C.C. Kuranz

Spline-Based Emulators for Radiative Shock Experiments With Measurement Error

Radiation hydrodynamics and radiative shocks are of fundamental interest in the high-energy-density physics research due to their importance in understanding astrophysical phenomena such as supernovae. In the laboratory, experiments can produce shocks with fundamentally similar physics on reduced scales. However, the cost and time constraints of the experiment necessitate use of a computer algorithm to generate a reasonable number of outputs for making valid inference. We focus on modeling emulators that can efficiently assimilate these two sources of information accounting for their intrinsic differences. The goal is to learn how to predict the breakout time of the shock given the information on associated parameters such as pressure and energy. Under the framework of the Kennedy–O’Hagan model, we introduce an emulator based on adaptive splines. Depending on the preference of having an interpolator for the computer code output or a computationally fast model, a couple of different variants are proposed. Those choices are shown to perform better than the conventional Gaussian-process-based emulator and a few other choices of nonstationary models. For the shock experiment dataset, a number of features related to computer model validation such as using interpolator, necessity of discrepancy function, or accounting for experimental heterogeneity are discussed, implemented, and validated for the current dataset. In addition to the typical Gaussian measurement error for real data, we consider alternative specifications suitable to incorporate noninformativeness in error distributions, more in agreement with the current experiment. Comparative diagnostics, to highlight the effect of measurement error model on predictive uncertainty, are also presented. Supplementary materials for this article are available online.

Demonstration of x-ray fluorescence imaging of a high-energy-density plasma

Experiments at the Trident Laser Facility have successfully demonstrated the use of x-ray fluorescence imaging (XRFI) to diagnose shocked carbonized resorcinol formaldehyde (CRF) foams doped with Ti. One laser beam created a shock wave in the doped foam. A second laser beam produced a flux of vanadium He-α x-rays, which in turn induced Ti K-shell fluorescence within the foam. Spectrally resolved 1D imaging of the x-ray fluorescence provided shock location and compression measurements. Additionally, experiments using a collimator demonstrated that one can probe specific regions within a target. These results show that XRFI is a capable alternative to path-integrated measurements for diagnosing hydrodynamic experiments at high energy density.

Investigation of the hard x-ray background in backlit pinhole imagers.

Hard x-rays from laser-produced hot electrons (>10 keV) in backlit pinhole imagers can give rise to a background signal that decreases signal dynamic range in radiographs. Consequently, significant uncertainties are introduced to the measured optical depth of imaged plasmas. Past experiments have demonstrated that hard x-rays are produced when hot electrons interact with the high-Z pinhole substrate used to collimate the softer He-α x-ray source. Results are presented from recent experiments performed on the OMEGA-60 laser to further study the production of hard x-rays in the pinhole substrate and how these x-rays contribute to the background signal in radiographs. Radiographic image plates measured hard x-rays from pinhole imagers with Mo, Sn, and Ta pinhole substrates. The variation in background signal between pinhole substrates provides evidence that much of this background comes from x-rays produced in the pinhole substrate itself. A Monte Carlo electron transport code was used to model x-ray production from hot electrons interacting in the pinhole substrate, as well as to model measurements of x-rays from the irradiated side of the targets, recorded by a bremsstrahlung x-ray spectrometer. Inconsistencies in inferred hot electron distributions between the different pinhole substrate materials demonstrate that additional sources of hot electrons beyond those modeled may produce hard x-rays in the pinhole substrate.

Spectral analysis of x-ray emission created by intense laser irradiation of copper materialsa)

We have measured the x-ray emission, primarily from K(α),K(β), and He(α) lines, of elemental copper foil and foam targets irradiated with a mid-10(16) W/cm(2) laser pulse. The copper foam at 0.1 times solid density is observed to produce 50% greater He(α) line emission than copper foil, and the measured signal is well-fit by a sum of three synthetic spectra generated by the atomic physics code FLYCHK. Additionally, spectra from both targets reveal characteristic inner shell K(α) transitions from hot electron interaction with the bulk copper. However, only the larger-volume foam target produced significant K(β) radiation, confirming a lower bulk temperature in the higher volume sample.