An analytic model for the asymptotic growth in the linear Richtmyer-Meshkov instability is presented. Analytic formulae for the interface velocity are obtained both in the weak and the strong shock limits, whether a shock or a rarefaction are reflected. For weak shocks, the irrotational approximation is used. For strong shocks, the vorticity in the bulk must be also taken into account. It is seen that this bulk vorticity actually lowers the velocity predicted by the irrotational approximation. An explicit approximate formula is given in this case. It agrees very well with a previously reported numerical solution. Perturbation freeze-out is also considered in the weak shock limit. It is concluded that this instability is driven by the vorticity left by the shocks at the interface and in the fluids.

A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

Three-dimensional (3D) relativistic electromagnetic subcycle solitons were observed in 3D particle-in-cell simulations of an intense short-laser-pulse propagation in an underdense plasma. Their structure resembles that of an oscillating electric dipole with a poloidal electric field and a toroidal magnetic field that oscillate in phase with the electron density with frequency below the Langmuir frequency. On the ion time scale, the soliton undergoes a Coulomb explosion of its core, resulting in ion acceleration, and then evolves into a slowly expanding quasineutral cavity.

The interaction of relativistic electrons produced by ultrafast lasers focusing them on strongly precompressed thermonuclear fuel is analytically modeled. Energy loss to target electrons is treated through binary collisions and Langmuir wave excitation. The overall penetration depth is determined by quasielastic and multiple scattering on target ions. It thus appears possible to ignite efficient hot spots in a target with density larger than 300 g/cm 3 . [S0031-9007(96)01191-X]