Ultracold plasmas blur the classical boundaries between the different states of matter. Newly observed electron-density waves could become useful probes of how electrons behave in this exotic regime.
The complex soups of ions and electrons known as plasmas are ubiquitous in nature, whether in a simple flame, the aurora borealis, the Sun or elsewhere. They are also crucial for technologies such as fluorescent lighting, or for plasma processing in microelectronics. Determining how properties such as temperature and density change inside a plasma is often challenging, but it is necessary for optimizing technological applications and also for understanding fundamental physical phenomena. Some of the most valuable probes developed to determine these properties are based on collective motions of the charged particles that are sensitive to conditions in a plasma. Writing in Physical Review Letters, Fletcher et al.1 describe observations in an ultracold plasma of what seem to be oscillations in electron density known as Tonks–Dattner resonances. The history of these resonances reads like a good detective novel, and the results imply that they may become a powerful diagnostic tool.
Students taking a first course in plasma physics learn that, in an infinite, homogeneous plasma, the electron density oscillates naturally at a frequency, ωp, that is proportional to the square root of the electron density. This ‘electron plasma oscillation’ has a simple physical description: if the electron density drops because electrons are, on average, moving away from the more massive and sluggish ions, strong electric fields develop that pull the electrons back. As there is little damping for electron motion, however, the electrons overshoot, and the local electron density tends to oscillate around its equilibrium value.
In plasmas with densities that vary over a length scale greater than that of the electron oscillations, the structure of these electron collective modes becomes richer. This fact was discovered in the 1950s, during experiments motivated by a prediction2 that radio waves with a frequency of ωp should reflect off plasma in the tail of a meteor. To general surprise, cylindrical plasmas designed to simulate meteor tails in fact scattered incident radio waves at multiple frequencies near ωp, indicating the existence of additional collective modes besides the electron plasma oscillation expected from the theory of homogeneous plasmas.
The additional modes were later named Tonks–Dattner resonances, and their frequencies increased as the diameter of the plasma column decreased3, in a manner reminiscent of the increase in pitch from a pipe organ as the pipe becomes shorter. A quantitatively accurate model of this resonance phenom-enon4 drew on the insight that the thermal motion of the electrons can transform the electron plasma oscillation into an extended density wave that propagates rather like a sound wave. In the experiment, the plasma density — and so ωp — increased towards the central axis. The Tonks–Dattner modes were resonant density waves of various frequencies ω, each confined to a region at the outer edge of the plasma where their ω was greater than ωp (Fig. 1). Farther in, at the inner radius at which ω=ωp, the Tonks–Dattner wave decayed abruptly (became ‘evanescent’), because at this point the higher-density electrons were moving quickly enough to cancel, or screen, the oscillating electric field underlying the wave. Higher-frequency resonances represented shorter-wavelength ‘standing waves’, for which more wavelengths of the density wave fitted between the edge of the plasma and the radius at which evanescence occurred. This explained the multiple reflections observed in the cylindrical-plasma experiment.
The experiments of Fletcher et al.1 probed ultracold plasmas, which are formed from laser-cooled atoms by the ionizing action of an intense laser pulse. With electron temperatures ranging from 1 to 103 kelvin, and ion temperatures near 1 K, these plasmas push the envelope of neutral-plasma physics beyond the conventional range of between 103 K (for a flame) and 107 K or higher (for the solar core or a nuclear fusion reactor). At such very low temperatures, interactions between the particles can dominate the particles' random thermal motion, creating a ‘strongly coupled’ plasma that acts as a liquid or a solid rather than as a standard, gaseous plasma. Studying this strong coupling in the ultracold regime in a laboratory could illuminate the properties of systems that are strongly coupled as a result of their high density, for example the interiors of gas giant planets such as Jupiter, or the surfaces of neutron stars.
Ultracold plasmas are also notable for their well-defined density distribution, which drops off in a gaussian fashion in all directions radiating out from a central point, as well as their small characteristic size of about 1 mm or less. They are also formed far from their thermal equilibrium: electrons are confined in the plasma by electric attraction to the ions, and after plasma formation, the entire distribution expands into a surrounding vacuum and dissipates in about 100 microseconds.
To study electron oscillations, Fletcher et al.1 applied radio waves to their ultracold plasma, just as in the meteor experiments. When the radio frequency matched the resonance of a collective mode, the applied radio field pumped energy into the electron cloud. This caused some electrons to boil out of the plasma and escape the pull of the ions, allowing them to be counted by a charged-particle detector. At low excitation intensity, only a single resonance, matching the electron plasma oscillation, was observed.
Fields of higher intensity, however, excited a series of higher-frequency modes. As the plasma expanded, the mode frequencies decreased in accordance with what would be expected for Tonks–Dattner modes. It might seem surprising that thermal electron motion — which is crucial to the formation of such modes — would be important in ultracold plasmas. But the small plasma size means that the resonant wavelength must be small, which increases the likelihood that resonant modes form.
One difference between the observed modes and the classic Tonks–Dattner picture is that the gaussian-shaped ultracold plasmas have no hard edge like that of the confined cylindrical plasmas of the earlier experiments. How exactly a standing wave forms in this open geometry still needs to be worked out. With that theoretical input, however, the resonance frequencies should provide an accurate measure of the electron temperature, a quantity that is essential for studying the approach towards thermal equilibrium of ultracold plasmas near, or in, the strongly coupled regime.
The approach towards equilibrium is a fundamentally challenging problem, as there are many competing processes that affect the electron temperature, such as cooling through adiabatic expansion of the plasma, or heating caused by the recombination of electrons and ions to form neutral atoms. The collective modes observed by Fletcher and colleagues1 could prove to be the best probe for investigating it.