I. Energy Concentrating Phenomena
Fluids and solids that are driven off equilibrium do not relax smoothly to equilibrium. Although the march to equilibrium is characterized by an ever increasing entropy, continuous media can nevertheless pass through configurations which display a wide range of phenomena which concentrate the energy density.
Sonoluminescence ÔSLÕ is the paradigm of energy focusing phenomena[1]. Here, a standing sound wave causes a trapped bubble to pulsate so violently [acceleration of the bubble wall can reach 1012g] that acoustic energy is transduced into flashes of ultraviolet light whose duration can be much shorter than a nanosecond. When water is used as the fluid, SL can be observed at sound fields with an amplitude of about 1atmosphere. At this amplitude each water molecule is vibrating with an energy of about 1.5x10-23erg, whereas a photon, which we assume originates from the region a single atom, has been observed to have an energy as high as 6eV. A comparison of these numbers indicates that SL involves a concentration of the energy density by at least a factor of 4x1011. The SL spectrum might extend to even higher energies but observations have been limited by the extinction coefficient for light traveling through water.
When a 30KHz sound wave acts on a bubble containing helium atoms the observed spectrum is accurately fit by PlanckÕs blackbody law [2] with a temperature of 20,000K, four times hotter than the surface of the sun. A condition for blackbody radiation is that the size of the hot spot be greater than the photon matter interaction distance. But this SL hot spot has a radius smaller than ½ micron and it is difficult to understand how it can be opaque. If the hot spot is smaller than the interaction length it would be transparent and the spectrum would look like Bremsstrahlung radiation from a plasma. A plasma forms because the contents of the imploding bubble get so hot that the atoms ionize. The free electrons will then zip around with a velocity determined by the temperature of the plasma. When the electrons collide with much heavier ions they accelerate and radiate light [Bremsstrahlung]. If the light escapes without absorption the plasma is transparent, if it is absorbed the plasma is a blackbody. For the alternative model of the hot spot, the transparent plasma scenario, the best fit [helium] spectrum would have a temperature of 50,000K [as compared to 20,000K for the blackbody model which displays a better overall fit to the data]. At acoustic frequencies of 1MHz, the bubble is smaller and the observed spectrum is now best fit by the transparent plasma model, and a temperature of about one million degrees[3].
Evidence that SL originates in a plasma has been provided by application of plasma diagnostics to argon bubbles in sulfuric acid[4]. At drive levels so low that these bubbles are dimmer than bubbles in water, lines from excited states of argon ion [Ar+] that are 37eV above the ground state can be observed. The width of emission from neutral Ar lines yields an average pressure of 1,500.atm which also matches the average pressure determined by light scattering measurements of the radius of these bubbles. At higher sound fields the lines are broadened and unresolvable but light scattering yields a pressure over 3,500 atm suggesting that the high drive bubbles are substantially hotter than the weakly driven case where the Ar+ lines were first discovered.
The densities and temperatures which can be accessed with modest sound fields are extraordinary. One is tempted to wonder if bubble acoustics can be used to reach conditions for nuclear fusion. Although this is an exciting and worthwhile direction of research claims of such a success [5] have met with strong skepticism[6]. Some optimism that cavitation will provide a route to fusion is provided by the observation that SL enjoys a big parameter space. For instance in the water hammer arrangement [7] the integrated light emission has been upscaled by a factor of 1 million as shown by the photo of a single such flash in Figure 1.
