Collision Time Measurements in a Sonoluminescing Microplasma with a Large Plasma Parameter

The plasma which forms inside of a micron-sized sonoluminescing bubble in water for under a nanosecond has been probed with 3 ns long laser pulses. A comparison of the response to 532 and 1064 nm light indicates that the plasma number density is about $2\times {10}^{21}{\mathrm{cm}}^{-3}$ and that transport properties are dominated by strong screening and correlation effects. The spherical shape, well-defined atomic density, and blackbody temperature make the sonoluminescing plasma a test bed for theories of strongly coupled plasmas. The plasma in this experiment distinguishes between competing theories of strong, intermediate, and weak effective screening.

Figure 1

Scatter plots showing the Mie scatter intensity (red dots) and the SL intensity (black dots) for (a) 532 and (b) 1064 nm. The SL intensity is normalized by the intensity distribution of SL flashes without an incident laser pulse and can be seen as a band of points centered on unity. For each SL intensity point, there is a corresponding Mie scatter point which is a measure of the bubbles’ radius and confirms successful spatial synchronization. SL-laser interactions only occur when the laser and SL flash overlap in time. The spread in Mie scatter points is due to the drift in bubble location relative to the laser focus during the laser’s repetition rate (10 Hz). As SL-laser interactions grow stronger, the accompanying Mie scatter signal increases due to an enlarged plasma radius.

Figure 2

Normalized histogram of the SL intensity for a range of laser intensities ($0.5–25\times {10}^9\mathrm{W}/{\mathrm{cm}}^2$) at 1064 (solid curve) and 532 nm (dotted curve). Only points within the interaction region of $-4$ to $+1\mathrm{ns}$ (532 nm) and $-8$ to $+1\mathrm{ns}$ (1064 nm) were used for the histogram. Although concurrent to the SL, a large number of laser shots did not result in an interaction due to the lack of spatial overlap caused by the bubbles’ drift in location.

Figure 3

Plasma reflection of 532 and 1064 nm light as a function of electron density for various collision theories. The Debye theory (solid curves) represents a highly screened plasma, where $\omega \tau \gg 1$ and high levels of reflection are observed for $\omega <{\omega }_p$. The dilute theory (dotted curves) diverges from the high reflectivity behavior due to strong damping ($\omega \tau \lesssim 1$) in the high density regime. The Daligault theory (dashed curves) experiences an intermediate level of reflection in the dense regime and is capable of describing both reflection at 1064 nm and spectral opacity at 532 nm.

Figure 4

Decay length of light in a dense plasma for 532 and 1064 nm using the collision theory of Daligault. Two absorption regimes are present for the electron density under consideration and are separated at the critical density (${\omega }_p=\omega$). Based on the suggested electron density of $\sim 2\times {10}^{21}{\mathrm{cm}}^{-3}$ for the SL measured in this experiment, the absorption is $\tau$ dominated for 532 nm and ${\omega }_p$ dominated for 1064 nm.

Figure 5

Collision time of 532 and 1064 nm light as a function of electron density for various collision theories. The collision time for the Debye theory (solid curves) is large for all electron densities and becomes density-independent for large plasma parameters. The dilute theory (dotted curves) represents the shortest collision time. The intermediate theory of Daligault (dashed curves) lies between these limiting theories and scales with ${\omega }_p$ for large densities.