Operator interpretation of resonances generated by some operator matrices

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.Comment: LaTeX, 15 pages, no figures; Contribution to Proceedings of the Mark Krein International Conference on Operator Theory and Applications, Odessa, August 18-22, 199

Generation of highly symmetric, cylindrically convergent shockwaves in water

We report on pulsed power driven, exploding copper wire array experiments conducted to generate cylindrical convergent shockwaves in water employing μs risetime currents >550 kA in amplitude and with stored energies of >15 kJ—a substantial increase over previous results. The experiments were carried out on the recently constructed Mega-Ampere-Compression-and-Hydrodynamics facility at Imperial College London in collaboration with colleagues of Technion, Israel. 10 mm diameter arrays consisting of 60 × 130 μm wires were utilized, and the current and voltage diagnostics of the load region suggested that ∼8 kJ of energy was deposited in the wires (and the load region close to the wires) during the experiments, resulting in the formation of dense, highly resistive plasmas that rapidly expanded driving the shockwaves in water. Laser-backlit framing images of the shockfront were obtained at radii 50:1. Framing images and streak photographs showed that the velocity of the shockwave reached ∼7.5 km s−1 at 0.1 mm from the axis. 2D hydrodynamic simulations that match the experimentally obtained implosion trajectory suggest that pressures >1 Mbar are produced within 10 μm of the axis along with water densities of 3gcm−3 and temperatures of many 1000 s of Kelvin. Under these conditions, Quotidian Equation of State suggests that a strongly coupled plasma with an ionization fraction of ∼0.7 would be formed. The results represent a “stepping stone” in the application of the technique to drive different material samples into high pressure, warm dense matter regimes with compact, university scale generators, and provide support in scaling the technique to multi-mega ampere currents

Quasi-isentropic compression using compressed water flow generated by underwater electrical explosion of a wire array

A major experimental research area in material equation-of-state today involves the use of off-Hugoniot measurements rather than shock experiments that give only Hugoniot data. There is a wide range of applications using quasi-isentropic compression of matter including the direct measurement of the complete isentrope of materials in a single experiment and minimizing the heating of flyer plates for high-velocity shock measurements. We propose a novel approach to generating quasi-isentropic compression of matter. Using analytical modeling and hydrodynamic simulations, we show that a working fluid composed of compressed water, generated by an underwater electrical explosion of a planar wire array, might be used to efficiently drive the quasi-isentropic compression of a copper target to pressures ∼2 × 10 11 Pa without any complex target designs