Inside a sonoluminescing microbubble, hints of a dense plasma

For nearly 60 years following its 1933 discovery, sonoluminescence (SL)—the conversion of acoustic energy into optical energy by way of bubble cavitation—was exclusively a multibubble phenomenon. In a liquid subjected to a sufficiently intense ultrasound field, rarefaction would cause micron-sized gas bubbles to form and expand, then compression would cause them to collapse into a shimmering cloud of light. (See the articles in PHYSICS TODAY by Lawrence Crum, September 1994, page 22 , and by Detlef Lohse, February 2003, page 36 .) The bursts of light are a consequence of adiabatic compression, which heats the bubbles to temperatures approaching 5000 K—sufficient to dissociate molecules and excite bound electrons.

In 1990, Lawrence Crum and Felipe Gaitan (then at the University of Mississippi) generated SL in a lone, acoustically levitated bubble. In single-bubble SL, one bubble can survive millions of acoustic cycles, emitting a burst of light each time it nears maximum compression. Thanks to its higher symmetry, an isolated bubble more efficiently focuses the energy of an acoustic wave. Spectral analyses suggest that single-bubble SL can generate bubble surface temperatures approaching 20 000 K—several times that of the Sun’s photosphere—which could make it a useful test bed for probing high-energy chemistry. ¹

But as to what conditions prevail inside the bubbles at the moment of SL, no one is exactly sure. Some experts think they are sparsely ionized, transparent plasmas. In that case, bremsstrahlung can explain the flash of light. ² Others think they are densely ionized and opaque and therefore function as blackbody radiators (see PHYSICS TODAY, May 2005, page 21 ). The bubbles’ emission spectra—one of the few available clues as to their inner workings—are ambiguous. Broad and usually featureless, the spectra can be reasonably fit by either a Planck curve for a blackbody or a bremsstrahlung curve for a transparent emitter.

Now, researchers led by Seth Putterman (UCLA) have administered the most direct test yet of a sonoluminescing bubble’s ionic makeup: They observed its response to a laser pulse. ³ Their finding, that even a relatively cool bubble becomes opaque during SL, is one that even they themselves can’t fully explain.

Target practice

The UCLA experiment follows on the heels of a similar effort in 2008 by Gerald Diebold and coworkers at Brown University. ⁴ Expecting that laser heating would enhance the radiance of a sonoluminescing bubble, the Brown researchers synchronized laser pulses with a 23-kHz acoustic field, which they applied to an air bubble immersed in water. Under those conditions, the bubble was no easy target: SL occurred for just a nanosecond or so each cycle while the bubble was less than 1 µm in diameter. Ultimately, the group had difficulty distinguishing SL photons from background radiation caused by laser scattering, and the experiment was inconclusive.

By contrast, Putterman and company drove their bubble at the gentler, audible frequency of 38 Hz. As a result, the bubble remained relatively large—over 100 µm in diameter at maximum compression—and emitted long, nearly 1-µs flashes of light. Also, instead of air in water, the group used a xenon bubble in phosphoric acid, a system known to produce exceptionally bright bursts of SL. The bigger, brighter target, and the larger window in which to hit it, allowed the researchers to time their laser with the onset of SL. “Their experiments were beautifully conceived,” says Diebold.

Figure 1 shows images, captured with a CCD camera, of a typical bubble response. Prior to irradiation by the laser pulse, SL shows up as a bright region in the bubble’s center. About 60 ns after the arrival of a laser pulse, a new bright spot is apparent at the bubble’s right edge near the pulse’s point of entry. Already, the implication is that the pulse is absorbed and reemitted before it can penetrate through to the bubble’s left side. Roughly 300 ns later, the bright spot at right remains. “Basically,” says Putterman of the bubbles, “you can’t see through them.”

Although the UCLA researchers weren’t able to pin down the precise mean free path of photons in the bubble, they could assume it was less than the bubble’s radius of about 85 µm. Given that the bubble absorbs light primarily via electron–ion interactions—the inverse of bremsstrahlung—the researchers concluded that at the moment of SL, the unbound charge density must have been at least 10²⁰ cm⁻³. In other words, nearly 20% of the bubble’s Xe atoms were ionized.

No shock wave

The results are consistent with measurements made in 2010 by Kenneth Suslick (University of Illinois at Urbana-Champaign) and his graduate student David Flannigan (now at Caltech). By analyzing spectral-line broadening in a sonoluminescing argon bubble, the two were able to infer that the bubble’s unbound charge density ranged from 10¹⁷ cm⁻³ to 10²¹ cm⁻³, depending on the acoustic pressure and frequency. ⁵ At the highest driving pressures, virtually all of a bubble’s Ar atoms ionized, some doubly or triply. The same bubble’s surface temperature, however, was estimated to be about 16 000 K, or 1.5 eV. That’s a mere 1/10 the ionization energy of Ar and less than 1/30 the double ionization energy. How could so many ions abound in so seemingly cool a system?

One possible explanation is the theory, proposed nearly two decades ago, that shock waves in a supersonically imploding bubble converge to generate an energetic, highly ionized core. The core might be orders of magnitude hotter than the surface. Indeed, hydrodynamic models suggest Suslick and Flannigan’s system was almost certainly in the shock-wave regime.

What’s surprising about the ionization fractions measured in Putterman and company’s experiment is that they were achieved with relatively weak acoustic forcing. “The implosions were at one-tenth the speed of sound,” says Putterman. “I would say our system doesn’t have a hot inner core.” If that’s true, then the standard statistical mechanical model—embodied in what’s known as the Saha equation—says that the bubbles should have been only about 1% ionized, based on their estimated peak temperature of 10 000 K. At so minuscule a charge density, the mean free path would not have been less than 85 µm; it would have been nearly 1000 times larger.

Aha, Saha

So what is wrong with the Saha equation? For one, says Putterman, it doesn’t account for Coulomb interactions between neighboring particles. Due to charge screening in plasmas, charges separated by more than some distance λ_D—the so-called Debye length—don’t feel each other’s fields. That means an electron doesn’t have to be kicked infinitely far from its parent ion to be ionized; it needs only to distance itself by more than λ_D. And since λ_D falls as the population of unbound charges grows, ionization is self-promoting. In a 2011 paper, Putterman and his coworkers described how the feedback mechanism might initiate a sudden transition from a dilute plasma to a dense one. ⁶

In fact, the UCLA group may already have witnessed the predicted phase transition. Last year they collected time-resolved emission spectra from a sonoluminescing Xe bubble. The spectra, presented in figure 2, seem to show the bubble transitioning from partially transparent to opaque and back, all within the span of a single SL burst. The clue is the peak at 823 nm, which corresponds to an excited-state transition and is visible in a transparent emitter but obscured in an opaque one.

At the moment, however, the phase-transition model remains speculative. Some plasma physicists doubt that λ_D can become small enough for the positive-feedback mechanism to take meaningful effect. And even if Coulomb interactions might plausibly destabilize the sparsely ionized state, it’s not yet clear what stabilizes the highly ionized one. Furthermore, according to Suslick, it’s conceivable that a hot core forms even at the gentle driving frequencies used in the UCLA experiments.

Nonetheless, the UCLA group’s feat is widely seen as a promising technical breakthrough: In a field that has long relied on passive observation, one can now give a sonoluminescing bubble laser nudges to find out what it’s made of.