 Figure 1: single flash of light emitted by a collapsing bubble of xenon gas in a vertically excited vibration |
Figure 2: Barometer light emitted where the Hg meniscus scrubs against the ascending glass wall of a cylinder rotating about the horizontal axis. |
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In the 1930Õs the well known phenomenon of frictional electricity formed the basis for the prediction of SL. A realization of frictional electricity that goes back to PicardÕs ÒBarometer LightÓ of 1676 is shown in Figure 2. Here the scrubbing of the Hg meniscus against the ascending wall of a glass tube with a rotational velocity of 1mm/sec around its horizontal axis generates picosecond electrical discharges where the electrons are accelerated to over 1% the speed of light[8]. The red line is light emission from the excited states of neon gas in the cell. Can ripping mercury off a dielectric surface create even more energetic emissions where electrons are accelerated to x-ray energies? Evidence that this may be possible comes from reports of just such observations when mica is fractured[9]. This work has not been independently reproduced, possibly because of its timing and context relative to ÔCold FusionÕ. After all, if a process delivers enough energy to accelerate electrons to 10Õs of keV then the delivery of that energy to individual ions will meet conditions for nuclear fusion if, of course, the appropriate ion such as deuterium is employed. That thermal gradients in a cubic centimeter size crystal can lead to x-ray emission has actually been known and patented and reproduced since the 1970Õs[10]. This effect is most prominent in ferroelectric crystals. These materials have an enormous spontaneous polarization. In fact freshly made Lithium Niobate has a spontaneous polarization of 70μC/cm2 which is equivalent to an internal electric field of about 107V/cm! In an uncontrolled environment stray charges attach to the surface and cancel the intrinsic field of the crystal. But by heating [or cooling] the crystal in a vacuum the dependence of spontaneous polarization on temperature creates an unbalanced charge on the surface. Typically tens of degrees creates a field of 100keV. If fractured mica really makes x-rays then it is likely due to the appearance of similar surface charges at the cleaved surfaces. Now if a modestly heated cubic centimeter crystal makes 100keV x-rays then configuring the crystal so as to deliver this energy to a deuterium ion should generate nuclear fusion. This has been achieved [11] via mounting a 100nm wide tungsten tip on the crystal [Figure 3]. Neutral deuterium molecules that drift into the region of the tip are dissociated and ionized by the huge electric field. If the crystal is oriented so that the field is positive then the freshly produced ions receive 100keV of potential and are energetic enough to fuse with a deuterium target. An example of the pattern of energetic ions striking a target is shown in Figure 4. |
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Figure 3: Lithium Niobate crystal mounted on a heater/cooler. A tungsten tip is attached to a copper electrode that is fixed to the surface of the crystal. |
Figure 4: image of ions striking a scintillator after being accelerated by the crystalÕs electric field. When the target is deuterated the bright areas locate the region where nuclear fusion occurs. |
Strong ferroelectricity such as observed in Lithium Niobate has its origin in the instability of high frequency modes of oscillation of an ionic crystal[12]. If for simplicity one imagines a crystal lattice where the short range repulsive forces are provided by springs and the attractive forces are due to long range coulomb interaction between the ions. Then there exists a range of values for the interatomic spacing and spring constant for which the small amplitude normal mode of oscillation becomes unstable for the long wavelength transverse optical mode. This results in a relative displacement of the ions to a state which has a spontaneous polarization. Calculation of the new equilibrium state is a matter of compelling current interest[13]. Sonoluminescence, frictional electricity, fracture and ferroelectric emission are phenomena characterized by energy density concentration. It will be interesting to see what additional natural processes can be added to this list. References [1] Advances referenced in the
following reviews are not separately referenced in this story:
Barber et al. Phys. Rep. 281, 65 (1997); S.Putterman, K. Weninger,
Ann. Rev. Fluid Mech., 32, 445 (2000); M.P. Brenner et al. Rev. Mod. Phys. 74, 425 (2002). [4] D. Flannigan et al. Phys. Rev. Lett. 96, 204301 (2006). [5] R. Taleyarkhan et al. Science 295, 1868 (2002). [6] S. Putterman et al. http://arxiv.org/abs/cond-mat/0204065 [7] A. Chakravarty et al. Phys. Rev. E69, 066317 (2004). [8] R. Budakian et al. Nature, 391 266 (1998). [9] V.A. Klyuev et al. Sov. Phys. Tech. Phys. 34, 361 (1989). [10] B. Rosenblum et al. Appl. Phys. Lett. 25, 17 (1974). [11] B. Naranjo et al. Nature 428, 1115, (2005). This paper provides a route to earlier work on ferroelectric emission. [12] W. Cochran, Adv. Phys. 9, 387 (1960). [13] I. Inbar, R.E. Cohen, Phys. Rev. B33, 1193 (1996). |
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