The experimental setup, (a) shows the optical setup external to the DAC. Although the probe pulses are shown as separated for the purpose of illustration, they overlap temporally and (b) shows a close up of a cross section of the DAC, where precompressed sample is shocked via ablation of a aluminum layer on the culet of the right side diamond. PBS is a polarizing beam splitter.
(a) A schematic of the stretcher with a knife edge and the unblocked beam path of red and blue components of the spectrum. G labels the gratings, and f is the focal length of the focusing optics. The knife edge blocks the spectrum, creating a fast rise in the intensity of the chirped pulse, (b) shows a typical spectrum of the laser pulse after the amplifier.
(a) A schematic of the pump and probe imaged at the spectrometer slit and (b) an image of a DAC from the pump side after an experiment. In this case, the sample was nitromethane, which reacted during the experiment and produced a black product which filled the DAC sample cavity. Although the reaction in this experiment was pump induced, it was not obviously correlated with interferometric probe data within 250 ps after the pump, and may have occurred after the probe time window. The short black horizontal line segments are camera artifacts.
(a) A measured breakout profile for a shocked, free aluminum surface expanding into air. These curves were generated in a single shot. Surface displacement is assumed to be proportional to the integrated finite derivative of the probe phase, as described in the text. Adjacent contours are separated by 10 ps of surface motion. Later curves are taller than earlier curves, (b) the finite derivative of the phase of the probe vs delay measured at the peak of the breakout profile. This data is directly analogous to the phase shift measured by traditional VISAR diagnostics and is proportional to the surface velocity. Assuming a particle velocity of 1/2 the surface velocity and the known Hugoniot of aluminum, we estimate the peak shock pressure for this experiment to be .
(a) A schematic of the probe interaction with the shocked region. Although only the first probe reflection from the shock front is shown, the shocked region is a dielectric film with multiple internal reflections of the probe. For a sufficiently small index rise at the shock front ( for compressed argon with a precompressed index of ), only the first order reflections need be considered. The pump diameter is much larger than the distance the shock wave travels over the duration of the experiment, (b) an example of the shock induced phase shift data in argon precompressed to 7.8 GPa, with a description of the parameterization, (c) the raw spectral data with the probe pulses only, corresponding to of bandwidth centered at 800 nm. Longer wavelengths are to the right. The probe pulse is chirped so that red wavelengths arrive at the sample earlier than blue wavelengths, so time in the raw spectral data runs from right to left, and (d) the raw spectral data with the pump. Light near the vertical center of the trace corresponds to the pump spatial position.
Schematic of the model. The incident probe is reflected from the shock front and the ablation layer. Only first order terms in are included in the approximation of the reflectivity. The particle velocity is assumed to be the same as the velocity of the interface between the ablator and the shocked sample. We assume the shocked refractive index is larger than the unshocked index. The magnitude of the reflectivity of the ablator is close to 1.
Reflectivities for terms in Eq. (7) in the complex plane. Reflectivities corresponding to and rotate in opposite directions and are symmetric about a perpendicular to . The phase which corresponds to oscillations in the signal, , is at a maximum or minimum when and are parallel. In the acoustic wave case, remains stationary while the sum oscillates sinusoidally along a perpendicular to . In the shock case, the reflectivities all rotate with the time dependence of .
Shock induced phase shift data taken at precompressions labeled by initial pressure. The data are vertically offset for clarity.
The pressure and density of argon shocked from precompressed states (points labeled by precompression) and from the liquid state at 84 K (unlabeled points). The curves are the cryogenic 84 K liquid argon Hugoniot (the lowest solid curve), the calculated boundaries of the equilibrium liquid and solid states (dashed curves), and the room temperature isotherm (the highest solid curve). Argon at equilibrium is liquid at densities below the dashed boundary of the melt line. The error bars indicate systematic error due to variation between the data and the model. The error for pressure is given by Eq. (20), and the error for density is given by an analogous expression for density. Scatter between points at the same precompression is due to shot to shot variation in laser power, variation in the thickness of the ablated film between shots, and alignment of the pump with the spectrometer slit. Nonetheless, all shots are estimates of states along the Hugoniot for a given precompression.
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