Tin coupons were shock damaged/melted under identical conditions with a diverging high explosive shock wave. Proton Radiography images and velocimetry data from experiments with seven different tin coupons of varying thickness are analyzed. Comparing experiments with identical samples allowed us to distinguish between repeatable and random features. Shapes and velocities of the main fragments are deterministic functions of the coupon thickness; random differences exist only at a small scale. Velocities of the leading layer and of the main fragment differ by the same value independently of coupon thicknesses, which is likely related to the separation energy of metal layers.
Dynamic phase change in shocked materials is one of the most challenging topics in equation-of-state research. The physical conditions are extreme, resembling rather late stages of stellar evolution than typical engineering processes. When pressure increases sufficiently, metals can undergo a solid-liquid phase transition. This article considers such experiments with tin [1].
All experiments considered here have the same axially symmetric setup. Tin coupons 5.1 cm in diameter and 4.76 mm -12.7 mm thick are placed on a high explosive (HE) 12.7 mm thick disk also 5.1 cm in diameter. A point detonator is glued to the opposite side of the HE in the center. The experimental data obtained are Proton Radiography (PRAD) [2,3,4] image series and 1-D signals from Velocity Interferometer System for Any Reflector (VISAR). VISAR records the coupon’s external surface velocity [5] by measuring the Doppler shift of the 532 nm laser light. The reflected, Doppler shifted beam is split, delayed, and interfered with itself. This produces a signal (i.e. phase) related to the acceleration of the observed surface. This produces a very precise measurement of the reflective surface velocity. The main limitation of this type of velocity measurement is that only surfaces possessing good reflective quality can be measured this way. Internal material and density fluctuations inside a disintegrating/melting coupon cannot be observed in this way. During an interval of 10’s of microseconds after detonation, a series of PRAD images are obtained using a proton beam orthogonal to the axis of symmetry. A proton beam is used instead of X-rays to ensure proper penetration into a relatively dense metal coupon. Complexity and cost limits the number of experiments and increases the need for extracting quantitative information with enhanced accuracy from PRAD images.
Knowing which features of the system’s evolution are deterministic and which are stochastic is important for understanding the physical process and for quantitative comparison of experiments with hydrocode modeling. To establish these information three experiments with coupon thicknesses 3.175 mm, 8 mm, and 12.7 mm were repeated.
Each pixel of a PRAD image represents a 0.1 x 0.1 mm 2 square of a 2D radiogram of the 3D distribution of the material. The radiogram is made by a parallel proton beam. Overlapping and then subtracting images from the same stage of the damage/melting evolution in repeated experiments provides qualitative analysis of the process. All the main axially symmetric features of the system of compared experiments are the same. Their location, velocities, and macroscopic shape evolution are also the same.
These features are deterministic within 1 mm precision in shape changes and less than 1.5% in leading surface velocity. Thus, these features should be reproducible in a model or a numerical simulation. On the other hand, all visible non-axially symmetric structures, in particular shapes and locations of density fluctuations in the central area vary stochastically from experiment to experiment. Only the average properties of these fluctuations (size, number) are reproducible.
A method to quantify image-to-image comparison, presented here, as a measure of distances between the overlapped images, is required to enhance accuracy of this comparison. Since large differences between color values of corresponding pixels indicate low overlapping areas, we propose an l 2 measure. More important, this imagery technique introduces only small value fluctuations for all the pixels.
In this measure D(I1,I2) is a distance between images I1 and I2, C1(i,k) and C2(i,k) are color values of their pixels with coordinates (i,k), and XY is a scaling factor. This measurement returns 255 as the maximum possible distance between images (a black square minus a white square), whereas the distance of an image to itself is 0. The difference between two identical static PRAD images measures c0.5, while typically the distance between two consecutive images from the same experiment is 15-20. Correspondingly, the distance between overlapping images from a pair of repeated experiments with a thick coupon, when non-axially symmetric density fluctuations are observed, is around 10. When no such fluctuations are visible, the distance is around 2 for the same stage of a pair of experiments with a thin coupon. This shows that experiments are repeatable with high accuracy.
Tracking shape evolution of metal fragments and their movement requires precise contour detection. Since 5 cm diameter tin coupons strongly attenuate the 800 MeV protons of PRAD, many of the images have low contrast. Additionally, a PRAD-specific overshot-undershot limbing artifact [6] is present in the images (Fig. 2). Fig. 2. Gray step represents material density change imaged by PRAD. 2.1 Resulted artifact when magnetic lenses collimating the proton beam are perfectly focused. 2.2 The artifact when magnetic lenses are not perfect
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