Shock compression experiments provide access to high pressures in a laboratory setting. Matter at extreme pressures is often studied by utilizing a well controlled planar impact between two flat plates to generate a one dimensional shock wave. While these experiments are a powerful tool in equation of state (EOS) development, they are inherently limited by the velocity of the impacting plate. In an effort to dramatically increase the range of pressures which can be studied with available impact velocities, a new experimental technique is examined. The target plate is replaced by a composite assembly consisting of two concentric cylinders and is designed such that the initial shock velocity in a well characterized outer cylinder is higher than in the inner cylinder material of interest. After impact, conically converging shocks are generated at the interface due to the impedance mismatch between the two materials and the axisymmetric geometry. Upon convergence, an irregular reflection occurs and the conical analog of a Mach reflection develops. This Mach reflection grows until it reaches a steady state, for which an extremely high pressure state is concentrated behind the Mach stem. The reflection is studied using a combination of analytical, numerical, and experimental techniques. Ideas from gas dynamics, such as shock polars, are connected to the classic treatment of one-dimensional shocks in solids to form a simple method for treating the oblique reflections in the Mach lens configuration. Numerical simulations provide detailed full-field solutions and illustrate a methodology for extracting EOS information. The technique is validated experimentally by studying the shock response of copper and iron. Two different confining materials, 6061-T6 aluminum and molybdenum, are used to drive the converging shock waves for which the high pressure state is measured through a combination of velocity interferometry and impedance matching techniques.
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