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A Bayesian approach to time-domain photonic Doppler velocimetry analysis

Review of Scientific Instruments

Allison, J.R.; Bordas, R.; Read, J.; Burdiak, G.; Beltran, Victor; Joiner, N.; Doyle, H.; Hawker, N.; Skidmore, J.; Ao, T.; Porwitzky, A.; Dolan, D.; Farfan, B.; Johnson, Christopher R.; Hansen, A.

Photonic Doppler velocimetry (PDV) is an established technique for measuring the velocities of fast-moving surfaces in high-energy-density experiments. In the standard approach to PDV analysis, the short-time Fourier transform (STFT) is used to generate a spectrogram from which the velocity history of the target is inferred. The user chooses the form, duration, and separation of the window function. Here, we present a Bayesian approach to infer the velocity directly from the PDV oscilloscope trace, without using the spectrogram for analysis. This is clearly a difficult inference problem due to the highly periodic nature of the data, but we find that with carefully chosen prior distributions for the model parameters, we can accurately recover the injected velocity from synthetic data. We validate this method using PDV data collected at the STAR two-stage light gas gun at Sandia National Laboratories, recovering shock-front velocities in quartz that are consistent with those inferred using the STFT-based approach and are interpolated across regions of low signal-to-noise data. Although this method does not rely on the same user choices as the STFT, we caution that it can be prone to misspecification if the chosen model is not sufficient to capture the velocity behavior. Analysis using posterior predictive checks can be used to establish whether a better model is required, although more complex models come with additional computational cost, often taking more than several hours to converge when sampling the Bayesian posterior. We, therefore, recommend it be viewed as a complementary method to that of the STFT-based approach.

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Four Channel Time Multiplexed Photonic Doppler Velocimetry using an Optical Switch

Bourdon, Gustav J.; Johnson, Christopher R.

Photonic Doppler Velocimetry (PDV) is a diagnostic commonly used in shock physics and dynamic compression experiments to reliably get velocity information from experiments. In PDV systems, a common method of reducing experimental cost is to use time and frequency multiplexing to increase the number of PDV probes. With time multiplexing, interference between probes is a frequent problem. In this report, we look at using a high-speed optical switch to reduce this interference, including measuring the amount of interference generated to determine if it has the potential to affect experiments and integrating a time multiplexing system into an experiment. We find that, when applied to PDV systems, there is approximately (-23.4 ± 0.9) dB of interference measured in the short time Fourier transform between switch inputs. When an optical switch based time multiplexing system was integrated into a dynamic compression experiment, the system was able to successfully combine the signals from four different PDV probes onto a single optical cable without unacceptable levels of interference in the spectrogram. An optical switch based time multiplexing system appears to be a promising method for reducing the cost of fielding larger numbers of PDV probes in an experiment.

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Shock compression of single-crystal austenitic FeCr18Ni12.5 stainless steel to 60 GPa

Journal of Applied Physics

Brown, Nathan P.; Johnson, Christopher R.; Specht, Paul E.

We measured the austenitic FeCr18Ni12.5 stainless steel Hugoniot as a function of crystallographic direction to approximately 60 GPa. We shock-compressed FeCr18Ni12.5 samples oriented along ⟨ 100 ⟩ , ⟨ 110 ⟩ , and ⟨ 111 ⟩ to mean stresses ranging 30.5-58.1 GPa via Ta plate impact in a large-bore powder gun and measured the free-surface velocities with laser interferometry. We unambiguously observed the largest post-shock free-surface velocity along ⟨ 100 ⟩ in each experiment, which consequently produced the lowest shock velocity along that orientation. However, the propagation of experimental uncertainties through the impedance matching scheme used to compute the shock velocity produced sufficient uncertainty overlap to preclude definitive conclusion of Hugoniot anisotropy.

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DEVELOPMENT OF DIFFUSION BONDED IMPACTORS FOR RELIABLE SHOCK-RESHOCK EXPERIMENTS

Proceedings of the 16th Hypervelocity Impact Symposium, HVIS 2022

Specht, Paul E.; Johnson, Christopher R.; Arata, Edward R.

Diffusion bonding of two immiscible, binary metallic systems, Cu-Ta and Cu-W was employed to make repeatable and predictable dual-layer impactors for shock-reshock experiments. The diffusion bonded impactors were characterized using ultrasonic imaging and optical microscopy to ensure bonding and the absence of excessive Cu grain coarsening. The diffusion bonded impactors were launched via a two-stage gas gun at [100] LiF windows instrumented with multiple interferometry probes spanning nearly the entire impactor area. Consistent interferometry data was obtained from all experiments with no evidence of release prior to recompression, indicating a uniform bond. Comparisons to hydrocode simulations show excellent agreement for all experiments, facilitating easy application of these impactors to future experiments.

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14 Results
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