Ultracold neutral plasmas

Plasmas are collections of charged particles that can exhibit an impressively diverse set of collective phenomena. They exist in an extraordinary variety of environments and span a great range of densities and temperatures, from 15 million kelvin in the core of the Sun to 200 K in the ionosphere and from 10³⁰ particles per cubic centimeter in a white dwarf to 1 particle per cm³ in interstellar space. They can find application in lighting sources, manufacturing of computer chips, and fusion energy research. Plasmas created in the laboratory are used to replicate and study those that occur naturally and to probe the fundamental and complex behavior of plasmas.

Plasmas tend to be hot, because collisional energies of 1 eV or higher are required to ionize atoms and molecules. But in the past decade, a new laboratory plasma has emerged on the scene—the ultracold neutral plasma. With electron and ion temperatures as low as 1 K, ultracold neutral plasmas extend the temperature range of neutral and quasi-neutral plasmas by two orders of magnitude, and they allow researchers to explore the boundary between traditional plasmas and those in which spatial correlations and so-called strong coupling become important. Several surprising new phenomena have already been revealed. The low temperature and well-controlled creation process also allow experimenters to cleanly demonstrate classic phenomena of plasma physics, such as collective modes and thermalization.

As described in box 1, ultracold neutral plasmas are formed through ionization of atoms or molecules that have been cooled well below 1 K. Such a cold initial sample is created by laser cooling of atoms or cooling of molecules seeded in a supersonic beam. A 10-ns laser pulse tuned near the ionization threshold creates the plasma, which is typically 1 mm across and has a density on the order of 10¹⁰ cm⁻³ for laser-cooled atoms and up to 10¹⁴ cm⁻³ for molecular beams. The electron energy equals the excess photon energy above the ionization threshold and can be tuned from about 1 K to 1000 K. The much heavier ions start with kinetic energies close to those of the original neutral particles.

Usual phenomena in an unusual plasma

Not every ionized gas is a plasma. Qualitatively, a system of charged particles becomes a plasma when collective motions and responses to external perturbations become organized and dominate over the behavior of individual particles. For example, charges in a plasma must be able to rearrange themselves to screen electric fields from penetrating significantly into the system. The length scale for screening is the Debye length, ${\lambda }_{\text{D}}=\sqrt{{\varepsilon }_0{k}_{b}T/n{e}^2}$ where T is the temperature and n is the density; a commonly stated formal requirement for a plasma is that its size must be much greater than λ _D so screening can be effective. An ionized gas sample that is too small or too dilute to satisfy that condition does not display complex behavior and can be described with much simpler physics. The Debye length at the center of an ultracold plasma is about a micron, so the requirement is satisfied. A closely related manifestation of the same condition is that all but a few percent of electrons in an ultracold plasma are trapped by the collective positive charge of the ions, and the plasma remains quasi-neutral with small internal electric fields over some 100 µs as it expands into the surrounding vacuum.

Another characteristic of plasmas is a rich spectrum of collective modes, or wave motions. The first collective mode seen in an ultracold plasma (and the first collective mode presented in virtually every plasma physics textbook) was the Langmuir oscillation, an oscillation of the electron density at the electron plasma frequency. ¹ The mode can be excited by an RF electric field, and as is common with plasmas, the excitation spectrum provides information about properties such as the electron density.

In a traditional plasma, electron-density oscillations such as the Langmuir oscillation are detected by inserting an electrical probe into the plasma. But that approach is practically impossible for ultracold systems, because the plasmas are so small and because heating would result from a connection to the outside environment. Langmuir oscillations are detected in ultracold plasmas by remotely collecting the electrons that escape from the plasma when energy is resonantly pumped into it.

The small plasma size and inhomogeneous density distribution were instrumental in the observation of collective modes beyond the fundamental Langmuir oscillations. In recent experiments by one of us (Rolston) and coworkers at the University of Maryland, a series of resonances were observed at radio frequencies above the Langmuir oscillation. We identified them as standing electron sound waves, similar to the so-called Tonks—Dattner resonances in traditional plasmas. Normally, and especially at low temperature, electron waves are local density oscillations and do not propagate like sound. But in the small ultracold plasma, the length scale of wave motion must also be small, which changes the oscillation into a sound wave. ² In the usual Tonks-Dattner situation, the resonant mode frequencies and wavelengths are determined by an outer boundary such as the metallic wall that confines the plasma; the inner boundary is the point in the inhomogeneous density where the wave becomes evanescent and can no longer propagate. But in an ultracold plasma freely expanding into vacuum, there is no obvious outer turning point. An ad hoc choice of an outer turning point of three times the plasma root-mean-square size gave good agreement with a Tonks-Dattner model, but a rigorous description of the mode structure of such a boundaryless system is still an open problem.

