Converting acoustic energy into useful other energy forms

Sonoluminescence is an off-equilibrium phenomenon in which the energy of a resonant sound wave in a liquid is highly concentrated so as to generate flashes of light. The conversion of sound to light represents an energy amplification of eleven orders of magnitude. The flashes which occur once per cycle of the audible or ultrasonic sound fields can be comprised of over one million photons and last for less 100 picoseconds. The emission displays a clocklike synchronicity; the jitter in time between consecutive flashes is less than fifty picoseconds. The emission is blue to the eye and has a broadband spectrum increasing from 700 nanometers to 200 nanometers. The peak power is about 100 milliWatts. The initial stage of the energy focusing is effected by the nonlinear oscillations of a gas bubble trapped in the liquid. For sufficiently high drive pressures an imploding shock wave is launched into the gas by the collapsing bubble. The reflection of the shock from its focal point results in high temperatures and pressures. The sonoluminescence light emission can be sustained by sensing a characteristic of the emission and feeding back changes into the driving mechanism. The liquid is in a sealed container and the seeding of the gas bubble is effected by locally heating the liquid after sealing the container. Different energy forms than light can be obtained from the converted acoustic energy. When the gas contains deuterium and tritium there is the feasibility of the other energy form being fusion, namely including the generation of neutrons.

I. BACKGROUND 
Being able to convert and concentrate acoustic energy into other energy 
forms can provide very significant uses. 
It is possible to convert acoustic energy into light energy whose 
characteristics provide multiple new applications in physics, chemistry, 
biology and many other sciences, technologies and industries. In 
particular this invention relates to the conversion of the energy of a 
resonant sound field into flashes of light whose duration is in the range 
of 100 picoseconds and whose spectrum is broadband. These flashes of light 
occur with clock-like synchronicity with a repetition rate set by the 
acoustic frequency represent an energy concentration of 11 orders of 
magnitude. 
The invention is further concerned with the generation of all other energy 
forms which could result from a concentration of the acoustic energy. 
Since the limit of the energy focusing mechanism is undetermined such 
energy forms would include localized hot spots, UV radiation, x-rays, 
fusion and by-products of such acoustic energy conversion and 
concentration. 
It is known to be possible to convert acoustic energy into light energy. 
Significant limitations exist in controlling that light energy and in 
rendering the light energy useful. To date therefore no technological use 
has been possible for such converted energy, and the conversion has 
remained a scientific curiosity. 
There is a need to have useful new energy forms. 
Throughout this application reference will be made to different texts. 
These texts are listed in the bibliography. The contents of these texts 
are incorporated by reference herein. 
II SUMMARY 
By this invention there is provided a technique to concentrate and convert 
acoustic energy into highly useful different energy forms. 
According to the invention there is provided a method of highly 
concentrating and converting acoustic energy into a different energy form. 
There is created a gaseous bubble in a liquid in a container. The bubble 
is located in the liquid under the action of acoustic energy applied to 
the liquid. Compressing and decompressing the bubble is effected under the 
action of a resonating pressure applied to the liquid by the acoustic 
energy. 
Increasing the resonating pressure generates from the bubble an emission of 
a different energy form. This energy form can be sonoluminescence, fusion, 
x-rays, neutrons, and heat. SL is light energy obtained from the acoustic 
energy input. 
In one preferred form of the invention, a characteristic of the different 
energy form is sensed and changes in the characteristics are fed back to 
the means for generating the acoustic energy thereby to sustain the 
generation of the different energy form. In a different preferred form of 
the invention this motion of a bubble can be sensed or the changes in the 
acoustic energy sensed. Anyone or more of these sensed characteristics can 
be used in the feedback. 
In a preferred form of the invention the liquid is sealed in the container 
prior to the formation of a gaseous bubble in the liquid. The liquid is 
preferably degassed and the container is sealed against the ingress or 
egress of fluid, namely liquid and/or gas. 
One form of creating the bubble in the liquid is applying heat energy to a 
selected area in the liquid thereby to develop a cavity or gaseous bubble 
in the liquid. The bubble is subjected to the acoustic energy thereby to 
locate the bubble under the action of the resonating acoustic energy at a 
selected location in the body of a liquid. 
In a preferred form of the invention the acoustic energy applied to the 
gaseous bubble and the liquid is at a pressure sufficient to generate an 
imploding shock wave. Such an imploding shock wave travels towards its 
focal point, and during such travel heats the gas in the bubble. 
Reflecting from the focal point the gas is further heated to a temperature 
greater than about 10.sup.4 .degree. K., and preferably greater than 
10.sup.8 .degree. K. in an area adjacent to the focal point of the 
spherical shock wave. 
In those forms of the invention where the gas contains deuterium and 
tritium, the different energy form can include the generation of a fusion 
energy, namely including generation of a predetermined number of neutrons 
per second. 
In those forms of the invention where the different energy form is light, 
the light energy, namely sonoluminescence has a repetition rate 
substantially equivalent to the frequency of the acoustic energy imparted 
to the liquid. Such frequency, is preferably between about 100,000 cycles 
per second and 1,000 cycles per second. It is preferably about 35,000 
cycles per second. The pulse width of the sonoluminescence light energy is 
less than about 100 picoseconds, and the peak power is about 100 
milliwatts. The spectrum is between 200 nanometers to 700 nanometers. 
In a preferred form of the invention the ambient radius of the bubble after 
emitting light energy is less than about 5 microns, and preferably less 
than 2 microns on average. Prior to emitting light the maximum radius is 
greater than about 10 microns, and more preferably about 50 microns. 
The radiation pressure of a resonant sound field in a liquid traps a small 
gas bubble at a velocity node. At a sufficiently high sound intensity the 
pulsations of the bubble are large enough to prevent its contents from 
dissolving in the surrounding liquid. For an air bubble in water, a still 
further increase in intensity causes these pulsations to become so 
enormous and nonlinear that the supersonic inward collapse of the bubble 
concentrates the acoustic energy by over twelve orders of magnitude so as 
to emit picosecond flashes of broadband light which extend well into the 
ultraviolet and which furthermore are synchronous with the sound field to 
picosecond accuracy. 
The liquid can be cooled to increase the output of the different energy 
form. Thus cooling from about 40.degree. C., to 1.degree. C. increases the 
output about 200 fold. Cooling also decreases the size of the bubble, and 
increasing the ratio of maximum radius relative to the ambient radius. 
This is consistent with increased light output, namely a larger value for 
this ratio and with a smaller ambient radius the greater will be the 
output of the different energy form, namely light. Also as the ratio 
increases the larger is the imploding shock wave.

IV DESCRIPTION 
IV.1 Sonoluminescence 
Sonoluminescence (SL) is a far off equilibrium phenomenon in which the 
energy in a sound wave spontaneously concentrates so as to generate 
flashes of light in a liquid. 
From its discovery in 1934 up until the work of Crum and Gaitan, SL had 
been a transient and erratic effect. Bubbles would cavitate at random and 
unpredictable locations throughout the insonated fluid. As they collapsed 
they emitted flashes of light also in some unpredictable fashion. Crum and 
Gaitan observed SL from a single isolated cavitating bubble (Gaitan, F. 
and Crum, L. 1990: "Sonoluminescence from Single Bubbles," J. Acoust. Soc. 
Am. Suppl. 1, 87, S141/Gaitan, F. 1990: Ph.D. Thesis, National Center for 
Physical Acoustics, University of Mississippi). 
IV.2 Energy Conversion, Concentration and Amplification of 
Sonoluminescence. 
In the standard model for sonoluminescence, collapse of a bubble formed by 
cavitation occurs in a sufficiently spherical and adiabatic manner so the 
energy of collapse is delivered to a small number of molecules, which are 
thus excited or dissociated to the point at which they emit light (as 
chemiluminescence) when they recombine (Verrall, R. and Sehgal, C. 1987: 
"Sonoluminescence," Ultrasonics 25, 29-30). The phenomenon of SL involves 
an extraordinary degree of energy focusing. A typical SL sound field has a 
pressure swing P of 1 Atmosphere, which in water corresponds to a Mach 
number M of 10.sup.-5 (M=u/c where u is the speed of the fluid motion and 
c is the propagation speed of a sound wave). The energy density of the 
sound field is then: 
##EQU1## 
where .rho. is the liquid density and 
EQU 1 eV=16.times.10.sup.-19 J=1.6.times.10.sup.-12 erg 
As a photon must originate from a molecule, ion or atom and as a blue 
photon has an energy of .about.3 eV, this phenomenon involves a focusing 
or amplification of greater than 11 orders of magnitude (Barber, B., 
Lofstedt, R., and Putterman, S. 1991: "Sonoluminescence," J. Acoust. Soc. 
Am. 89, 1885, Barber, B. and Putterman, S. 1991: "Observation of 
synchronous picosecond sonoluminescence," Nature 352, 318-320.). The size 
of the spontaneous energy concentration, which characterizes SL, is 
extremely large. The limits of amplification achievable with this type of 
non-equilibrium phenomenon are unknown. 
IV.3 THE PROPERTIES OF SL 
Sonoluminescence involves the repetitive emission of light flashes one per 
cycle of the driving audible or ultrasonic sound field. The width of each 
flash is conservatively less than 100 picoseconds. Flashes containing more 
than 1 million photons are producible. By conservatively choosing the 
average photon to carry 3 eV (blue) then the lower limit on peak power is 
10 mW. 
This lower bound is increasing because as new ways to produce more photons 
are found, a large fraction of the SL emission is in the UV. This lower 
bound on peak power will increase if the SL flashes are narrower than 50 
ps. 
The flashes occur with a clock-like synchronicity; the jitter in time 
between consecutive flashes is less than 50 picoseconds. A valuable use 
for the pulse-to-pulse synchronicity is to generate a trigger connected to 
SL. No other trigger, which can be generated prior to the SL flash it is 
connected to, has a jitter of less than a nanosecond. An immediate 
application of the synchronicity is to provide the trigger for a streak 
camera to be used to measure the flash width. 
