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Tregillis, Ian Lee

Publications and source records attributed to Tregillis, Ian Lee.

15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Jets from shocked metal surfaces with grooves: Missing experiments

Many studies have investigated the mass outflows generated when a planar shock transits an imperfect (“defected”) metal surface, where the defects are symmetric triangular or sinusoidal grooves. Yet a fundamental question remains unanswered: how does the quantity of outflow mass and its maximum velocity vary as a function of the groove cross-sectional aspect ratio? We identify two sets of missing experiments that must be addressed to answer the question. The aspect ratio (groove depth over width) is equivalently represented by θ, the cross-sectional half angle, or by η 0 k, the amplitude multiplied by an effective wavenumber. Low θ (high η 0 k) grooves comprise the first set of missing experiments, which are necessary to determine the validity of theoretical predictions of the nonlinear regime (η 0 k ≥ 1, θ < 57.5°). The second set of missing experiments are those in which the volume of the groove (or equivalently, the axial cross-sectional area) has been held constant as θ or η 0 k are varied. Such experiments are necessary to independently measure the effects of variations in groove volume and groove aspect ratio on the resulting jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Jets from shocked metal surfaces with grooves: Missing experiments

Many studies have investigated the mass outflows generated when a planar shock transits an imperfect (“defected”) metal surface, where the defects are symmetric triangular or sinusoidal grooves. Yet a fundamental question remains unanswered: how does the quantity of outflow mass and its maximum velocity vary as a function of the groove cross-sectional aspect ratio? We identify two sets of missing experiments that must be addressed to answer the question. The aspect ratio (groove depth over width) is equivalently represented by θ, the cross sectional half angle, or by η 0 k, the amplitude multiplied by an effective wavenumber. Low θ (high η 0 k) grooves comprise the first set of missing experiments, which are necessary to determine the validity of theoretical predictions of the nonlinear regime (η 0 k ≥ 1, θ < 57.5°). The second set of missing experiments are those in which the volume of the groove (or equivalently, the axial cross-sectional area) has been held constant as θ or η 0 k are varied. Such experiments are necessary to independently measure the effects of variations in groove volume and groove aspect ratio on the resulting jets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A mathematical framework for ejecta cloud dynamics with application to source models and piezoelectric mass measurements

We present a mathematical framework for describing the dynamical evolution of an ejecta cloud generated by a generic ejecta source model. We consider a piezoelectric sensor fielded in the path of an ejecta cloud, for experimental configurations in which the ejecta are created at a singly shocked planar surface and fly ballistically through vacuum to the stationary sensor. To do so, we introduce the concept of a time- and velocity-dependent ejecta “areal mass function.” We derive expressions for the analytic (“true”) accumulated ejecta areal mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltages. In this way, we derive an exact expression and upper bound for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation, which is commonly required for momentum diagnostic analyses. This error term is zero for truly instantaneous source models; otherwise, the standard piezoelectric analysis is guaranteed to overestimate the true mass. When combined with a piezoelectric dataset, this framework provides a unique solution for the ejecta particle velocity distribution, subject to the assumptions inherent in the data analysis. The framework also leads to strong boundary conditions that any ejecta source model must satisfy in order to be consistent with apparently global properties of piezoelectric measurements from a wide range of experiments. We demonstrate this methodology by applying it to the Richtmyer–Meshkov instability+self-similar velocity distribution ejecta source model currently under development at Los Alamos National Laboratory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗
DOE OSTI2020

Notes on Asay Foil Analysis

As is the norm for momentum diagnostic analyses (i.e., both piezopin and Asay foil measurements), we begin by assuming all particles are created instantaneously at the moment of shock breakout; that all particles move collinearly through a perfect vacuum from source to sensor with a long mean free path to scattering (i.e., so that particle velocities and areal masses do not change in flight); and that the particles collide perfectly inelastically with the sensor. We also assume the foil supports have a negligible effect on the trajectory, as has been demonstrated experimentally, and the foil is sufficiently thin that corrections for thick-plate effects (e.g., time delays between particle impacts on the collecting side and velocity changes on the probe side) can be disregarded. We seek an exact analytic treatment of an ideal system that perfectly embodies these characteristics.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Analytically Derived Piezoelectric Ejecta Data Transformations, with Implications for Claims of Experimentally Observed Self-Similarity

