phase. These results reinforce confidence in the predictive capability of calculations that are paramount to illuminating the path toward ignition.

Novel characterization of capsule x-ray drive at the National Ignition Facility.

Indirect drive experiments at the National Ignition Facility are designed to achieve fusion by imploding a fuel capsule with x rays from a laser-driven hohlraum. Previous experiments have been unable to determine whether a deficit in measured ablator implosion velocity relative to simulations is due to inadequate models of the hohlraum or ablator physics. ViewFactor experiments allow for the first time a direct measure of the x-ray drive from the capsule point of view. The experiments show a 15%-25% deficit relative to simulations and thus explain nearly all of the disagreement with the velocity data. In addition, the data from this open geometry provide much greater constraints on a predictive model of laser-driven hohlraum performance than the nominal ignition target.

Measurements of an ablator-gas atomic mix in indirectly driven implosions at the National Ignition Facility.

We present the first results from an experimental campaign to measure the atomic ablator-gas mix in the deceleration phase of gas-filled capsule implosions on the National Ignition Facility. Plastic capsules containing CD layers were filled with tritium gas; as the reactants are initially separated, DT fusion yield provides a direct measure of the atomic mix of ablator into the hot spot gas. Capsules were imploded with x rays generated in hohlraums with peak radiation temperatures of ∼294 eV. While the TT fusion reaction probes conditions in the central part (core) of the implosion hot spot, the DT reaction probes a mixed region on the outer part of the hot spot near the ablator-hot-spot interface. Experimental data were used to develop and validate the atomic-mix model used in two-dimensional simulations.

Early-time symmetry tuning in the presence of cross-beam energy transfer in ICF experiments on the National Ignition Facility.

On the National Ignition Facility, the hohlraum-driven implosion symmetry is tuned using cross-beam energy transfer (CBET) during peak power, which is controlled by applying a wavelength separation between cones of laser beams. In this Letter, we present early-time measurements of the instantaneous soft x-ray drive at the capsule using reemission spheres, which show that this wavelength separation also leads to significant CBET during the first shock, even though the laser intensities are 30× smaller than during the peak. We demonstrate that the resulting early drive P2/P0 asymmetry can be minimized and tuned to <1% accuracy (well within the ±7.5% requirement for ignition) by varying the relative input powers between different cones of beams. These experiments also provide time-resolved measurements of CBET during the first 2 ns of the laser drive, which are in good agreement with radiation-hydrodynamics calculations including a linear CBET model.

Source geometric considerations for OMEGA Dante measurements.

The Dante is a 15 channel filtered diode array which is installed on the OMEGA laser facility at the Laboratory for Laser Energetics, University of Rochester. The system yields the spectrally and temporally resolved radiation flux from 50 eV to 10 keV from various targets (i.e., Hohlraum, gas pipes, etc.). The absolute flux is determined from the radiometric calibration of the x-ray diodes, filters, and mirrors and an unfold algorithm applied to the recorded voltages from each channel. The unfold algorithm assumes an emitting source that is spatially uniform and has a constant area as a function of photon energy. The emitting x-ray source is usually considered to be the laser entrance hole (LEH) of a given diameter for Hohlraum type targets or the effective wall area of high conversion efficiency K-shell type targets. This assumption can be problematic for several reasons. High intensity regions or "hot spots" in the x-ray are observed where the drive laser beams strike the target. The "hot spots" create non-uniform emission seen by the Dante. Additionally, thinned walled (50 µm) low-Z targets (C(22)H(10)N(2)O(5)) have an energy dependent source size since the target's walls will be fully opaque for low energies (E < 2-3 keV) yet fully transmissive at higher energies. Determining accurate yields can be challenging for these types of targets. Discussion and some analysis will be presented.

Application of spatially resolved high resolution crystal spectrometry to inertial confinement fusion plasmas.

High resolution (λ∕Δλ ∼ 10 000) 1D imaging x-ray spectroscopy using a spherically bent crystal and a 2D hybrid pixel array detector is used world wide for Doppler measurements of ion-temperature and plasma flow-velocity profiles in magnetic confinement fusion plasmas. Meter sized plasmas are diagnosed with cm spatial resolution and 10 ms time resolution. This concept can also be used as a diagnostic of small sources, such as inertial confinement fusion plasmas and targets on x-ray light source beam lines, with spatial resolution of micrometers, as demonstrated by laboratory experiments using a 250-µm (55)Fe source, and by ray-tracing calculations. Throughput calculations agree with measurements, and predict detector counts in the range 10(-8)-10(-6) times source x-rays, depending on crystal reflectivity and spectrometer geometry. Results of the lab demonstrations, application of the technique to the National Ignition Facility (NIF), and predictions of performance on NIF will be presented.

Soft x-ray images of the laser entrance hole of ignition hohlraums.

Hohlraums are employed at the national ignition facility to convert laser energy into a thermal x-radiation drive, which implodes a fusion capsule, thus compressing the fuel. The x-radiation drive is measured with a low spectral resolution, time-resolved x-ray spectrometer, which views the region around the hohlraum's laser entrance hole. This measurement has no spatial resolution. To convert this to the drive inside the hohlraum, the size of the hohlraum's opening ("clear aperture") and fraction of the measured x-radiation, which comes from this opening, must be known. The size of the clear aperture is measured with the time integrated static x-ray imager (SXI). A soft x-ray imaging channel has been added to the SXI to measure the fraction of x-radiation emitted from inside the clear aperture. A multilayer mirror plus filter selects an x-ray band centered at 870 eV, near the peak of the x-ray spectrum of a 300 eV blackbody. Results from this channel and corrections to the x-radiation drive are discussed.