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

Tregillis, Ian Lee; Koskelo, Aaron C.; Harrison, Alan Kent

doi:10.1063/5.0065961

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

Journal Article · Tue Sep 28 00:00:00 EDT 2021 · Journal of Applied Physics

DOI:https://doi.org/10.1063/5.0065961· OSTI ID:1826524

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1826524

Report Number(s):: LA-UR--21-27789

Journal Information:: Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 12 Vol. 130; ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (34)

Μeasurements of Sn Ejecta Particle-Size Distributions Using Ultraviolet In-line Fraunhofer Holography Sorenson, D. S.; Capelle, G. A.; Grover, M. Journal of Dynamic Behavior of Materials, Vol. 3, Issue 2 https://doi.org/10.1007/s40870-017-0105-7	journal	April 2017
Investigation of Ejecta Production from Tin at an Elevated Temperature and the Eutectic Alloy Lead–Bismuth Bell, D. J.; Routley, N. R.; Millett, J. C. F. Journal of Dynamic Behavior of Materials, Vol. 3, Issue 2 https://doi.org/10.1007/s40870-017-0106-6	journal	March 2017
Ejected Particle Size Distributions from Shocked Metal Surfaces Schauer, M. M.; Buttler, W. T.; Frayer, D. K. Journal of Dynamic Behavior of Materials, Vol. 3, Issue 2 https://doi.org/10.1007/s40870-017-0111-9	journal	April 2017
Advances in Ejecta Diagnostics at LLNL Steele, P. T.; Jacoby, B. A.; Compton, S. M. Journal of Dynamic Behavior of Materials, Vol. 3, Issue 2 https://doi.org/10.1007/s40870-017-0119-1	journal	May 2017
Photonic doppler velocimetry in shock physics experiments Mercier, P.; Benier, J.; Azzolina, A. Journal de Physique IV (Proceedings), Vol. 134 https://doi.org/10.1051/jp4:2006134124	journal	July 2006
Velocity sensing interferometer (VISAR) modification Hemsing, Willard F. Review of Scientific Instruments, Vol. 50, Issue 1 https://doi.org/10.1063/1.1135672	journal	January 1979
Piezoelectric probe for the detection of shock‐induced spray and spall Speight, C. S.; Harper, L.; Smeeton, V. S. Review of Scientific Instruments, Vol. 60, Issue 12 https://doi.org/10.1063/1.1140443	journal	December 1989
Ejecta particle size distributions for shock loaded Sn and Al metals Sorenson, D. S.; Minich, R. W.; Romero, J. L. Journal of Applied Physics, Vol. 92, Issue 10 https://doi.org/10.1063/1.1515125	journal	November 2002
Laser interferometer for measuring high velocities of any reflecting surface Barker, L. M.; Hollenbach, R. E. Journal of Applied Physics, Vol. 43, Issue 11 https://doi.org/10.1063/1.1660986	journal	November 1972
Limiting Conditions for Jet Formation in High Velocity Collisions Walsh, J. M.; Shreffler, R. G.; Willig, F. J. Journal of Applied Physics, Vol. 24, Issue 3 https://doi.org/10.1063/1.1721278	journal	March 1953
Piezoelectric characterization of ejecta from shocked tin surfaces Vogan, W. S.; Anderson, W. W.; Grover, M. Journal of Applied Physics, Vol. 98, Issue 11 https://doi.org/10.1063/1.2132521	journal	December 2005
Investigation of Ejecta Production in Tin Using Plate Impact Experiments Rigg, P. A. SHOCK COMPRESSION OF CONDENSED MATTER - 2005: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.2263559	conference	January 2006
Compact system for high-speed velocimetry using heterodyne techniques Strand, O. T.; Goosman, D. R.; Martinez, C. Review of Scientific Instruments, Vol. 77, Issue 8 https://doi.org/10.1063/1.2336749	journal	August 2006
Dynamic comparisons of piezoelectric ejecta diagnostics Buttler, W. T.; Zellner, M. B.; Olson, R. T. Journal of Applied Physics, Vol. 101, Issue 6 https://doi.org/10.1063/1.2712177	journal	March 2007
Effects of shock-breakout pressure on ejection of micron-scale material from shocked tin surfaces Zellner, M. B.; Grover, M.; Hammerberg, J. E. Journal of Applied Physics, Vol. 102, Issue 1 https://doi.org/10.1063/1.2752130	journal	July 2007
Surface preparation methods to enhance dynamic surface property measurements of shocked metal surfaces Zellner, M. B.; Vogan McNeil, W.; Gray, G. T. Journal of Applied Physics, Vol. 103, Issue 8 https://doi.org/10.1063/1.2906107	journal	April 2008