Building upon a previously documented analytic formalism, we derive a set of data transformations that relate piezoelectrically inferred time-dependent ejecta masses, dynamical ejecta cloud densities, and "radiographic" ejecta cloud density distributions. These transformation rules are derived rigorously, with careful attention to the assumption of instant ejecta production which is inherent in the piezoelectric mass inference procedure. Some of these relationships have not appeared previously in the literature, including solutions for the unique ejecta velocity distribution and radiographic ejecta cloud density distribution consistent with the instant-production assumption for a given piezoelectrically inferred mass dataset. In deriving the latter, we prove that—again subject to the ubiquitous instant-creation assumption—measurements at a single sensor are sufficient to determine properties of the ejecta cloud everywhere at all times. Other data transformation relationships have appeared in the literature without a rigorous derivation, or have been stated in forms that obscure the key mathematical relationships. We apply these results to arguments for self-similar ejecta cloud evolution, thereby deriving mathematical expressions by which claims of self-similarity may be examined. We prove that one analysis used in the literature to claim experimental evidence of a short ejecta production timescale—and consequently of self-similar cloud evolution—in fact places no constraint the ejecta production interval and therefore does not support the associated conclusion. We also provide a potentially useful uniqueness proof.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2018

(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions

We show that certain apparently universal features of the piezoelectric voltage traces measured in HE-driven tin coupon experiments [1, 2] constrain the functional form of any ejecta source model with a stationary velocity distribution. Building on an analytic formalism that has been extensively documented elsewhere [3, 4, 5, 6, 7], we derive simple expressions for V(t 0 a ), V'(t 0 a ), and the discontinuity in V(t break ) where t 0 a is the time of first ejecta arrival at the sensor and t break is the “depletion” time for the fastest particles arriving at the sensor. These three quantities appear to be zero, or nearly so, in the Vo- gan voltage data [1] (modulo noise and any smoothing effects created by the circuit); however, the predicted voltages for this general class of source models do not automatically achieve these conditions unless special boundary conditions are met. Source models which violate these boundary conditions will produce voltage predictions at odds with the measurements. The RMI+SSVD ejecta source model in its current formulation satisfies none of these boundary conditions, and therefore predictions from a stationary-velocity-distribution approximation to the RMI+SSVD source model deviate significantly from the voltage data. This analysis suggests straightforward methods for potentially improving the predictions of the RMI+SSVD ejecta source model. We test this with a simple adjustment to the SSVD and find, as anticipated, the adjustment corrects three properties of the voltage prediction. Furthermore, the adjusted model’s prediction for ejecta mass accumulation at the sensor exhibits a smoother and more gradual rise from the baseline than that produced by the original source model, thereby improving overall model/data agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Supplement to LA-UR-17-21218: Application to SSVD

We apply the formalism derived in LA-UR-17-21218 to the prescription for an RMI-based self-similar velocity distribution (SSVD) derived by Ham- merberg et al.. We compute analytically the true [mt(t)] and inferred [mi(t)] ejecta mass arriving at the piezoelectric sensor for several shots de- scribed in the literature and compare the results to the data. We nd that while the \RMI + SSVD" prescription gives rise to decent estimates for the nal accumulated mass at the pin, the time-dependent accumulation rises too sharply and linearly to agree with data. We also compute the time-dependent pressure and voltage at the sensor, and compare the latter to data. The pres- sure does not rise smoothly from zero, instead exhibiting a strong surge as the leading edge of the ejecta cloud arrives, which produces an initial sharp spike in the voltage trace, which is not observed. These inconsistencies result from a discontinuity in the prescribed self-similar velocity distribution at maximum relative velocity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Development on the National Ignition Facility of a High Energy Density Opacity Platform

