The nonlinear, time- dependent, one-dimensional fluid dynamic equations with the el ectrostrictive driving force arising from Stimulated Brill ioun Scattering (SBS) are solved by a finite difference method. The medium is assumed to be an ideal gas with a finite viscosity and thermal conductivity, and the electrostrictive driving force has the form of a time modulated sine wave propagating along the optic axis (+z direction) at the acoustic velocity with respect to the medium. The modulating envelope is assumed to be Gaussian, which defines the pulse shape.
These calculations were carried out for pulses from a Raman shifted XeF laser (with an optical wavelength of .413 microns) incident upon a 10 amagat SF6 cell. The peak electrostrictive energy loading on the medium was taken as 944 Joules/liter, and the pulse widths were taken 50, 100, 500, and 1000 nanoseconds.
The spatial density profile at maximum energy loading was plotted for each pulse width. Due to nonlinear terms in the fluid equations, these profiles have amplitudes considerably smaller than those predicted by the linear fluid theory. Also, deviations in the profile shape from that of an ordinary sine wave were noted, indicating the presence of higher acoustical harmonics.
Of particular interest is the acoustical streaming predicted by these calculations. As the pulse interacts with the medium, the stream velocity increases from zero to a finite value, and remains at this value 1ong after the pulse decays. This final stream velocity increases with pulse width. Since acoustical resonances propagate at the acoustic velocity with respect to the medium, the scattered wave is Doppler down-shifted by the stream velocity as well as the acoustic velocity. Therefore, different portions of the scattered pulse receive different Doppler shifts.