Streak cameras can be used to measure the duration of a single flash, or 
many flashes can be overlaid using the camera's repetitive sampling mode. 
Using a streak camera it is possible to resolve pulse widths down to a few 
picoseconds. Using a Hamamatsu camera the duration of the 34 ps PLP-01 
pulses were measured by taking advantage of the pulser's hard trigger to 
use the camera in its repetitive sampling mode. 
The spectrum of the SL light emission is broadband extending from 700 to 
200 nanometers, the UV cutoff of water (FIG. 1.) The spectrum is 
increasing into the UV but because water does not transmit energy between 
6 eV and 5 keV the peak in light emission is unknown. 
The light emission is spherically symmetric and of uniform intensity from 
flash to flash. The intensity is a sensitive function of experimental 
parameters. The intensity per flash increases with decreasing drive 
frequency. The extreme sensitivity of SL to external parameters, such as 
the water temperature and the sound field amplitude, is indicated in FIG. 
2A. As the water temperature decreases from about 40.degree. C. to 
1.degree. C., the intensity of the light emission increases by a factor of 
over 200. At 1.degree. C. the purple light emitted by the bubble is so 
bright that it can be seen by the unaided eye even in the presence of 
external lighting. At about 40.degree. C. the SL is barely visible even in 
a darkened room. The difference in the position of the .DELTA. at about 
the 34.degree. C. location to the position at the 1.degree. C. location 
indicates this increase. The intensity is also a strong function of the 
various gasses dissolved in the fluid and the extent to which the fluid is 
degassed (FIGS. 3 & 4). 
IV.4 BUBBLE DYNAMICS 
The initial stages of energy focusing in SL involve the nonlinear 
oscillations of a gas bubble in the fluid. Acoustic radiation pressure 
traps the bubble at a pressure antinode of the driving sound field. There 
it oscillates in response to the compressions and rarefactions of the 
sound field. The bubble's oscillation maintains it against dissolution 
into the degassed fluid. When the drive pressure is sufficiently large the 
bubbles oscillation is so nonlinear that the supersonic collapse of the 
bubble launches an imploding shock wave into the gas. 
Light-scattering measurements show that the transition to SL is 
characterized by a bifurcation in the dynamics of a trapped pulsating 
bubble. In the 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. 
Since an understanding of this remarkable sensitivity would provide insight 
into the as yet unexplained mechanism of light emission as well as 
providing a critical test of theoretical models, a recently described 
light scattering technique is employed to determine the corresponding 
temperature dependence of the parameters which characterize the highly 
nonlinear pulsations of the bubble. These include its maximum radius 
R.sub.m, the dynamic acoustic pressure amplitude P.sub.a at the location 
of the bubble and the ambient radius R.sub.0 when its contents are at 1 
Atmosphere. 
According to our results, which are shown in FIG. 2A, the more than 
hundredfold increase in light intensity is accompanied by changes of only 
10%-20% in the key physical quantities that describe the motion of the 
trapped bubble of air. The location of the .cndot. at the different 
temperature positions indicates this change. FIG. 2B further describes the 
relationship of temperature, pressure and ambient radius. 
Even when the fluid temperature is fixed the intensity of SL is a rapidly 
increasing function of P.sub.a until, as shown in FIG. 5, an upper 
threshold is reached. With the goal of understanding the dynamical effects 
that limit the extent to which sound can be converted into light, there is 
displayed in FIG. 5 the measurements of radius versus time for a trapped 
bubble as a function of a slowly increasing drive level. The increasing 
drive level is the increasing intensity or pressure applied by the 
acoustic energy on the liquid. 
In FIG. 5 are the following regimes: (a) at the lowest amplitudes shown, 
the sound field can trap the bubble but the oscillations are not 
sufficiently violent to make light: this is depicted by the unshaded 
distributions, namely below about 1.05 Atmosphere acoustic pressure; (b) 
as the amplitude is increased the bubble abruptly becomes significantly 
smaller while the collapse ratio R.sub.m /R.sub.0 becomes significantly 
larger: This is indicated by the shaded distributions, namely immediately 
above the about 1.05 Atmosphere acoustic pressure; (c) a still further 
increase in amplitude leads to a more violent collapse and a stronger 
light emission until an upper threshold is reached. This is indicated by 
the increased difference in R.sub.M and R.sub.0 as the pressure increased 
up to about 1.3 Atmosphere. Above the threshold at about 1.3 Atmosphere 
acoustic pressure, it is impossible to maintain a stable bubble of any 
radius. The data for FIG. 2A were taken at the top of the SL regime where 
the number N of photons per flash is nearly its maximum, namely at about 
the 1.3 Atmosphere pressure. Before the light emission the bubble maximum 
radius is about 50 microns, and after the emission the ambient radius is 
less than about 5 microns, and about 2 microns. 
The actual creation, generation and establishment of the light emitting 
mechanism SL is also extremely sensitive to small changes in P.sub.a. A 
detailed comparison of the radius versus time curves just above and just 
below the abrupt transition between the regimes (a) and (b) is shown in 
FIG. 6. It can be seen that, as the acoustic drive is increased by a few 
percent, the bubble adopts a new steady state with a significantly smaller 
ambient radius; also, the collapse, first studied by Rayleigh, becomes 
more violent, as is evidenced by a lessening of the afterbounces. The low 
drive side of the threshold is characterized by an easily noticeable 
jiggling or `dancing` of the bubble's position through a few multiples of 
R.sub.m, whereas on the SL side of the threshold the bubble is extremely 
stable. 
With other liquids, such as low viscosity silicon oil, a bubble has been 
trapped in the non-SL regime. It is not possible to achieve the transition 
to SL as shown in FIG. 6. The creation of SL is sensitive to small 
parametric variations. 
Although the threshold for establishing SL is sharp and well defined, the 
time required for the bubble to reach the SL steady state is very long, 
typically on the order of 10.sup.5 cycles of the imposed sound field. 
Displayed in FIG. 7B is the response of a bubble to a sudden jump in the 
sound intensity which takes it from a state of low (or zero) SL to one of 
high SL. In this case the short term response is followed by a long time 
response on the scale of seconds during which the bubble seeks a steady 
state characteristic of a more violent collapse. One physical process with 
this long time scale is mass diffusion for which a typical time is 
EQU t.sub.d =.rho..sub.g R.sup.2 /DC.sub.0. 
where .rho..sub.g is the gas density, R is a typical bubble radius, 
EQU D=2..times.10.sup.-9 m.sup.2 /s 
is the coefficient of mass diffusion for air in water and 
EQU C.sub.0 
is the saturated concentration of air in water in the close vicinity of the 
ambient bubble. Due to the possible importance of mass diffusion, the data 
for FIG. 2A were taken at similar concentrations, in the range of 5%-10% 
of saturation for dissolved air in water. The dynamical method for 
determining the concentration has been described. That the water should be 
degassed was an important aspect of the discovery of single bubble SL. The 
transient response of the bubble to a sudden increase in P.sub.a at the 
upper threshold is shown in FIG. 7A. In this case the bubble disappears on 
the faster time scale required for the sound field to exceed the upper 
threshold appreciably, but not before an initial increase in the maximum 
radius and SL intensity is seen. 
IV.5 Shock waves 
It has been suggested that SL is due to thermal bremsstrahlung emitted from 
a plasma generated by an imploding spherical shock wave. 
As shown in FIGS. 2A and 2B the shock wave theory also yields SL 
intensities that are extremely sensitive to the drive parameters and 
furthermore the calculated values are in reasonable agreement with 
experiment. Since this model does not allow for mass exchange of air 
between the interior of the bubble and its surroundings through the 
interface, the model cannot determine R.sub.0 and cannot explain the two 
thresholds described above. 
For this reason a comparison of this model to the experimentally observed 
SL intensity requires the use of data for R.sub.0 and P.sub.a as obtained 
from our light scattering measurements. The range of values attached to 
the theoretical results shown in FIGS. 2A and 2B arises not from the model 
but from uncertainties of roughly 0.025 Atmospheres for P.sub.a and 0.25 
.mu.m for R.sub.0 in the experimental input parameters. 
The integrated spectrum for this model is proportional to .lambda..sup.-1.5 
where .lambda. is the wavelength of the emitted light. This is a somewhat 
weaker dependence on .lambda. that than observed, but corrections to the 
formula for the spectrum of bremsstrahlung, due to the fact that the light 
is emitted from a region smaller than the wavelength of light, may explain 
this. Furthermore the flash widths of 150 ps, as determined by this model, 
are reasonably consistent with experiment. 
According to the shock wave model the temperature increases without limit 
provided the shock remains spherical and transport processes can be 
neglected. For example, a simple calculation for an ideal gas indicates 
that the shock attains a temperature of 3..times.10.sup.8 K. when its 
radius returns through 10 .ANG. just after the moment of focusing. In the 
limit of large Mach numbers, a self-similar solution of Euler's equations 
can be found in which the radius of the shock is 
EQU R.sub.S =At.sup..alpha., 
(1) where t is the time to the moment of focusing and a depends upon the 
equation of state (for air a.about.0.7). The determination of A requires 
knowledge of the launch conditions which are that the shock is moving at 
Mach 1 (relative to c.sub.0, the ambient sound velocity in the gas) when 
the bubble is collapsing through its ambient radius R.sub.0. In fact 
energy conservation implies that the collapse rate of the bubble obeys 
##EQU2## 
where g is the heat capacity ratio and 
EQU .rho..sub.0 /.rho. 
is the ratio of densities of the ambient gas and the liquid. Applying the 
launch condition to (1), 
EQU M=R.sub.S /c.sub.0 =(t.sub.0 /t).sup.1-.alpha., R.sub.S =R.sub.0 
(t/t.sub.0).sup..alpha., 
(2) where t.sub.0 is the time that elapses between the moment when the 
bubble radius is R.sub.0 and the instant when the shock focuses; 
EQU t.sub.0 =.alpha.R.sub.0 /c.sub.0. 
