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For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

Light-scattering measurements have enabled us to determine that the transition to sonoluminescence is characterized by a bifurcation in the dynamics of a trapped pulsating bubble. These experiments also reveal that in the sonoluminescence (SL) state, changes in bubble radius of only 20% are associated with factors of 200 in the intensity of emitted light. This sensitivity of SL suggests that it originates from the kind of singular behavior that arises from the implosion of a shock wave. Theoretical extrapolations of this model to energy scales for fusion are discussed.PACS numbers: 78.60. Mq, 42.65.Re, 43.25.+y, 47.40.Nm The radiation pressure of a resonant sound field in a liquid can trap a small gas bubble at a velocity node [1].At a sufltciently high sound intensity the pulsations of the bubble are large enough to prevent its contents from dissolving in the surrounding liquid [2,3]. For an air bubble in water, a still further increase in intensity causes these pulsations to become so enormous and nonlinear that the supersonic [4] inward collapse of the bubble concentrates the acoustic energy by over 12 orders of magnitude [5] so as to emit picosecond flashes [6] of broadband light which extend well into the ultraviolet [7] and which furthermore are synchronous [8] with the sound field to picosecond accuracy.We now use light scattering techniques to determine the dependence of the light emitting mechanism on the bubble dynamics. In particular we find that the transition to sonoluminescence (SL) involves a sudden decrease in the bubble's size. In the SL state changes in experimental parameters which vary the bubble radius by 20% cause a hundredfold increase in light emission. Measurements of the bubble's dynamic susceptibility suggest that while the parameter spacer for SL is sharply delineated, the establishment of a steady state involves long time scales on the order of seconds. Our calculations suggest that this extremely sensitive dependence of sonoluminescence on bubble dynamics originates from the singularity which forms when a shock wave implodes [9]. Idealized theoretical extrapolations indicate that as the shock radius passes through 60 A the temperatures and densities are high enough for fusion.The extreme sensitivity of SL to external parameters such as the water temperature and the sound field amplitude, is indicated in Fig. 1 which shows that, as the water temperature decreases from 40 C to 1 C, the intensity of the light emission increases by a factor of over 200.

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