Evolution of shock waves formed by laser-induced breakdown in air

The evolution of shock waves produced by 7 ns laser pulses in air is investigated by time-resolved shadowgraph. A nodular structure of the shock wave is observed. It is found that the origin of the structure is the multi-longitudinal-microfocus caused by the astigmatism of the laser beam. The spherical shock waves formed by each microfocus expand gradually and collide with each other, resulting in the nodular structure of the shock wave.     

Gravitational shock waves

This paper reports on and summarizes some recent progress on gravitational shocks, i.e., discontinuities in the Riemann curvature tensor. It is shown how the constraint equations play a crucial rôle in determining the nature and propagation of the shocks. Existence results are stated and are illustrated by some examples from numerical relativity.     

Brane-induced-gravity shock waves

We construct exact gravitational field solutions for a relativistic particle localized on a tensional brane in brane-induced gravity. They are a generalization of gravitational shock waves in 4D de Sitter space. We provide the metrics for both the normal branch and the self-inflating branch Dvali-Gabadadze-Porrati brane worlds, and compare them to the 4D Einstein gravity solution and to the case when gravity resides only in the 5D bulk, without any brane-localized curvature terms. At short distances the wave profile looks the same as in four dimensions. The corrections appear only far from the source, where they differ from the long distance corrections in 4D de Sitter space. We also discover a new nonperturbative channel for energy emission into the bulk from the self-inflating [corrected] branch, when gravity is modified at the de Sitter radius.     

Turbulence in argon shock waves

Irregular density fluctuations with turbulent-like behaviors are found in ionizing shock fronts produced by our arc driven shock tube. We use electric probes as the primary diagnostic. Spectral analyses show statistical patterns which seem frozen-in and characterizable by a dominant mode and its harmonics.     

Converging shock waves in metals

Study of propagation of a spherically converging shock wave has been carried out by Whitham’s method. The variation of shock velocity and pressure along the radius of curvature has been calculated numerically for a number of metals. Attempt has also been made to compare the experimental results of velocity of detonation wave with those reported elsewhere by the application of Whitham’s method. A good agreement between experimental and theoretical results has been obtained in this study.     

Ignition of cyclopropane in shock waves

The values of the ignition delay time of cyclopropane–oxygen–argon (cyclo-C₃H₆–O₂–Ar) mixtures of different compositions (φ = 0.333, 1, and 3) behind reflected shock waves at temperatures of 1200–1640 K and a pressure of (0.55 ± 0.05) MPa are measured. A kinetic mechanism of cyclopropane ignition using the known rate constants for the most important elementary reactions is developed. The mechanism closely describes both our own and published experimental data on the delay time of ignition of cyclopropane in shock waves over wide ranges of temperature (1200–2100 K), pressure (0.1–0.55 MPa), cyclopropane concentrations (0.05–11 vol %), and oxygen concentrations (0.25–21 vol %). It is shown that, with increasing fraction of diluent gas in the mixture, the dependence of the ignition delay time on the fuel-to-oxidizer equivalence ratio changes.     

Autoignition of ethylene in shock waves

The delay time of ignition of various C₂H₄-O₂-Ar mixtures behind reflected shock waves were measured at temperatures of 1090–1520 K and a pressure of 0.65 ± 0.05 MPa. A kinetic scheme of the ignition of ethylene based on the known rate constants of the key elementary reactions was developed. The scheme satisfactorily describes our own and published data on the ignition of ethylene in shock waves over wide ranges of temperature (1100–2400 K), pressure (0.006–0.64 MPa) and ethylene (0.1–17.4 vol %) and oxygen (0.6–20.7 vol %) concentrations.     

Simulations of shock waves in solids

Molecular dynamic shock wave simulations have been carried out for face centered cubic (f.c.c.) and body centered cubic (b.c.c.) solids using Lennard-Jones and Morse potentials for the interatomic interactions. The Hugoniot conservation relations were accurately obeyed in all of these calculations. The shock wave profiles may vary with the interatomic potential and the crystal structure, effects most clearly shown by the temperature profile near the shock front. The Lennard-Jones solids are intensitive to a change in structure but the Morse solids appear sensitive to crystal structure, at least in comparing b.c.c. with f.c.c. It was shown that the average shock wave temperature can be calculated from a combination of the Hugoniot conservation relations and the Mie-Grüneisen equation of state. The temperature calculated this way is in good agreement with the average shock wave temperature obtained in the computer simulations.     

Thermal diffusion shock waves

The Ludwig-Soret effect or thermal diffusion, which refers to the separation of liquid mixtures in a temperature gradient, is governed by a nonlinear, partial differential equation in space and time. It is shown here that the solution to the nonlinear differential equation for a binary mixture predicts the existence of shock waves completely analogous to fluid shocks and obeys an expression for the shock velocity that is an exact analogue of the Rankine-Hugoniot relations. Direct measurements of the time dependent, spatial absorption profile of a suspension of nanometer sized particles subjected to a sinusoidal temperature field generated by a pair of continuous laser beams, as well as self-diffraction experiments, show motion of the particles in agreement with the predictions of nonlinear theory.     