(3) The temperature jump across a strong shock is proportional to the 
square of the Mach number. But after reflection from the origin the 
outgoing shock moves into the gas previously heated by the incoming shock, 
and the increase in temperature after focusing is approximately given by 
EQU T/T.sub.0 =M.sup.A 
where 
EQU T.sub.0 =300 K. 
is the ambient temperature. In this way one verifies that, 100 ps after 
focusing, M=4 R.sub.s =0.1 .mu.m and T=10.sup.5 K. in agreement with the 
measured characteristics of SL. 
IV.6 LIGHT FLASH CHARACTERISTICS 
The properties of a single, stable, light-emitting bubble in an imposed 
sound field, indicate that the SL comes via the clock-like emission of 
picosecond flashes of light. 
1) SL flashes are remarkably short lived. An upper bound of 50 ps has been 
placed upon these flash widths using the fastest PMTs available. There is 
the potential for development of a cheap variable intensity, broad 
spectrum picosecond light pulser. Attempts to resolve the flash width with 
a streak camera are hindered by low light levels. 
2) SL is synchronous. The jitter in the time between successive SL flashes 
is less than 50 ps. This is remarkable when it is compared to the 40 ms 
sound period. The synchronicity provides the closest thing to a "hard 
trigger" that is connected to the SL flashes. 
3) The SL pulses are dim. You can see the bubble "glow" in a darkened room. 
Bright pulses from a bubble, initially seeded as air into degassed water 
at room temperature and pressure, can contain a million photons. By simply 
changing drive parameters there is no regime where the SL gets anomalously 
bright. The flashes have uniform intensity and are spherically symmetric. 
V PRODUCING SONOLUMINESCENCE 
The technique used to produce single bubble, synchronous sonoluminescence 
with enough intensity and stability to measure the properties is 
described. 
V.1 Preparing and Driving Resonators. 
The resonators used consisted of a set of piezoelectric transducers (PZTs) 
epoxied to the outer wall of a transparent spherical flask containing 
distilled water. The PZTs are the source of the sound field used to trap 
and drive the bubble. A spherical flask was chosen because of its high 
quality factor (Q) radially symmetric modes. These modes would aid in the 
production of the large amplitude sound field necessary to produce SL. 
Because these modes have a pressure antinode at r=0, they trap the bubble 
at the sphere's center. The glass or quartz walls thus have little 
aberrant effect on the SL originating from the sphere's center. 
A PZT is a crystal or ceramic that produces sound by changing its size when 
a voltage is introduced across it. The PZTs used were lead 
titanate-zirconate piezo ceramics. Hollow cylinders polarized radially and 
disks polarized longitudinally were used. They were ordered with 
electrodes already present on the appropriate surfaces (Channel 
Industries, Vernatron, Transducer Products). The cylinders were epoxied to 
the spheres with their z axis along a diameter of the sphere. The disks 
were attached by epoxying one of the circular faces to the wall of the 
sphere. 
As shown in FIG. 8, the PZTs are epoxies to the equator of the sphere, with 
the sphere's neck pointing upward. The epoxy used was a common two-part 
5-minute epoxy. This epoxy adequately transmitted the sound energy into 
the liquid and also allowed the later nondestructive removal of PZTs. 
Striking a razor blade positioned at the glass-epoxy interface with a 
hammer separated the PZT from the sphere allowing it to be reused. 
A one-liter Pyrex boiling flask was the first resonator used to observe SL. 
Spheres of various sizes, materials, brand names and properties were 
eventually tried. The largest sphere in which SL was observed was a five 
liter glass sphere; the smallest sphere was a ten milliliter quartz 
sphere. Initially different sized spheres were used to measure SL 
properties at each sphere's different resonant frequencies. Smaller 
spheres were eventually used exclusively because they degas faster and 
require less clean water for each run. Most importantly, smaller flasks 
can be brought closer to optical instruments, such as streak cameras, 
monochromators or PMTs, which then catch a greater fraction of the total 
light emitted. The first flasks used were made out of glass because of its 
availability (Pyrex.RTM., Kontes.RTM.). Later quartz (G. M. & Assoc. 
synthetic fused silica) was used because it passes more of the UV light 
emitted during SL. 
Any vibration of the sphere changes the shape of the surface of the water 
in the neck. The pressure field in the sphere is adversely affected. The 
properties of the SL will accordingly be altered. Smaller flask necks lead 
to a lessening of surface deformation. Smaller necks also generally make 
an off-the-shelf flask more spherical. It is also necessary to find at 
what water level the bubble is most centered and moves least as the drive 
frequency is changed. There exist water levels at which undesired 
parasitic vibrations of the system greatly reduce the stability of the 
bubble's motion. 
A resonator can have a single PZT attached to a sphere. Regardless of which 
sphere was used, the trapped bubble was always positioned slightly off 
center away from the lone PZT. In addition, the location where the sound 
field trapped the bubble would change as the drive parameters were 
modified. This was an indication of imperfect spherical mode shape. With 
symmetry as a guide, resonators were constructed with 2 PZTs, on opposite 
sides of the sphere. Although it did not seem necessary to epoxy the PZTs 
at the equator, this convention was adopted because of its pleasing 
symmetry. When more than one PZT was used on a sphere, care was taken to 
have the polarization vectors and applied electric fields oriented to get 
an additive sound amplitude at the center of the sphere. Adding a second 
PZT greatly improved bubble performance. The bubble was located closer to 
the dead center of the sphere and when the drive parameters were changed, 
the bubble moved very little. 
PZTs are capacitors (Hueter, T. 1955: Sonics, Wiley & Sons; Wilson, O. 
1988: Introduction to Theory and Design of Sonar Transducers, Peninsula; 
Vigoureux, P. 1950: Ultrasonics, Chapman & Hall). To improve the driving 
amplifier's performance high power inductors are located in series with 
the PZTs. The inductance was chosen so the impedance would be purely real 
at the drive frequency .omega.. 
It is a LRC circuit so: 
EQU .omega..sup.2 .ident.1/LC. 
Using the inductor brings the current in phase with the voltage so less 
voltage would be needed to deliver the same power. 
Where many different PZTs and drive frequencies are used it is necessary to 
be able to adjust the inductance. Variable inductors can be used. 
Alternatively two inductors can be used. The pair of inductors could be 
brought closer together or further apart, changing their total inductance 
due to the fringing fields. The otherwise formidable voltage needed to 
produce sufficient sound amplitudes was greatly reduced by use of the 
tuned induction circuit. The use of a transformer has also been suggested 
(Hueter, T. 1955: Sonics, Wiley & Sons) to match the high impedance of a 
PZT to the amplifier used. 
A drawback to using the inductors was the formidable electromagnetic 
radiation they emitted. Detection equipment and cables were kept as far 
from them as possible. Shielded coaxial cable was used to carry the drive 
signal whenever possible, and the shield kept as close to earth ground as 
possible to reduce cross talk into microphones, lock-ins and pre-amps. 
The typical acoustical resonances have frequencies from 10 kHz to 60 kHz 
and Qs of roughly 1000. This means an oscillator with precision and 
stability of single Hz at these frequencies is necessary to drive the 
acoustical resonances appropriately. 
V.2 Acoustical Resonances of a Liquid Filled Sphere. 
The normal modes of a liquid-filled sphere are found by subjecting 
solutions of the wave equation in spherical coordinates to the appropriate 
boundary conditions. The necessary math and descriptions of the relevant 
functions can be found in the literature (Arfken, G. 1985: Mathematical 
Methods for Physicists, Academic Press.). 
The wave equation for the pressure wave 
EQU .delta.P 
in spherical coordinates is: 
##EQU3## 
where c is the speed of sound in the liquid. Assume the solution is 
separable and formulate a trial solution: 
EQU .delta.P(r,.theta.,.phi.,t)=.delta.P.sub.0 
R(r).THETA.(.theta.).PHI.(.phi.)T(t). [2.2.2] 
The wave to be oscillatory with frequency so: 
EQU T(t)=e.sup..delta. [ 2.2.3] 
Inserting trial solution into wave equation and dividing the result by dP 
leads to 
##EQU4## 
The part of this equation that depends only on .phi. can be set equal to a 
constant: 
##EQU5## 
The function is seen to have a sinusoidal solution .PHI. 
EQU .PHI.=sin m.phi.. [2.2.6] 
After substituting Equation 2.2.5 into Equation 2.2.4, the part depending 
only on .phi. is set equal to the constant l(l+1) 
The result is: 
##EQU6## 
The solutions to this equation are the associated Legendre functions 
EQU .THETA.=P.sub..delta..sup.l (cos .theta.) [2.2.8] 
Equation 2.2.4 is now reduced to a function of r only 
##EQU7## 
This can be written as 
##EQU8## 
where the wavenumber k is introduced via 
EQU .omega.=ck. 
The standing wave solutions to this equation, which behave nicely at the 
origin, are the spherical Bessel functions of order l: 
EQU R=j.sub.l (kr). [2.2.11] 
In summary the standing wave modes inside the sphere will have the form: 
EQU .delta.P(r,.theta.,.phi.,t)=.delta.P.sub..alpha. j.sub.l (kr)P.sub.2.sup.t 
(cos .theta.) sin m.phi.e.sup.1. [2.2.12] 
Since the acoustic impedance of air is far less than water (Kinsler, L., 
Frey, A., Coppens, A. and Sanders, J. 1982: Fundamental of Acoustics, 
Wiley & Sons) there must be a pressure node at the sphere's boundary. 
