ROUGH DRAFT authorea.com/7354

# Christopher Spencer UCLA Physics and Astronomy Professor Gary Williams 02 June 2014

Time between pulses of SL was found to be $$3.069×10^{−5}±0.01$$ seconds, width of an SL pulse was found to be $$1.925∗10^{−6}±0.04$$ seconds and Sonoluminescence was observed.

# Introduction

Sonoluminescence was first observed in 1934 by H. Frenzel and H. Schulte indirectly by looking at acoustic radar in an ultrasonic water bath [1]. Sonoluminescence is the production of light from sound. Sonoluminescence or SL is the phenomena in which a bubble on the scale of microns is spatially trapped and oscillated by an acoustic field where each compression on the bubble causes a small burst of light [2]. Light emission comes in the form of extrmely short bursts when sonoluminescing. In the case of this experiment a bubble was trapped in a cylinder fileld with liquid where then the acoustic field can be applied. If a laser is but on the trapped bubble then with a photomultiplier the scattering from the bubble can be measured, known as mie scattering. The purpose of this lab is to observe the sonoluminescing phenomena, measure mie scattering,to determine the radius of the bubble in time, and obtain the optical spectrum of SL using diffrent fliters in front of the photomuliplier.

## Theory

A discussion about how the bubble gets trapped is necessary here. We have a cylindrical acoustic resonator drive by piezoelectric drivers on both endcaps. Something that is piezoelectric has the property that when there is an applied stress to that material an electric charge accumulates in that material. A bubble is injected by running a current through a heater wire which is inside our resonantor. If the acoustic field is tuned to a resonant mode that has an antinode at the center then the resulting bubble from the heater wire will be attracted to antinode and be trapped there. The pressure needs to be a max in all directions to trap the bubble described by the equation$\delta p=\delta p_0 J_{mn}(k_rr)cosm\theta \cos\frac{n_z\pi}{L_z}z$ need m=0 modes of J to have a maximum at r=0. The Rayleigh–Plesset equation governs the dynamics of a spherical bubble in an infinite body of liquid and it cab be used here as $R\ddot{R}+3/2\dot{R}^2=\frac{1}{\rho}(p_0 +2\frac{r}{R})(\frac{R}{R_0})^{3\gamma} -2\sigma-p_{\infty}$ where $$\gamma$$ is an adiabatic index and $$\sigma$$ is surface tension of water. The light that gets emitted has a max temperature which we will define as $T_{max}=T_0[(\frac{R_{max}}{R_0})^3]^{\gamma-1}$ where we take $$R_0 \approx 3 \mu m$$
Mie scattering is the scattering of electromagnetic radiation by a sphere. In this lab a laser beam is put on the bubble and a photomultiplier picks up the intensity of the scattered light. The intensity of the light goes as $$I\approx R^2$$ and this can allow us to measures how the bubble radious changes in time. If the acoustic drive amplitude can reach a threshold value where the bubble can emit SL. This matches with the collapse point of the bubble on each acoustic cycle and has a pulse on order of $$10^6$$ photons emitted in about 100 ps. $$\frac{1}{2}$$

## Apparatus and Procedure

A schematic of the cylinder resonator is shown in figure 1. A bubble was created by briefly made by using a trigger to send quick pulses of current in the cylinder. This is not a perfect process and often took a while to get a steady bubble. The PMT has a gain of 50-100 k. It is powered by a 12 V supply and in brief works by the photoelectric effect. A photon comes in and hits a biased photocathode material biased at -2000 V. For every 5 photons an electron comes out of the photocathode and then goes through a “ramping” process and continues to hit biased electrodes. One electron is too small to make enough current for us to actually measure it so it is amplified. The amplified current comes out to be about $$10^{-12}$$ for every electron. This current then comes out and can be read by an oscilloscope. Figure 2 shows a photo of what was used in this lab. The laser,cylindrical resonator, PMT, and oscilloscope are shown.