The noise spectrum from which stimulated Brillouin scatter grows has two sources in laser fusion plasmas; a broadband source due to ion-acoustic fluctuations, and a line source, usually much larger, which is the nonabsorbed light returning from the plasma critical surface. We give a theoretical description of stimulated Brillouin backscatter when the fluctuation source may be neglected and the scatter grows exclusively from the nonabsorbed light. Gradients of background density, velocity, and temperature are allowed. Theoretical predictions are compared to numerical simulations of scatter for parameters of recent experiments. It is found that stimulated Brillouin scatter can be greatly enhanced by the presence of a critical surface and that it can become an important part of the total energy balance.

A three-dimensional finite-difference ͑FD͒ method is used to simulate sonic wave propagation in a borehole with an inhomogeneous solid formation. The second-order FD scheme solves the first-order elastic wave equations with central differencing in both space and time via staggered grids. Liao's boundary condition is used to reduce artificial reflections from the finite computational domain. In the staggered grids, sources have to be implemented at the discrete center in order to maintain the appropriate symmetry in an axisymmetric borehole environment. The FD scheme is validated for multipole sources in three special media: ͑i͒ a homogeneous medium; ͑ii͒ a homogeneous formation with a fluid-filled borehole; and ͑iii͒ a horizontally layered formation. The staircase approximation of a circular borehole introduces little error in dipole wave fields, although it causes a noticeable phase velocity error in the monopole Stoneley wave. This error has been drastically reduced by using a material averaging scheme and finer grids. Numerical examples show that the FD scheme can accurately model 3-D elastic wave propagation in complex borehole environments.

The interpenetration of two supersonically moving plasmas is affected by both collective modes of oscillation and Coulomb collisions. Two potentially important plasma instabilities, an electrostatic ion two stream and an electromagnetic ion Weibel, are considered and shown to be stabilized if only a small fraction of ion kinetic energy is converted to heat. For low-density, highly supersonic flows, the mean free path for slowing down (dominated in most cases of interest by ion-ion collisions) can be larger than or comparable to the system size. To develop an understanding of these plasmas, a unique hydrodynamic model has been developed that allows interpenetration but explicitly converts kinetic energy into heat as the ions slow down. The model is applied to the collision of two plasmas created by heating two parallel foils.

A 2.5-D velocity-stress finite-difference code is described that models acoustic propagation in a borehole penetrating a generally anisotropic formation. The excitation may be a dilatation (monopole), or a point force (dipole) in an arbitrary direction. The anisotropic formation is homogeneous along the axis of the borehole but may be inhomogeneous in the transverse plane. The borehole cross section and location of the source in the borehole are arbitrary. Synthetic time-domain waveforms are displayed for arrays of monopole and dipole receivers deployed along the borehole axis in both fast and slow anisotropic formations. The specific anisotropy model employed for the numerical results is a transversely isotropic (TI) formation with its axis of symmetry inclined with respect to the borehole axis by an arbitrary angle.Flexural/shear and Stoneley wave slowness and attenuation estimates are extracted from the synthetic waveforms using a variant of Prony's method for a range of borehole inclinations relative to the formation axis of symmetry. In a fast formation, with borehole and formation symmetry axes perpendicular, flexural mode dispersion curves for quasi-SV and $H polarizations separate only at low frequency where moderate attenuation is also observed. In a slow formation, distinct dispersion curves are obtained for quasi-$V and $H polarizations over the entire frequency range. Moderate attenuation is again observed at low frequency. Scaled laboratory experiments confirm the numerical procedure. Experimental and numerical waveforms for monopole and several polarizations of dipole excitation in a transversely isotropic model formation overlay with excellent agreement.

This paper describes an absorbing boundary condition for finite‐difference modeling of elastic wave propagation in two and three dimensions. The boundary condition is particularly effective for obliquely incident waves, typically quite troublesome for absorbing boundaries. Analytical predictions of the boundary reflection coefficients of a few percent or less for angles of incidence up to 89° are verified in example finite‐difference applications. The algorithm is appropriate for use in a velocity‐stress finite‐difference (vs‐fd) formulation. It is computationally simpler than a similar absorbing boundary given previously for the standard displacement formulation. A second algorithm is presented which may be advantageous when the boundary of interest is exposed to strong evanescent waves. Both algorithms require that the adjacent elastic medium be locally homogeneous.