EQU (.delta.P(.alpha.)=0) 
The resonant frequencies 
EQU f.sub.l,K 
are: 
##EQU9## 
where 
EQU .alpha..sub.l,K 
are the zeros of the l th order spherical Bessel function: 
EQU j.sub.l (.alpha..sub.l,K)=0. [2.2.14] 
It should be noted that Equation 2.2.13 does not depend on m and for a 
given l there are l+1 possible values of m (0.ltoreq.m.ltoreq.l). 
This means there are l+1 degenerate modes with resonance frequency 
EQU f.sub.l,K. 
Exciting the spherically symmetric modes is affected because they have high 
Q, have a pressure antinode at r=0, and there is no degeneracy. The 
spherically symmetric solutions are those for which l=0 and thus m=0. In 
this case 
EQU .PHI.=l 
and 
EQU .THETA.=l. 
The zeroth order spherical Bessel function is simply: 
##EQU10## 
and the zeros of this function are: 
EQU .alpha..sub..alpha.K =.eta..pi. [2.2.16] 
After finding the speed of sound in the fluid (Kinsler, L., Frey, A., 
Coppens, A. and Sanders, J. 1982: Fundamental of Acoustics, Wiley & Sons), 
the resonant frequencies of the spherically symmetric acoustic modes are 
calculated from: 
##EQU11## 
The resonant frequencies for some common sizes of spherical flasks filled 
with water are tabulated in Table 2.2.1. 
TABLE V.2.1 
______________________________________ 
Theoretical Resonant Frequencies of Water Filled Spherical Flasks 
speed of sound = 1.5 .times. 10.sup.5 cm/s 
Volume Radius f.sub..alpha.1 
f.sub..alpha.2 
f.sub..alpha.3 
(ml) (cm) (kHz) (kHz) 
(kHz) 
______________________________________ 
10 1.34 56.0 112 168 
100 2.88 26.0 52.1 78.1 
250 3.91 19.2 38.4 57.5 
1000 6.20 1 24.2 36.3 
2.1 
______________________________________ 
Modes that are not spherically symmetric have resonance frequencies found 
scattered between these spherically symmetric modes, but the l=0,n=1 mode 
is the lowest frequency mode of the sphere. 
V.3 Water Degassing. 
Degassing the water is required. Consider a bubble, in water saturated with 
air, oscillating due to a sound pressure amplitude of a few atmospheres. 
Rectified diffusion will cause the bubble to gradually intake air from the 
water. The bubble will grow, its oscillation will become unstable and 
eventually it will become too large to remain trapped by the sound field. 
In order to keep a bubble stable and drive it with the sound pressures 
necessary to produce SL, the air in the water must be removed. Techniques 
for degassing liquids include boiling the liquid, stirring the liquid 
under vacuum (Battino, R., Banzhof, M., Bogan, M., and Wilhelm, E. 1972: 
"Apparatus for Rapid Degassing of Liquids, Part III," Anal. Chem. 54, 
806-807) and applying a large amplitude sound field to the liquid under 
vacuum (Leonard, R. 1950: "The Attenuation of Sound in Liquids by a 
Resonator Method," Technical Report, UCLA). The sound field degassing 
technique and found it to be effective for removing the necessary amount 
of air from the water. 
FIG. 8 illustrates the apparatus used during the degassing of water 
contained in a spherical flask. Degassing the water in the flask prevented 
contamination, especially reaeration, during liquid transfer. The water 
used was filtered through sub-micron filters and then sterilized by a UV 
lamp until a typical resistivity of about 18 M.OMEGA. was achieved. A 
roughing pump provided the necessary vacuum. A Drierite.RTM. CaSO.sub.4 
water trap kept water vapor from intruding into the pump's oil. A small 
metal spike attached to the cork burst large bubbles climbing the flask's 
neck. These bubbles would have otherwise been sucked into the vacuum line. 
Sound pressure amplitudes of a few atmospheres were sufficient to create 
many bubbles in the liquid, especially near the walls of the flask, which 
would then oscillate and grow as they rose to the surface. Driving the 
sphere in one of its radially symmetric modes described took advantage of 
the large sound field generated at resonance. The drive was shut off 
periodically, which allowed bubbles to rise to the surface after they had 
been created and enlarged by rectified diffusion. Degassing a 1 liter 
sphere took over thirty minutes. One of the benefits of using 100 ml 
spheres was that it took only fifteen minutes to degas these smaller 
resonators. The bubbling can continue indefinitely, probably due to the 
creation of vapor filled cavities. The only way to know if the water had 
been sufficiently degassed was to stop degassing and check if stable SL 
was possible. 
V.4 Finding Sonoluminescence. 
Finding the correct parameters to produce SL in a given spherical flask are 
as follows: 
Step I: degas the water, as described in the previous section. 
Step II: adjust the inductor. Set the drive oscillator to the calculated 
acoustic resonant frequency. If the current through the PZT circuit leads 
the voltage across it, increase the inductance until they are in phase. 
Two inductors in series, wired with opposing helicity, increases in total 
inductance when brought closer together due to the effect of the fringing 
fields. If a single inductor is used, the inductance can be increased by 
bringing a piece of iron close to it. A variable inductor could be used, 
but the use of the mutual inductance phenomenon allows for quick 
adjustment over a large range of inductances. 
Step III: precisely find the acoustic resonant frequency. A microphone can 
be used outside the sphere to detect the increase in pressure amplitude at 
the resonance. It is easier to locate the resonance using the 
characteristic dip in the drive current's amplitude and the "glitch" in 
the drive current's phase seen at the resonance frequency. FIG. 9A shows 
the amplitude and the phase of the drive current when the drive voltage is 
used as a phase reference. FIG. 9B illustrates the phase of the current 
relative to the voltage. The broad amplitude peak and slow change in phase 
(Q.about.50) are due to the resonance of the LRC circuit made by the 
tunable inductor and the capacitance of the PZTs. The narrow dip in 
amplitude and glitch in the phase at about 25.2 kHz are due to the change 
in the impedance seen by the drive, caused by the acoustic resonance 
(Q.about.1000). It is easy to see these effects on the oscilloscope 
already used to adjust the inductance, so the drive frequency can be tuned 
to resonance using no extra equipment. After tuning to the acoustic 
resonant frequency, make one final adjustment of the inductance to 
maximize the current. 
Step IV: introduce a bubble. Draw a small amount of water into a syringe or 
an eyedropper bulb attached to a hypodermic needle. Withdraw the needle 
from the liquid and with the acoustic drive on, squirt some water through 
the surface. This will drag some air bubbles into the water. Alternatively 
thrusting a probe, a thin metal rod, through the surface will usually drag 
air bubbles into the water. This second method typically introduces less 
excess air into the fluid, slowing the need for additional degassing. If 
an overtone of the resonator is being used, unwanted bubbles will usually 
get trapped at the spherical antinode shells in addition to the desired 
bubble being trapped at r=0. The unwanted bubbles can be remove by 
lowering a probe near them, then after they adhere to the probe, simply 
remove them. This will usually not interfere with the bubble at r=0. 
Step V: adjust the amplitude of the drive. FIG. 10 is a reproduction of a 
figure indicating qualitative behavior of bubbles driven by different 
pressure amplitudes (Gaitan, F. 1990: Ph.D. Thesis, National Center for 
Physical Acoustics, University of Mississippi). At a low drive level the 
radiation forces, are so weak that the bubble will not be trapped at the 
center of the sphere. As the drive level is increased above the trapping 
threshold, the bubble will be attracted to the center, but the drive level 
is too low to provide adequate rectified diffusion. The bubble will slowly 
shrink and disappear on the scale of seconds. Above the dissolving 
threshold the bubble will remain trapped indefinitely at the center of the 
sphere. 
As seen in FIG. 10, the bubble again loses its stability when the drive is 
increased beyond the dancing threshold. In this regime the bubble moves 
violently around the center of the sphere, and has the appearance of a 
collection of bubbles. As the drive is increased above the lower SL 
threshold, the dancing ceases and the now stabilized bubble appears very 
small. The bubble glows very dimly at the threshold but gets ever brighter 
as drive is increased. Unfortunately there is an upper limit. Near the 
upper SL threshold the light emitting bubble will begin to blink; it dims 
suddenly then returns to its original brightness gradually on the scale of 
a few seconds. Above the upper SL threshold the bubble will be destroyed 
during one of these blinks. When data are to be acquired from the SL 
emission, a drive level should be chosen to make the SL bright enough for 
the measurement, but the drive level should also be kept low enough so 
that the bubble's stability is not sacrificed. 
VI Apparatus and Methods 
With a sealed system, the SL cell creates and generates picosecond flashes 
of light useful for different technologies. The spectrum of light is broad 
band and concentrated in the UV. The flashes have a peak power reaching 
100 mW. The flashes come out in a clock-like fashion from 1,000 cycles up 
to 100,000 per second. The light emission is uniform in all directions, 
namely directed spherically from a point source. 
VI.1 Sealed system: 
When a gas and a liquid mixed together partially fill a vessel, the mole 
fraction of the gas dissolved in the liquid is related to the partial 
pressure of the gas in the gas-vapor mixture in the space above the 
liquid. Reviews of the extensive experiments relating the partial pressure 
and the mole fraction are in the literature. We then adequately can 
describe the gas concentration by measuring the total pressure above the 
liquid and accounting for the vapor pressure. 