X-ray opacity is a crucial factor in all radiation-hydrodynamics calculations, yet it is one of the least validated of the material properties in simulation codes for high-energy-density plasmas. Recent opacity experiments at the Sandia Z-machine have shown up to factors of two discrepancies between theory and experiment for various mid-Z elements (Fe, Cr, Ni). These discrepancies raise doubts regarding the accuracy of the opacity models which are used in ICF and stewardship as well as in astrophysics. Therefore, a new experimental opacity platform has been developed on the National Ignition Facility (NIF), not only to verify the Z-machine experimental results, but also to extend the experiments to other temperatures and densities. Within the context of the national opacity strategy, the first NIF experiments were directed towards measuring the opacity of iron at a temperature of ~160 eV and an electron density of ~7xl021 cm-3(Anchor 1). The Z data agree with theory at these conditions, providing a reference point for validation of the NIF platform. Development shots on NIF have demonstrated the ability to create a sufficiently bright point backlighter using an imploding plastic capsule, and also a combined hohlraum, sample and laser drive able to produce iron plasmas at the desired conditions. Spectrometer qualification has been completed, albeit with additional improvements planned, and the first iron absorption spectra have now been obtained.

36 MATERIALS SCIENCE↗
DOE OSTI2017

(U) An Analytic Study of Piezoelectric Ejecta Mass Measurements

We consider the piezoelectric measurement of the areal mass of an ejecta cloud, for the specific case where ejecta are created by a single shock at the free surface and fly ballistically through vacuum to the sensor. To do so, we define time- and velocity-dependent ejecta “areal mass functions” at the source and sensor in terms of typically unknown distribution functions for the ejecta particles. Next, we derive an equation governing the relationship between the areal mass function at the source (which resides in the rest frame of the free surface) and at the sensor (which resides in the laboratory frame). We also derive expressions for the analytic (“true”) accumulated ejecta mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltage traces. This approach enables us to derive an exact expression for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation. We verify that when the ejecta are created instantaneously (i.e., when the time dependence is a delta function), the piezoelectric inference method exactly reproduces the correct result. When creation is not instantaneous, the standard piezo analysis will always overestimate the true mass. However, the error is generally quite small (less than several percent) for most reasonable velocity and time dependences. In some cases, errors exceeding 10-15% may require velocity distributions or ejecta production timescales inconsistent with experimental observations. These results are demonstrated rigorously with numerous analytic test problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

(U) An Analytic Examination of Piezoelectric Ejecta Mass Measurements

Ongoing efforts to validate a Richtmyer-Meshkov instability (RMI) based ejecta source model [1, 2, 3] in LANL ASC codes use ejecta areal masses derived from piezoelectric sensor data [4, 5, 6]. However, the standard technique for inferring masses from sensor voltages implicitly assumes instantaneous ejecta creation [7], which is not a feature of the RMI source model. To investigate the impact of this discrepancy, we define separate “areal mass functions” (AMFs) at the source and sensor in terms of typically unknown distribution functions for the ejecta particles, and derive an analytic relationship between them. Then, for the case of single-shock ejection into vacuum, we use the AMFs to compare the analytic (or “true”) accumulated mass at the sensor with the value that would be inferred from piezoelectric voltage measurements. We confirm the inferred mass is correct when creation is instantaneous, and furthermore prove that when creation is not instantaneous, the inferred values will always overestimate the true mass. Finally, we derive an upper bound for the error imposed on a perfect system by the assumption of instantaneous ejecta creation. When applied to shots in the published literature, this bound is frequently less than several percent. Errors exceeding 15% may require velocities or timescales at odds with experimental observations.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

(U) Estimating the Photonics Budget, Resolution, and Signal Requirements for a Multi-Monochromatic X-ray Imager

This document examines the performance of a generic flat-mirror multimonochromatic imager (MMI), with special emphasis on existing instruments at NIF and Omega. We begin by deriving the standard equation for the mean number of photons detected per resolution element. The pinhole energy bandwidth is a contributing factor; this is dominated by the finite size of the source and may be considerable. The most common method for estimating the spatial resolution of such a system (quadrature addition) is, technically, mathematically invalid for this case. However, under the proper circumstances it may produce good estimates compared to a rigorous calculation based on the convolution of point-spread functions. Diffraction is an important contribution to the spatial resolution. Common approximations based on Fraunhofer (farfield) diffraction may be inappropriate and misleading, as the instrument may reside in multiple regimes depending upon its configuration or the energy of interest. It is crucial to identify the correct diffraction regime; Fraunhofer and Fresnel (near-field) diffraction profiles are substantially different, the latter being considerably wider. Finally, we combine the photonics and resolution analyses to derive an expression for the minimum signal level such that the resulting images are not dominated by photon statistics. This analysis is consistent with observed performance of the NIF MMI.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