On gravitational shock waves

The discontinuity planes of the Riemann curvature tensorR _klm ⁱ in the Einsteinian vacuumR _kl =0 are isotropic hypersurfaces. These surfaces are to be conceived as being constructed of lightlike geodesics, which form, in the eikonal approximation, gravitational radiation. The discontinuity planes themselves describe the wave fronts of disturbances of the metricg _ik , propagating with the velocity of light. By successively applying continuity conditions for the derivatives of theg _ik that follow from Einstein's equations, we obtain the universal expression of gravitational wave fields in space-time strips (or representations) of arbitrarily selected Einstein spaces.     

Interactions of dispersive shock waves

Collisions and interactions of dispersive shock waves in defocusing (repulsive) nonlinear Schrödinger type systems are investigated analytically and numerically. Two canonical cases are considered. In one case, two counterpropagating dispersive shock waves experience a head-on collision, interact and eventually exit the interaction region with larger amplitudes and altered speeds. In the other case, a fast dispersive shock overtakes a slower one, giving rise to an interaction. Eventually the two merge into a single dispersive shock wave. In both cases, the interaction region is described by a modulated, quasi-periodic two-phase solution of the nonlinear Schrödinger equation. The boundaries between the background density, dispersive shock waves and their interaction region are calculated by solving the Whitham modulation equations. These asymptotic results are in excellent agreement with full numerical simulations. It is further shown that the interactions of two dispersive shock waves have some qualitative similarities to the interactions of two classical shock waves.     

Dispersive shock waves in nonlinear arrays

We experimentally study dispersive shock waves in nonlinear waveguide arrays. In contrast with gap solitons, the nonlinearity here pushes the propagation constant further into the transmission bands, facilitating Bloch mode coupling and energy transport. We directly observe this coupling, both within and between bands, by recording intensity in position space and power spectra in momentum space.     

Intense shock waves in bubble media

Shock waves in bubble media are studied experimentally. Data are obtained on the structure, velocity of propagation, and pressure of shock waves incident on a solid boundary and reflected from it. The experimental data are compared with the results of calculation of shock wave parameters.     

Elastic-plastic phenomena in ultrashort shock waves

A physical model of shock-wave phenomena in metals irradiated by a femtosecond laser pulse has been developed. The use of the experimental results (reported in S.I. Ashitkov et al., Pis’ma Zh. Eksp. Teor. Fiz. 92, 568 (2010) [JETP Lett. 92, 516 (2010)] together with the molecular dynamics simulation makes it possible to study the elastic properties of aluminum crystals at extreme shear stresses comparable in amplitude with the shear modulus. As a result, the elastic Hugoniot adiabat has been continued to the region of metastable elastic states at very high pressures, which are one or two orders of magnitude higher than the commonly accepted values for the dynamic elastic limit. It has been shown that the ultrashort elastic shock wave of superhigh pressure precedes the formation of the known split-shock wave structure consisting of an elastic precursor and a plastic shock wave.     

Electron kinetics in collisionless shock waves

We study the kinetic model of the formation of the energy spectrum of nonthermal electrons near the front of a quasilongitudinal, supercritical, collisionless shock wave. Nonresonant interactions of the electrons and the fluctuations generated by kinetic instabilities of the ions in the transition region inside the shock front play the main role in the heating and preacceleration of electrons. We calculate the electron energy spectrum in the vicinity of the shock wave and show that the heating and preacceleration of electrons occur on a scale of the order of several hundred ion inertial lengths in the vicinity of the viscous discontinuity. Although the electron distribution function is significantly nonequilibrium near the shock front, its low-energy part can be approximated by a Maxwellian distribution. The effective electron temperature T _eff ² behind the front, obtained in this manner, increases with the Mach number of the shock wave slower than it would if it followed the Hugoniot adiabat. We determine the condition under which the electron heating is ineffective but the electrons are effectively accelerated to high energies. The high-energy asymptotic behavior of the distribution function is that of a power law, with the exponent determined by the total compression ratio of the plasma, as in the case of acceleration by the first-order Fermi mechanism. The model is used to describe the case (important for applications) of acceleration of electrons by shock waves with large total Mach numbers, with the structure of these waves modified by the nonlinear interaction of nonthermal ions and consisting of an extended prefront with a smooth variation of the macroscopic parameters and a viscous discontinuity in speed with a moderate value of the Mach number. Zh. éksp. Teor. Fiz. 115, 846–864 (March 1999)     

Cosmological shock waves in general relativity

The problem of finding spherically symmetric self-similar solutions of Einstein's field equations with a barotropic perfect fluid, which can be joined through a shock wave to some cosmological models, is considered. It is found that such solutions comprise an expanding shell of matter surrounding a horizon with an interior singularity.