A preferred gas passing manifold is pictured in FIG. 11 and a preferred 
method of preparing gas and filling the resonator are described in this 
section. An aspirator bottle is a nice choice for the preparation vessel 
because it comes with a port at the bottom for transferring of the liquid 
into the resonator after the gas concentration has been determined. When 
gas is being added to or removed from the liquid, the steady state is 
reached more quickly if the water is stirred vigorously by a magnetic 
stirrer. If a gas other than air is to be used for an experiment, the 
naturally dissolved air must first be removed from the liquid. An empty 
container of comparable or greater volume than the space above the liquid 
in the aspirator bottle is evacuated to a pressure far below that in the 
bottle. The vacuum pump is valved off and the gas-vapor mixture from the 
aspirator bottle is allowed to expand into the second container through 
some fine mesh CaSO.sub.4 dessicant to remove the vapor. After many 
repetitions a Pirani pressure gauge in contact with the secondary volume 
after the dessicant shows that little gas remains in the liquid (we are 
typically happy with 0.1 mm when we add back 10s of mm of another gas 
because Nitrogen has little effect in trace amounts). Regassing the liquid 
with the desired gas can then be done through a valve at the top of the 
aspirator bottle. A mechanical gauge (Wallace & Tiernan e.g.) is used to 
measure the pressure above the liquid because electrical pressure gauges 
are gas dependent and typically calibrated for air only. Before regassing, 
the gauge shows the vapor pressure at the room's current temperature. The 
gas is then added to the desired pressure correcting for the vapor 
pressure. 
The resonator to be filled is in communication with the vapor-gas mixture 
during the degassing-regassing so that transfer does not change the 
concentration. The transfer is achieved by gravity or assisted by a sealed 
pump, but a gas return line is necessary in addition to the liquid fill 
line to return the displaced gas for a complete fill. The resonator is 
completely filled and some liquid is allowed to enter the gas return line 
such that the liquid level is outside each of the resonator's valves. The 
hydrostatic pressure in the water is the same as read from the mechanical 
gauge if gravity is neglected. We typically wish to push the liquid to a 
higher hydrostatic pressure because the liquid is saturated with respect 
to the gas if it remains at this pressure and bubbles will form everywhere 
once it is sonicated. This is the incorrect state for single bubble SL. 
To control the static pressure in the liquid, the resonator incorporates a 
movable element to communicate the pressure of the fluid with the 
atmosphere (to maintain 1 Atm) or to a vessel of known pressure. In one 
arrangement the moveable element is a piston, one side of which sees the 
pressure in the resonator; the other face is open to a reference pressure. 
The piston is clamped against the low pressure during degassing, regassing 
and transfer, and is allowed to move once the resonator is filled and 
sealed. Another arrangement is to allow the fluid to partially fill a 
latex balloon which communicates with the resonator. The pressure on the 
outside of this balloon can be changed by placing it in a 
pressure-controlled vessel. 
The pressure in a completely stiff resonator would change with the 
laboratory temperature due to the thermal expansion of the liquid. For 
example, changing the temperature from 1.degree. C. to 40.degree. C. 
causes the density of the water to change by .about.1%. Any pressure 
relieving mechanism keeps the pressure at a desired and known pressure 
regardless of temperature. 
Other realizations of sealed systems are found in FIGS. 12 and 13. 
In an open resonator the liquid's surface remains exposed to the air and a 
preferred way to seed a bubble was done by jetting a small quantity of 
liquid through the surface. Small bubbles are introduced into the water 
and these were forced to the center of the sphere by radiation pressure. 
The bubbles coalesce and the remaining single bubble's size is determined 
by diffusion dynamics coupled with the bubble's oscillation. Introducing a 
bubble into a sealed system requires use of the elements present in the 
liquid-gas mixture. A preferred method of creating a bubble in a sealed 
system involves locally boiling the liquid by sending a high current 
through a small piece of Nickel-Chromium (NiCr) wire welded to large gauge 
copper wire makes cavities into which air diffuses and these bubbles 
result in a single bubble at the center as before. The boiling method has 
the advantage over electrolysis that it will work in nonionic liquids. The 
heat introduced is a small perturbation and dissipates quite rapidly. 
Preferred NiCr wire has a diameter of 10 mils and a typical length of 3 
mm. A power supply and momentary switch provide .about.1 Amp to heat this 
wire. 
A preferred way to connect the Copper wire to the NiCr wire is to use an 
Acetylene-Oxygen torch. The Copper wire is heated until its tip melts into 
a ball. Simultaneously a piece of NiCr is heated to red hot but not 
melted. This is easiest if the NiCr is a long piece so heat is carried 
away from the tip. The heated NiCr is then stabbed into the molten ball of 
copper. The NiCr is then cut to its final size and during production of 
the second joint, the copper wire past the first joint carries sufficient 
heat away to keep the NiCr from melting. 
Another preferred method for creating a bubble is to momentarily increase 
the drive to produce cavitation (typically 10 to 20 times above the drive 
necessary for producing sonoluminescence). As with the NiCr heater, gas 
diffuses into the cavities from the liquid to form bubbles which coalesce 
at the center. 
VI.2 A Self Starting SL System 
A set of electronics has been developed which can introduce a bubble by 
cavitating the liquid through a high sound field and then corrects itself 
to drive the bubble at a desired level. 
A relaxation oscillator is one whose amplitude is growing to a steady state 
which it never reaches because some catastrophic event happens to reduce 
the amplitude. This event takes a large amplitude to get started but can 
be sustained to low amplitudes as it reduces the oscillation. The event 
ends as the amplitude gets too small. The process then repeats. The 
classic example is a capacitor being charged until a spark in a lamp is 
excited and the capacitor drains. 
A feedback oscillator is one such that a signal derived from the output of 
the oscillator is phase shifted, amplified and sent back into the system 
such that the oscillation will grow. The differential equation has a form 
like: 
EQU Mz+bz+kz=T(z,z,z)Ge.sup.i.phi. 
Where T is a function of 
EQU z, z, or z 
G is the feedback gain and .phi. is the feedback phase shift. The phase 
.phi. can be adjusted so that the signal fed into the system is 180 
degrees out of phase with the dissipation 
EQU (bz) 
and G can be adjusted to be larger than b. If this is done the circuit is 
unstable to oscillation buildup at its natural frequency. If during 
oscillation the gain is adjusted to exactly 1, the amplitude will remain 
constant because feedback is precisely balancing dissipation. 
The feedback oscillator used drives an acoustic resonator to produce SL 
(FIG. 22); a signal measuring the acoustic oscillations in the resonator 
is amplified and phase shifted and sent to driving transducers. Unlike the 
oscillator above, the acoustic resonator has many modes so the driving 
circuit incorporates a band-pass filter to select only the desired 
acoustic mode. After choice of a proper feedback gain and phase shift, the 
oscillation exponentially increases to such an amplitude that a bubble is 
created in the system by exceeding the cavitation threshold. Gas dissolved 
in the liquid diffuses into the cavities, forming bubbles which coalesce 
at the pressure antinode to form an SL bubble. The bubble acts as an 
additional source of dissipation, effectively increasing b in the equation 
above. 
Unlike the classic relaxation oscillator a single catastrophe can occur. A 
final steady state can be reached if the bubble remains in the system and 
it reduces the gain of the loop to 1. If the loop gain (G-b) is chosen to 
be slightly above 1 when no bubble is present, a bubble is created during 
loop run away, and this bubble grows and dissipates more energy until the 
dissipation exactly matches the feedback and a steady state oscillation is 
achieved. Once a bubble has established a steady state, increasing G 
increases the acoustic amplitude, but a new steady state is achieved when 
the bubble increases its dissipation to the point where the total gain is 
returned to 1. Thus the amplitude of the sound field with a captured 
bubble may be adjusted by changing the gain of the feedback. If the gain 
is set so high that the drive is too large for the bubble to exist, 
repeated creation of bubbles and driving them to their death occurs thus 
recovering the classic relaxation oscillation. 
This system of drive also has the advantage that if the natural frequency 
of the system changes, the resonance is tracked. If the function T 
described above varies slowly with frequency, the amplitude of oscillation 
remains constant as the frequency changes if the phase shift is kept 
unchanged. 
The circuit used provides both the phase shift and gain necessary to the 
technique. In FIG. 14 an Operation Amplifier (op-amp) #1 is a differential 
amplifier used so that two shielded coaxial cables can be used to reduce 
noise on the input line. The gain is1/10 because the voltages from PZTs 
can be quite large. Op-amp 2 is a unity gain buffer which can drive a low 
input impedance without draining the other circuitry. Op-amps 3 and 4 act 
as a unity gain phase shifter at the resonance frequency allowing an 
inductive shift or typically providing 90 degrees of inductive shift so 
the next stage provides -90 to 90 degrees of capacitive shift instead of 0 
to 180 because a resolution of around 0 degrees is needed. Op-amp #5 
provides the high input impedance necessary to make the first phase 
shifter work correctly. Op-amps 6 and 7 provide unity gain capacitive 
phase shift at the resonant frequency. Op-amp #8 is a variable gain 
non-inverting amp used to adjust the G discussed above and it provides a 
high input impedance for the output of the capacitive phase shifter. 
A variation on this circuit does not create a bubble automatically but does 
not rely on the dissipation of the bubble to define the final acoustic 
amplitude. If a comparator is triggered from the phase shifted signal 
correlated to SL, the phase information is preserved but the amplitude of 
the comparator's oscillation is constant. The resulting square wave is 
filtered to a sine wave and amplified before using it to drive the source 
transducers. This circuit tracks with a changing frequency and is driven 
at any chosen level. 
VI.3 Mode Locking the SL System 
The ability to maintain constant intensity SL depends on keeping the sound 
field felt by the bubble as constant as possible. Certain conditions which 
change in the operating environment such as temperature can change the 
acoustics and the use of feedback is necessary. 
