Moving shock

Abstract: The central idea of diffusive shock acceleration is presented from microscopic and macroscopic viewpoints; applied to reactionless test particles in a steady plane shock the mechanism is shown to produce a power law spectrum in momentum with a slope which, to lowest order in the ratio of plasma to particle speed, depends only on the compression in the shock. The associated time scale is found (also by a macroscopic and a microscopic method) and the problems of spherical shocks, as exemplified by a point explosion and a stellar-wind terminator, are treated by singular perturbation theory. The effect of including the particle reaction is then studied. It is shown that if the scattering is due to resonant waves these can rapidly grow with unknown consequences. The possible steady modified shock structures are classified and generalised Rankine-Hugoniot conditions found. Modifications of the spectrum are discussed on the basis of an exact, if rather artificial, solution, a high-energy asymptotic expansion and a perturbation expansion due to Blandford. It is pointed out that no steady solution can exist for very strong shocks; the possible time dependence is briefly discussed.

Abstract: An ignition and growth concept is used, within the framework of a one‐dimensional Lagrangian hydrodynamic code, to model the shock initiation of heterogeneous solid explosives. The leading shock wave of an initiating pulse is assumed to ignite a small fraction of the explosive at localized heated regions. These ignited regions then grow as material is consumed at their boundaries. The growth rate for a particular material is assumed to have the characteristic pressure dependence of high‐pressure laminar burning experiments. Results of the model calculations are in good quantitative agreement with recent manganin pressure gage and particle velocity gage measurements of the buildup of the initiating shock front to detonation for both sustained and short duration pulses in four solid explosives: PBX−9404, TATB, cast TNT, and PETN. The predicted run distances to detonation as functions of shock pressure at various initial densities and the predicted reaction zone lengths of the fully developed detonation waves also correlate well with experimental data for these four solid explosives.

Abstract: We study the properties of cosmological shock waves identified in high-resolution, N-body/hydrodynamic simulations of a ΛCDM universe and their role on thermalization of gas and acceleration of nonthermal, cosmic-ray (CR) particles. External shocks form around sheets, filaments, and knots of mass distribution when the gas in void regions accretes onto them. Within those nonlinear structures, internal shocks are produced by infall of previously shocked gas to filaments and knots and during subclump mergers, as well as by chaotic flow motions. Due to the low temperature of the accreting gas, the Mach number of external shocks is high, extending up to M ~ 100 or higher. In contrast, internal shocks have mostly low Mach numbers. For all shocks of M ≥ 1.5, the mean distance between shock surfaces over the entire computed volume is ~4 h-1 Mpc at present, or ~1 h-1 Mpc for internal shocks within nonlinear structures. Identified external shocks are more extensive, with their surface area ~2 times larger than that of identified internal shocks at present. However, especially because of higher preshock densities but also due to higher shock speeds, internal shocks dissipate more energy. Hence, the internal shocks are mainly responsible for gas thermalization as well as CR acceleration. In fact, internal shocks with 2 M 4 contribute about one-half of the total dissipation. Using a nonlinear diffusive shock acceleration model for CR protons, we estimate the ratio of CR energy to gas thermal energy dissipated at cosmological shock waves to be about one-half through the history of the universe. Our result supports scenarios in which the intracluster medium contains energetically significant populations of CRs.