A Minimum Detectable Signal Specification for Photon Doppler Velocimetry
Draft of paper for the Journal of Dynamic Behavior of Materials
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Draft of paper for the Journal of Dynamic Behavior of Materials
The apparent velocity measured by an interferometric surface velocimeter is a function of both the surface velocity and the time derivative of the refractive index along the measurement path. We employed this dual sensitivity to simultaneously measure km/s surface velocities and 10 18 cm -3 average plasma densities with combined VISAR (velocity interferometer system for any reflector) and PDV (photonic Doppler velocimetry) measurements in experiments performed on the Z Pulsed Power Facility. We detail the governing equations, associated assumptions, and analysis specifics and show that the surface velocity can be extracted without knowledge of the specific plasma density profile.
Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when η 0 k , the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same η 0 k but different length scales, characterized by the wavelength λ varying by a factor of 4.9 from 65 to 130 to 320 µ m . Three such targets with different fixed η 0 k ′ s were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as λ decreased. The different η 0 k targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for 320 − 65 µ m wavelength perturbations, the effective strain rates increased from 8.7 × 10 6 to 3.3 × 10 7 s − 1 , a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates. Published by the American Physical Society 2024
High-purity [100] lithium fluoride (LiF) is the most widely used optical window in dynamic compression experiments due to its wide bandgap and well-characterized mechanical response. Recent plate-impact experiments established the [100] LiF Hugoniot to ∼230 GPa and demonstrated shock-induced melting onset at 182 GPa with complete melting by 195 GPa; theoretical models predict LiF optical transparency to nearly 900 GPa. To experimentally examine the optical transparency of [100] LiF at higher pressures and in the liquid state, laser-driven shock experiments were performed at peak stresses ranging from 223 to 363 GPa. Optical response was examined by measuring the particle velocity histories at the Kapton/LiF interface using laser interferometry at 532 and 1550 nm wavelengths; in-material particle velocities were obtained using established refractive-index corrections. Continuous photonic Doppler velocimetry fringes were observed across the entire stress range, demonstrating that LiF remains transparent to 1550 nm light throughout the multi-megabar regime investigated. At 532 nm, fringe visibility depended on the reflector coating: aluminum mirrors provided signals to ∼235 GPa, while gold mirrors extended this limit to 270.5 GPa, indicating that the shorter-wavelength response is likely sensitive to experimental configuration rather than to the loss of LiF transparency. Continued optical transparency to at least 360 GPa indicates that shock-melted LiF does not display bandgap closure over the stress range explored. Furthermore, these results provide direct experimental constraints on the high-pressure optical response and establish LiF (100) as a robust optical window material for laser-driven dynamic compression experiments approaching 400 GPa.
Shock-ramp experiments place high demands on the precision, accuracy, and temporal resolution of transformed velocimetry signals. To minimize uncertainty after total propagation of a shockramp experiment, ideally multiple PDV traces are used. However, each trace has some uncertainty that is a function of the PDV system and analysis of the velocimetry data. In order to determine a reasonable experimental estimate of minimum uncertainty, we calculate observed uncertainties in as-fielded PDV systems using multiple channels to sample the velocity on each shot. We also calculate the uncertainty’s sensitivity to choice of analysis methods.
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A new experimental setup for diagnosing hydrotest performance was designed, built, and implemented at DARHT. The setup consists of 128 points of fourth generation (Gen4) multiplexed photonic Doppler velocimetry (MPDV) and 128 separate points of modulation based ranging (MBR) to serve as a direct complement to the MPDV. The diagnostics were designed to overcome limitations in the third generation of the MPDV diagnostic that limited laser launch power to ~10 mW per point. As the main failure mechanism identified in the third generation MPDV system arose from stimulated Brillouin scattering, a nonlinear optical phenomenon inherent in standard single mode fiber, the fourth generation MPDV system reduced the number of time-multiplexed channels by a factor of two. This has allowed laser launch power to be increased to as much as 200 mW per channel which is a 20 times increase in the signal to noise ratio (SNR) as compared with the third generation system. This document will first discuss the previous limitations and describe the design of the system. This will be followed by the results of a simple flyer plate experiment used to demonstrate the improved SNR as well as calibrate the phase errors in the system that MBR is sensitive to.
Various optical diagnostic techniques such as laser induce fluorescence, Raman spectroscopy, laser Doppler velocimetry, and laser light scattering have been employed to study the flowfield downstream of a single injector element in a optically accessible rocket chamber at Penn State for a number o years. These techniques have been used with both liquid and gaseous oxygen at pressures up to 1000 psia which is the limit of the facility. The purpose of the test programs at Penn State were to develop the techniques and to study the flow field from various injector designs. To extend these studies to higher pressure and ultimately to multiple injectors require the capabilities of the Marshall Space Flight Center. These studies will extend the data base available for the various injector designs to higher pressure as well as to determine the interaction between multiple injectors. During this effort the Princeton Instruments ICCD camera was set up and checked out. The functionality of the system has been thoroughly checked and the shutter compensation time was found to be not working. The controller was returned to the manufacturer for warranty repair. The sensitivity has been measured and found to be approximately 60 counts per photon at maximum gain which agrees with the test data supplied by the manufacturer. The actual value depends on wavelength. The Princeton Instruments camera was been installed in a explosion proof tube for use with the rocket combustor. A 35 mm camera was also made ready for taking still photos inside the combustor. A fiber optic was used to transmit the laser light from an argon-ion laser to the rocket combustor for the light scattering images. This images were obtained for a LOX-hydrogen swirl coax injector. Several still photos were also obtained with the 35 mm camera for these firings.