The change in the phase of the acoustic oscillation in the resonator, or of 
the light emitted by the bubble is used to correct the drive frequency so 
that the response amplitude remains constant (FIG. 23). A lock-in 
amplifier is used to measure the phase difference between its input and a 
reference which we choose to be the drive. As the resonance frequency 
shifts, perhaps due to temperature changes, there is an associated phase 
change between the drive and the response signal. The phase changes 
monotonically with frequency near resonance so that the voltage produced 
by the lock-in proportional to this phase can be used to make corrections 
to the oscillator frequency. The lock-in reference phase is adjusted to 
produce 0 V at the resonant frequency. The lock-in phase output is 
integrated to provide and error signal which controls the frequency of a 
voltage-controlled oscillator (VCO). The frequency may be adjusted over a 
small range near resonance by changing the lock-in reference phase. 
Signals used for input to the lock-in show the phase change associated with 
the natural frequency change. Choices which have been successfully used 
include the voltage from a microphone outside but near the sphere, the 
voltage from a PZT cemented to the sphere, the current drawn by the PZTs 
and the signal from a photomultiplier tube (PMT) detecting the SL. 
The integrator circuit used is shown in the FIG. 15. R.sub.0 is used to 
provide a large but finite input impedance. The input current V.sub.1 
/R.sub.1 flows through the capacitor C.sub.1 around the first operational 
amplifier, op-amp 11 producing an output voltage which is -1/(R.sub.1 
C.sub.1) times the integral of V.sub.in with respect to time. The op-amp 
II is trimmed to reduce input offset voltage. The resistor R.sub.5 is used 
to reduce the effects of input bias current. R.sub.2 provides dc feedback 
to keep the circuit stable from drifts by reducing the action of the 
op-amp below frequencies of .about.1/(R.sub.2 C.sub.1). Since the first 
op-amp 11 inverts the integral of V.sub.in, the second op-amp is used 
re-invert the signal and also to provide the necessary gain by adjusting 
R.sub.3 and R.sub.4 to keep the VCO at the correct frequency. C.sub.2 
keeps the second op-amp from oscillating. Op-amp 22 is also trimmed to 
reduce the input offset voltage and R.sub.6 is used to reduce the effects 
of input bias current. The feedback loop is broken by closing the reset 
switch, effectively grounding the input to op-amp 22. The reset switch is 
closed to initially set the VCO to the natural frequency of the resonance 
and initially zero the phase signal from the lock-in. 
VII Applications 
VII.1 Light Scattering 
As illustrated in FIG. 16, it is possible to determine the radius of the 
bubble by a light scattering technique. A laser is directed towards the 
center of the cell, the laser being a 1 to 10 mW He--Ne laser. There is a 
trigger PMT located with a short pass filter between the trigger and the 
cell. With a digital delay this acts to trigger or be triggered by the 
laser as necessary. There is a second signal PMT which has a long pass 
filter and a line pass filter between it and the cell. The intensity of 
light scattered is related to the radius of the bubble. Through this 
system the size of the radius of the bubble can be measured. These 
measurements are depicted in FIG. 6 (upper curve) wherein the radius is 
measured as a function of time for the bubble driven with an amplitude 
below the SL threshold. The radius of the bubble as a function of time is 
matched to the solution of the diffusion equation 
##EQU12## 
where C.sub..infin. is the concentration of dissolved gas in the fluid, 
C.sub.0 is the saturated concentration of gas in the fluid, T.sub.a is the 
acoustic period, R.sub.0 is the ambient radius and 
##EQU13## 
This yields the concentration of the dissolved gas in the liquid. For the 
bouncing motion the measurement is in accordance with the equation. As the 
solution becomes gassy the light scattering measurements approach the 
saturated value of the equation. 
VII.2 Fluorescence Measurement 
As illustrated in FIG. 17, a sample is located adjacent to an SL source. 
The sample is excited by the SL source so that fluorescent light emanates 
from the sample. The SL source provides a broad band, for instance, 
between 200 nanometers and 700 nanometers of short wavelength light. This 
is directed in a spherical direction. The fluorescent light from the 
sample is passed through a monochrometer or a filter and is then read by a 
photodetector. The photodetector will sense the SL flash and also the 
fluorescent response from the sample. The difference in the time, 
.DELTA.T, is the time delay for decay to being. .DELTA.T maybe zero. The 
fluorescent decay time is 1/.alpha., the so called lifetime of the 
fluorescence sample. In this manner it is possible to ascertain whether 
one or more fluorescent elements are contained in the sample and the 
particular wavelength of fluorescence. The device can excite a spectrum of 
multiple lights at the same time. 
VII.3 Calibration 
It is possible with the invention to calibrate instruments such as 
photomultiplier tubes or arrays of detectors. 
As illustrated in FIG. 18, an SL is located adjacent to five detectors. 
There is also a mark flash segment for indicating the timing of the 
initial flash. 
The detectors and the marker detector respond to the SL flash, and has 
indicated the different time delays of each detector gives an indication 
of how the detectors need to be calibrated. In this sense the radiation of 
this light from the SL is directed over 4.pi. stearadiants and is 
synchronized in that sense. Accordingly, detector calibration can be 
accurately performed. 
VII.4 FUSION 
VII.4.1 Fusion Energy 
The invention has been illustrated extensively with regard to the 
converting acoustic energy to the different energy form, namely SL. The 
data and theory strongly support that the invention is equally applicable 
to the energy form of fusion. The following description of the invention 
relates to the prospective exemplification of the invention in relation to 
fusion. 
The passage of a sound wave through a fluid with a trapped bubble of air 
can lead to the emission of picosecond flashes of light whose repetition 
rate is synchronous with the sound. As indicated in FIG. 1 the spectrum of 
the emitted light increases into the ultraviolet. This phenomenon, SL 
involves the concentration of acoustic energy by at least 12 orders of 
magnitude so as to generate light. 
The energy amplification characteristic of SL could extend an additional 3 
orders of magnitude to the regime where thermonuclear fusion would occur. 
In particular, the 14-MeV neutrons would be emitted from the 
deuterium-tritium fusion reaction, 
EQU D+T.fwdarw..alpha.+n. 
This remarkable possibility exists because the spectrum shown in FIG. 1 has 
no apparent peaks or energy scales. This data must therefore lie on the 
tail of some process which is peaked at a much higher energy. It is 
important to note that the measurements shown in FIG. 1 stop at 200 
nanometers [6 eV] because the water surrounding the bubble does not 
transmit light of shorter wavelength, namely higher energy. Since the 
transmission does not turn on again until 5 keV, the limits of the energy 
amplification which can be achieved with SL have yet to be determined. 
SL is due to the energy concentration which results from the implosion of a 
spherical shock wave. The shock is launched inward through the gas bubble 
as it collapses supersonically during the compressional part of the sound 
cycle. Collapse velocities in excess of Mach 1 are apparent in FIG. 19 
which shows light scattering measurements of the bubble radius vs. time. 
The breathing motion of the bubble during a complete cycle of sound is 
shown in FIG. 20. There are three characteristic bubble radii: the ambient 
radius R.sub.0 (.about.4 microns) which is the average or 1 Atmosphere 
radius of the bubble, the maximum radius R.sub.m (.about.40 microns), and 
the minimum radius R.sub.c. In addition the collapsing bubble launches a 
shock wave into the gas which continues inward and generates excitations 
of order 6 eV when its radius is about 1,000 Angstroms. And if the shock 
holds together when its radius is as tiny as 60 Angstroms, then portions 
of the bubble should reach the conditions appropriate to fusion. For a 
deuterium-tritium bubble this idealized model yields about 40 neutrons per 
second. 
For SL a coherent phonon field primes the collapse of the small spherical 
bubble containing a D-T mixture. The key parameter which controls the 
efficiency of the energy concentration is the sphericity of the shock 
wave. Finally SL also involves a preheating of the bubble contents. In 
this case the collapse of the bubble radius to R.sub.c adiabatically heats 
the entire bubble contents to about 1 eV at which point the imploding 
shock is then launched. A typical SL experiment yields 35,000 implosions 
per second. 
A block diagram of the system for creating fusion energy is shown in FIG. 
13. A D-T bubble is trapped at the center of a flask driven in its 
fundamental acoustic resonance. When the drive is turned up to the point 
where the bubble implodes so as to generate SL a neutron emission could 
occur and be measured. 
The basis for this emission are summarized in the Table, which shows the 
increasing degrees of energy concentration that are achieved as the 
imploding shock wave reaches smaller radii. 
TABLE 
______________________________________ 
Energy Concentration Due to Shock Wave Implosion 
(Calculated for R.sub.o .about.4 .mu.m) 
Time 
After 
Focusing 
Shock Radius 
Mach # Temperature 
Phenomenon 
______________________________________ 
100 ps 1,500 .ANG. 
4 10.sup.5 K. 
Sonoluminescence 
5 ps 200 .ANG. 10 3 .times. 10.sup.6 K. 
Soft X-Rays.dagger. 
0.1 ps 15 .ANG.-(60 .ANG.)* 
30 3 .times. 10.sup.8 K. 
Fusion 
______________________________________ 
*Computed for Van der Waals equation of state. 
.dagger.Note that soft xrays do not propagate through water. 
The neutron detection scheme uses liquid scintillators which are capable of 
resolving both the neutron energies and times. This scheme allows the 
measurement of the neutron time of flight which can be conveniently 
compared to the accompanying flash of light from the sonoluminescence. The 
SL provides an event marker that will enable a tiny (1 ns) window in time 
can be picked out during which events will be accepted, thereby 
dramatically lowering the background. 
VII.4.2 Sonoluminescence from a D-T Gas Bubble in Water 
FIG. 13 shows the overview of the apparatus. The central part of the 
apparatus is a spherical quartz flask on the surface of which are mounted 
ceramic PZT transducers. When driven at a frequency corresponding to the 
fundamental resonance of the water-filled flask, amplitudes can be reached 
where a bubble of gas can be trapped at the velocity node, namely=pressure 
antinode, at the center of the flask. As the amplitude is increased the 
pulsations of the bubble become large enough that they generate imploding 
shock waves which lead to the emission of one flash of light for each 
cycle of the sound field. Normally this effect is observed with 
photomultiplier tubes. The contents of the bubble are controlled to that 
of an appropriate D-T mixture. 