Probing the underlying physics of ejecta production from shocked Sn samples Zellner, M. B.; McNeil, W. Vogan; Hammerberg, J. E. Journal of Applied Physics, Vol. 103, Issue 12 https://doi.org/10.1063/1.2939253	journal	June 2008
Exploring Richtmyer–Meshkov instability phenomena and ejecta cloud physics Zellner, M. B.; Buttler, W. T. Applied Physics Letters, Vol. 93, Issue 11 https://doi.org/10.1063/1.2982421	journal	September 2008
Thick‐plate technique for measuring ejecta from shocked surfaces Asay, J. R. Journal of Applied Physics, Vol. 49, Issue 12 https://doi.org/10.1063/1.324545	journal	December 1978
Ejection of material from shocked surfaces of tin, tantalum and lead-alloys Andriot, P.; Chapron, P.; Olive, F. AIP Conference Proceeding Volume 78 https://doi.org/10.1063/1.33316	conference	January 1982
Accuracy and precision in photonic Doppler velocimetry Dolan, D. H. Review of Scientific Instruments, Vol. 81, Issue 5 https://doi.org/10.1063/1.3429257	journal	May 2010
A class of ejecta transport test problems Oro, David M.; Hammerberg, J. E.; Buttler, William T. SHOCK COMPRESSION OF CONDENSED MATTER - 2011: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.3686531	conference	January 2012
Experimental study of ejecta from shock melted lead Chen, Yongtao; Hu, Haibo; Tang, Tiegang Journal of Applied Physics, Vol. 111, Issue 5 https://doi.org/10.1063/1.3692570	journal	March 2012
Skew photonic Doppler velocimetry to investigate the expansion of a cloud of droplets created by micro-spalling of laser shock-melted metal foils Loison, D.; de Rességuier, T.; Dragon, A. Journal of Applied Physics, Vol. 112, Issue 11 https://doi.org/10.1063/1.4769304	journal	December 2012
Ejecta source model based on the nonlinear Richtmyer-Meshkov instability Dimonte, Guy; Terrones, Guillermo; Cherne, F. J. Journal of Applied Physics, Vol. 113, Issue 2 https://doi.org/10.1063/1.4773575	journal	January 2013
Experimental observations on the links between surface perturbation parameters and shock-induced mass ejection Monfared, S. K.; Oró, D. M.; Grover, M. Journal of Applied Physics, Vol. 116, Issue 6 https://doi.org/10.1063/1.4891449	journal	August 2014
Second shock ejecta measurements with an explosively driven two-shockwave drive Buttler, W. T.; Oró, D. M.; Olson, R. T. Journal of Applied Physics, Vol. 116, Issue 10 https://doi.org/10.1063/1.4895053	journal	September 2014
Ejected particle size measurement using Mie scattering in high explosive driven shockwave experiments Monfared, S. K.; Buttler, W. T.; Frayer, D. K. Journal of Applied Physics, Vol. 117, Issue 22 https://doi.org/10.1063/1.4922180	journal	June 2015
Proton radiography measurements and models of ejecta structure in shocked Sn Hammerberg, J. E.; Buttler, W. T.; Llobet, A. AIP Conference Proceedings https://doi.org/10.1063/1.5044848	conference	January 2018
Ejection of material from shocked surfaces Asay, J. R.; Mix, L. P.; Perry, F. C. Applied Physics Letters, Vol. 29, Issue 5 https://doi.org/10.1063/1.89066	journal	September 1976
Velocity and mass density of the ejecta produced from sinusoidal grooves in laser shock-loaded tin Prudhomme, G.; de Rességuier, T.; Roland, C. Journal of Applied Physics, Vol. 128, Issue 15 https://doi.org/10.1063/5.0022940	journal	October 2020
A mathematical framework for ejecta cloud dynamics with application to source models and piezoelectric mass measurements Tregillis, I. L.; Koskelo, Aaron Journal of Applied Physics, Vol. 130, Issue 14 https://doi.org/10.1063/5.0065960	journal	October 2021
The Physics of Inertial Fusion Atzeni, Stefano; Meyer-ter-Vehn, Jürgen https://doi.org/10.1093/acprof:oso/9780198562641.001.0001	book	January 2004
Analytic Solutions as a Tool for Verification and Validation of a Multiphysics Model Tregillis, I. L.; Koskelo, Aaron Journal of Verification, Validation and Uncertainty Quantification, Vol. 4, Issue 4 https://doi.org/10.1115/1.4045747	journal	December 2019

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