Characteristics of the system are derived from the following: 
a) Cooling the water in which the SL occurs to 1.degree. C. dramatically 
increases the SL emission and furthermore shifts it into the far 
ultraviolet. The spectrum for air at 1.degree. C. is shown in FIG. 1 and 
the dramatic change of SL intensity with water temperature is shown in 
FIG. 2A. 
b) Generating SL in a sealed system, i.e. no free surface, enables one to 
use gases other than air. The problem to overcome is that of seeding a 
bubble of gas into a sealed flask of liquid. This has been achieved with a 
nichrome wire heater. A burst of current into the heater creates a vapor 
bubble which then promptly fills with whatever gas is dissolved in the 
liquid. The gas bubble then gets yanked to the center of the flask where 
it undergoes the oscillations that generate SL. 
c) Dissolving gases of choice into the water, degassing of liquids, and 
fluid transfer all under a controlled atmosphere. Careful control of this 
procedure is essential due to the effects of doping the gas bubble with 
small percentages of Argon. As shown in FIG. 4 a few percent of Argon 
dramatically increases the SL emission. The air is first removed from the 
water then the appropriate D-T argon mixture is dissolved into the water 
and then the bubble is seeded and the effects measured. 
d) Mode locking SL to the sound field enables it to be stabilized over long 
periods of time. The appropriate feedback loops are used for this 
procedure. 
In the event of a positive signal the "controls" are a key aspect. In this 
direction the SL fusion is run with hydrogen bubbles, deuterium bubbles 
and the D-T mixture. In addition these bubbles are doped with argon or 
xenon. Various sources of noise including electrical cross-talk, should be 
resolved by comparing these different configurations. In addition the 
neutron counting scheme provides three cross checks for a positive signal. 
VII.4.3 Imploding Shock Wave Theory of Sonoluminescence: Extension to 
Acoustically Driven Fusion 
As shown in FIGS. 19 and 20, there is a portion of each acoustic cycle 
during which the bubble radius collapses at a rate which is faster than 
the speed of sound of the gas in the bubble. This collapse then radiates 
an imploding shock wave which is directed inward toward the center of the 
bubble. The radius of the bubble-water interface is denoted by R and the 
radius of the launched shock R.sub.S, then this situation is pictured in 
FIG. 21. As the shock implodes towards the focus or origin, the 
temperature and pressure increase with decreasing R.sub.S. At the moment 
of focusing R.sub.S =0, the imploding shock is converted into an outgoing 
shock which then slams into the already heated matter and therefore 
results in yet an additional heating. The simplest model for SL which is 
reasonably consistent proposes that the light emission is due to the 
thermal Bremsstrahlung generated by the shock wave heating of the gas in 
the bubble. Shown in FIG. 2 is a comparison of this model with our 
measurements. The fact that the calculated values of SL intensity are the 
same order of magnitude as experiment and that they change by the 
requisite factor of 200 between 40.degree. C. and 1.degree. C. constitute 
strong evidence for the validity of this model. 
From the shock wave scaling arguments discussed previously, one can obtain 
the above Table which describes the degree of energy concentration as a 
function of the length scale on which the shock remains intact. Also shown 
is the time over which these temperatures apply. 
The measurable portion of the SL spectrum is reasonably consistent with the 
entry on line 1 of the table, namely 100,000 K. for 100 ps. Whether the 
shock remains intact down to length scales under 100 .ANG. will determine 
the feasibility of fusion. In addition to the analytic estimates derived 
above, the fluid mechanical equations have been simulated for a gas bubble 
with a van der Waals equation of state. The results are generally 
consistent with the table and for the bottom line yield 60 Angstroms 
instead of 15 Angstroms. 
The neutron yield is estimated based upon the bottom line of the table. The 
neutron emission rate is determined by the standard formula 
EQU N=n.sup.2 .sigma.vR.sub.n.sup.3 .DELTA.t.sub.n /.tau..sub.a 
where n is the number density of atoms (.about.10.sup.23 /cc at focusing), 
R.sub.n is the radius of the hot region, .DELTA.t.sub.n is the length of 
time during which the temperature is high enough for significant fusion to 
occur, .tau..sub.a is the acoustic period which determines the number of 
implosions per second, .sigma. is the reaction cross-section, and v is the 
relative velocity of reacting nuclei, the overbar indicates the 
statistical average of .sigma.v: 
EQU .sigma.v=4.10.sup.-12 (T.sup.-2/3) exp (-20T.sup.-1/3)cc/s 
where T=T/1.16.times.10.sup.7 K. The maximum value occurs when 
T.apprxeq.10; this motivated our choice of T in the preceding estimates. 
Calculations for the case P.sub.a =1.425 Atm, R.sub.0 =4 .mu.m, 
1/.tau..sub.a =25 kHz show that, for an air bubble modeled as a van der 
Waals gas (for which a.about.0.5), a temperature of 10.sup.8 K. is 
attained at a distance of R=60 .ANG. from the center of the bubble and 
lasts for a time of order 0.1 ps. This computation yields about 40 
neutrons/s, but the results are very sensitive to the launch conditions, 
in part because a depends strongly on these conditions in a van der Waals 
gas. For instance, at P.sub.a =1.375 Atm, the computed yield is less by a 
factor of 10. These computations neglect the emission of an outgoing shock 
by the bubble surface and the fusion rate given above may have to be 
modified for a dense system where binary collisions may not make the 
dominant contribution to N. A parallel exists between the shock wave model 
of SL and efforts aimed at developing inertial confinement fusion. In each 
case the level of energy concentration which can be attained is limited by 
the stability of an imploding shock wave. 
These estimates neglect thermal radiation transport, thermal conductivity, 
shock wave corrugation, and changes in the equation of state due to the 
high pressure and temperature. In a sense fusion is being used as a means 
of probing the level of focusing which is achieved by the imploding shock 
wave that leads to SL. 
VII.4.4 Neutron Detection 
There are several established methods for detecting neurons with energies 
E.sub.n in the 1-20 MeV range. Such neutrons are called "fast neutrons" or 
even "high energy neutrons" because they are more energetic that thermal 
or epithermal neutrons, but these "fast neutrons" actually have much lower 
energy than the neutron beams (many GeV) used in high energy physics. Fast 
neutron detectors are variously used in basic nuclear physics experiments 
and for monitoring nuclear reactor operation, fusion reaction tests, and 
radiation dosage to people and equipment. 
Different fast neutron detection techniques are possible. For each 
technique, a major goal is to suppress the background due to gammas which 
might be mistaken for neutrons. The preferred counter is a liquid 
scintillation counter. 
VII.4.4.1 .sup.3 He Proportional Counters 
Very low energy neutrons have a high cross section for capture on .sup.3 He 
via the reaction n+.sup.3 He .fwdarw..sup.1 H+.sup.3 H+765 keV. The 765 
keV of energy of released appears as kinetic energy of the proton (.sup.1 
H) and triton (.sup.3 H). Neutron detectors based on this reaction 
typically have the .sup.3 He gas in a proportional tube where by the 
recoiling proton and triton ionize the gas, and the ionization is 
amplified and collected on a wire. 
VII.4.4.2 Boron-loaded Plastic Scintillators 
In a scintillator, neutrons collide with protons, and the recoil protons 
create ionization which leads to light emission. Low energy gammas 
Compton-scatter off electrons, which also create ionization which leads to 
light emission. In plastic scintillator, these prompt light pulses are 
similar, so that an additional trick is needed to reject gammas. 
VII.4.4.3 Liquid Scintillators 
Unlike plastic scintillators, liquid scintillators such as NE213 respond 
differently to gammas than to neutrons [15, 16]. Crudely speaking, the 
scintillation light has a fast component which decays away in a few ns, 
and a slow component which decays away in about 100 ns. The 
heavily-ionizing recoil protons from neutrons yield more of the slow 
component than do the Compton-scattered electrons from gammas. The 
resulting difference in pulse shapes has for many years formed the basis 
of using liquid scintillators for detecting fast neutrons while giving 
good rejection against gammas. 
There are numerous published papers detailing electronic circuits which 
effect this "pulse shape discrimination" (PSD) of neutrons and gammas, 
typically demonstrated with the scintillator NE213 (NE Technology Ltd.) 
Using only PSD, gamma rejection of a factor of 100 is completely routine 
with off-the-shelf electronics, and a factor of 1000 is attainable. 
Neutron detection efficiencies of a few percent to 20% have been 
documented, with excellent timing. The timing allows neutron energy 
measurement via time-of-flight techniques if the neutron is emitted at a 
known time and location. At least two ultra-low background neutron 
detection systems have used NE213. 
In NE213, neutron energy measurement based solely on the pulse height is 
somewhat limited. This is because the energy imparted to the first recoil 
proton can vary over a wide range, and summing on the energies of recoil 
protons from further collisions is compromised by nonlinearities in the 
scintillator response and escape of neutrons before complete energy 
deposition. However, this liquid scintillator is available in deuterated 
form as NE230, in which all the protons (.sup.1 H) are replaced by 
deuterons (.sup.2 H). The neutron-deuteron elastic scattering cross 
section is strongly peaked in the backward (for neutron) direction, 
resulting in deuteron recoil-energy peak at about 8/9 of the neutron 
energy. Hence the observed line shape from mono-energetic neutrons 
impinging on NE230 should be distinctly sharper compared to NE213. 
The counter requires inter-changeable NE213 and NE230 scintillating 
elements (or equivalent). 
In SL, the neutrons would be emitted in a known, submillimeter, location at 
precisely reproducible, sub-nanosecond times relative to the accompanying 
flashes of SL light. Neutron arrival times should be easily measurable to 
a few nanoseconds with the scintillator, and SL light bursts occur every 
few microseconds. Hence, the timing allows an additional rejection of 
gammas by a factor of 1000, above and beyond that attained with PSD. 
Furthermore, the time-of-flight (TOF) of the neutrons can be measured from 
the SL source to the liquid scintillator detector, and hence the neutron 
energy with reasonable resolution can be inferred. With the NE230 
elements, this measurement is checked for consistency with the energy 
inferred from the pulse height information, for further background 
rejection. 
The precise power of the TOF information depends on the details of the 
scintillator design and the properties of the photo-multiplier tubes used. 
For a scintillator of a given size, there is a tradeoff between detection 
efficiency and TOF resolution, since the geometrical contribution to the 
detection efficiency worsens with distance from the source, while the TOF 
resolution improves. The mechanical design allows for optimization of 
efficiency while searching for a signal or while setting limits, at a cost 
in TOF resolution. On the other hand, if a clear signal exists, the 
detectors can be moved away from the source, sacrificing some detection 
efficiency in order to obtain better TOF resolution. 
A 4-element detection system is used with each element will be a glass 
container (cubical or cylindrical, approximately 10-15 cm each linear 
dimension) containing the liquid scintillator, sealed by the manufacturer 
to guarantee purity and lack of dissolved gas. Two photo-multiplier tubes 
(PMTs) will view each container in order to optimize light collection and 
guard against spurious noise. Two detection elements are placed at one 
distance from the SL spot, and other element at a different distance. In 
the event neutron candidates are observed, the expected fall-off with 
distance from the SL spot can thus be checked. 
The SL flash itself will be viewed by a separate PMT of the type being used 
for SL studies. 
For the first measurements, relatively conventional electronics modules are 
used. Commercial NIM discriminators, logic units, and single-channel 
analyzers will be used for providing triggers, gates, PSD signals, etc. 
Time intervals and pulse sizes are digitized using commercial TDCs and 
ADCs in CAMAC modules with standard interface to the data acquisition 
computer. 
Events will be written to disk and archived on 8-mm magnetic tape 
cartridges. Data analysis will proceed with custom FORTRAN programs 
interfaced to existing standard workstation histogramming packages such as 
PAW (CERN Program Library). 
Each event record will contain all the digitized information (pulse height, 
times, etc.) corresponding to one event trigger signal. Initially, 
implementing trigger signals at every SL pulse and at various times 
between SL pulses, provides a thorough set of data for background studies. 
Then pre-scale the trigger (i.e., record only every nth such trigger, 
where n is an adjustable integer) by a reasonable amount, and also 
implement a more restrictive trigger which demands some activity in the 
liquid scintillator system. The pre-scaled trigger and this latter trigger 
will be logically OR'ed to form the master trigger for computer 
acquisition. The precise nature of the demand for activity in the liquid 
scintillator (e.g., signals above some discriminator threshold for one or 
more tubes or analog sums of various tubes) will be flexible and tuned as 
experience is gained. These trigger requirements are as loose as possible 
so that the real data selection occurs in the off-line analysis where 
selection criteria can be better understood. 
The detector response, data acquisition, and analysis systems are exercised 
and calibrated using standard commercially available neutron sources, 
Californium-252 (.sup.252 Cf) and Am-Be. 
After completing check-out, initial data-taking, and preliminary data 
analysis, the detection elements and increase the sophistication of the 
electronics in order to increase the geometrical acceptance, increase the 
time-of-flight distance, or provide more pulse shape information can be 
modified. 
If no definite signal are detected and noise levels are not a problem, then 
more liquid scintillator detection elements are added in a way to increase 
the solid angle (as viewed from the SL spot) and hence increase neutron 
detection efficiency. If there are candidate neutron signals, more 
elements far enough away from the SL spot (up to 1.5 m) are added so that 
TOF measurements with excellent resolution can be used to measure the 
neutron energy. 
In the event of tentative identification of real neutrons emerging from the 
SL spot, pulse shape analysis will be effected. Conventional PSD use for 
neutron/gamma separation relies on a summary of the pulse shape contained 
in two numbers, roughly equivalent to the magnitude of the fast and slow 
components of light. The difference of these two numbers (or times 
containing that information) becomes a single "PSD" variable which is used 
to distinguish neutrons and gammas. To check a claim of the observation of 
neutrons, the entire waveform of the PMT pulses is digitized to be sure 
that the PSD electronics was not fooled by some bizarre noise pulse. 
At least two means can be used for such wave-form digitization. At a very 
low rate, one waveform at a time can be digitized by an oscilloscope, and 
transmitted to the computer via GPIB interface. For higher rate, wave form 
digitizers are used which have been developed for use in high energy or 
nuclear physics. For example, a French group has developed a 100-MHz 6-bit 
waveform sampling scheme for use in electron-neutron separation in 
lithium-loaded liquid scintillator NE320, with very encouraging results. 
They demonstrate not only improved neutron gamma separation compared to 
traditional PSD, but also the ability to recognize and reject sources of 
noise such as impedance mismatches and multiple pulsing. 
Also, a Boston University group has developed a 200-MHz 8-bit waveform 
digitizer for signals from the liquid scintillator of the MACRO magnetic 
monopole search. Even more ambitiously, a Brookhaven National Laboratory 
and Columbia University group has produced Fastbus-interfaced 500-MHz 
digitizers for use in the rare kaon decay experiment BNL E787. Each of 
their 200 channels has 8-bit dynamic range, zero suppression on the fly, 
deep memory up to 500 .mu.s, and fast readout time 100 .mu.s for the whole 
system. 
VII.4.4.4 Moderation of the Neutrons while escaping the SL sphere 
At least initially, the SL burst and source of neutrons will be in the 
center of a sphere of water with radius of about 2-3 cm. Using available 
total cross sections for n-p, n-d, and n-O scattering, the mean path in 
H.sub.2 O or D.sub.2 O is found to be about 4 cm for 2.5 MeV neutrons, and 
about 10 cm for 14 MeV neutrons. Hence, depending upon our setup, a 
neutron may have up to 50% chance of scattering off a proton on the way 
out of the sphere, thus degrading its energy and perhaps its timing. This 
will not be a serious problem for the initial neutron search. Other 
non-hydrogenous liquids, are possible, e.g., hydrocarbons in which 
hydrogen has been replaced by chlorine or fluorine. If such liquids 
replace water in the sphere, then neutron energy loss while exiting the 
sphere would be reduced even when scattering does occur. 
VII.4.4.5 Summary of the Neutron Detection Method 
With the above-described detection system, neutrons generated through D-D 
or D-T fusion in the SL bubble collapse would be characterized by: 
Energy disposition in the liquid scintillator (and subsequent PMT pulse) 
consistent with monoenergetic source of neutrons, as modeled by MCNP and 
scale calibrated using .sup.252 Cf and light pulsers, etc. 
Time-of-flight spectrum consistent with monoenergetic source of neutrons, 
with correct absolute energy as calibrated using .sup.252 Cf and light 
pulsers, etc. 
Pulse-shapes consistent with neutrons and inconsistent with gammas at high 
confidence level using traditional PSD. 
Pulse-shapes consistent only with neutrons using more modern wave-form 
digitizing. 
Timing correlation (good to few ns out of many .mu.s) with the SL visible 
light flash. 
Presence of signals when field is strong enough to cause SL and absence of 
signals when sound field amplitude is just below threshold for SL. 
Presence of signals when fusion reactants (D-D or D-T) are present in 
bubble and absence of signal when only ordinary hydrogen-1 and/or helium 
is present. 
In contrast, background in our search should fail most of the above tests. 
Moreover, the background rate in several redundant ways can be measured by 
loosening or eliminating the above criteria in various combinations. Since 
the above method adds time-of-flight and time-correlation cuts to the 
desired background rejection should be attainable. If a signal does exist, 
not only will it thus be virtually background-free, but all the above 
criteria will allow it to be conclusively associated with the SL bubble 
collapse. 
VIII GENERAL 
Many other forms of the invention exist each differing from the other in 
matters of detail only. 
The invention has been generally described with reference to air being 
degassed in the bubble and water being the liquid. It is possible to have 
many other variations. As illustrated in FIG. 3, the gas there is 
nitrogen. Different degrees of doping with argon are illustrated. The 
intensity of air cell varies according to these characteristics and also 
the degree to which gas saturates the liquid. Other than water, liquids 
can, for instance, be hydrocarbon, different oils, and other liquid 
combinations, for instance liquid nitrogen and liquid argon. Different 
gases such as oxygen, helium, nitrogen, argon, chlorine, neon, krypton, 
hydrogen and SF.sub.6 can be used. 
For instance, in some situations it may be possible to trap more than one 
bubble in the liquid at different locations or planes, and to obtain 
energy transfer from each of those bubbles in accordance with the 
principles of the invention. In other cases it is possible to develop 
appropriate chemical compounds or products under the action of the energy 
in the bubble. The high heat and pressure in the bubble would lend itself 
to such product developments. 
In yet other variations it is possible to focus or spot a laser into an 
area of the liquid, and create the zone for a bubble of gas to be 
performed. The bubble is found as gas dissolves out of the liquid into the 
heated area. 
In different variation the shape of the container can be selected as 
appropriate, for instance, cylindrical, cubic, or elongated as required. 
The walls of the container could be of any suitable material. For 
instance, Plexiglas, plastic or metal would also be operable. 
Although the temperature to which the liquid is cooled is indicated to be 
about 1.degree. C., it is possible, for instance, using liquid nitrogen, 
to have lower temperatures in the container or cell. 
In other cases the rate of repetition could be less than 1,000 cycles per 
second or greater than 100,000 cycles per second, namely as high as 1 
million cycles per second. 
The invention is to be determined solely in terms of the following claims. 
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