Collective modes in plasmas are often unstable. They can grow exponentially in oscillation amplitude until they become so large that they destroy the plasma or nonlinear effects start to limit the growth. In the pursuit of fusion power, instabilities can rob the plasma of the energy necessary for sustained fusion, so understanding, controlling, and eliminating them is critical. Ultracold plasmas also are susceptible to instabilities. In other work at the University of Maryland, an ultracold plasma subjected to crossed electric and magnetic fields emitted periodic bursts of electrons, as shown in figure 1. The cause of the bursts was identified as a high-frequency drift instability, in which harmonics of the cyclotron frequency couple to the electron motion driven by E x B drift. The magnetic field magnetizes the electrons, so that their cyclotron orbits are smaller than the plasma itself, and the dynamics are significantly altered. (The ions remain unmagnetized because they are so much more massive.) Because an ultracold plasma’s electrons have so little thermal energy, the fields necessary to see the instability are exceedingly small (1 G and 10 mV/cm) compared with those required for more energetic plasmas. The same instability also occurs in a plasma-based propulsion device called the Hall thruster, which has been used in hundreds of Russian spacecraft and is being evaluated as an option in US spacecraft. (See the Quick Study by Mark Cappelli, Physics Today, April 2009, page 76 .)

Surprising connections between ultracold plasmas arise with rather disparate fields of physics. Several authors, such as Pierre Pillet and Daniel Comparat at the Laboratoire Aimé Cotton in Orsay, France, have pointed out the similarity between the dynamics of particles in an ultracold plasma and the dynamics of stars in a globular cluster. For example, recombination in ultracold plasmas—the collision of two electrons and one ion to yield an energetic electron and a bound, highly excited atom or molecule—is analogous to binary-star formation: Some binaries form through the interaction of three stars, with the extra body carrying away the binary binding energy. Care must be taken in both systems to describe dynamics on different time scales, because the motion of tightly bound pairs is much faster than the drift of individual particles. The thermodynamics of open systems also arises in both cases. Both the electrons in an ultracold plasma and the stars in a globular cluster are trapped in a potential well of finite depth. Thus neither system can achieve equilibrium, since collisions can always promote electrons or stars above the energy needed to escape. But the rate of escape eventually slows down, and a quasi-equilibrium state is established. The Michie—King distribution, which describes the velocities of stars in a cluster, has been suggested as the correct description for ultracold plasmas as well. ³ Ultracold plasmas offer the opportunity—unavailable in the study of galaxies—to probe the underlying physics through direct detection of the evaporating electrons and control of the confining potential.

Ultracold plasmas have also proven to be a good testing ground for molecular dynamics simulations. ^{4 – 6} Simulating any plasma is a difficult computational challenge, since the relevant time scales for motion of the ions and electrons can differ by six orders of magnitude. So far, full simulations have been able to capture only the first few hundred nanoseconds after plasma creation, during which local thermal equilibrium is established and recombination begins. To model physics at longer time scales, researchers must make approximations, such as treating electrons as a smooth neutralizing background for ions. But under that approximation, electron-ion collisions and recombination cannot be treated exactly. Since ultracold plasmas can be precisely controlled and accurately monitored, they can serve as benchmarks for molecular dynamics simulations. Computational methods that reproduce the data well can then be applied to more complicated systems, such as plasmas created by intense laser irradiation of solid targets, in which diagnostics are more challenging because of their fast collisional time scales.

Strong coupling

Most elementary plasma textbooks restrict their attentions to systems whose Debye lengths are larger than their typical interparticle spacings; that is, nλ _D ³ > 1. The very idea of Debye shielding—that charges redistribute themselves to screen electric fields on the length scale of λ _D —is hard to picture when the probability of finding any charge within a volume λ _D ³ becomes small. The criterion nλ _D ³ > 1 also ensures that charged-particle interactions are dominated by many weak interactions with far-away neighbors rather than isolated collisions between local pairs. The nature of the interactions has implications for the rate of collisional thermalization of a plasma out of equilibrium, which was described in seminal calculations by Lev Landau and Lyman Spitzer. ⁷

Rydberg atoms

In any plasma, atoms produced by three-body recombination collisions are formed in highly excited Rydberg states. And since the recombination rate scales as T ^-9/2, Rydberg atoms are copiously produced in ultracold plasmas. The energy carried away by the third body in the collision heats the plasma significantly, but the overall temperature evolution also depends on subsequent collisions between the Rydberg atoms and the plasma electrons, which can add or subtract thermal energy. The fate of any one Rydberg atom in an ultracold plasma is uncertain: It can be reionized, it can be driven to higher or lower principal quantum number through electron collisions, or it can radiatively decay to a more tightly bound state.

In fact, the distinction between a dense gas of cold Rydberg atoms and a plasma is tenuous. Researchers have discovered that dense clouds of Rydberg atoms—created by tuning the excitation laser from slightly above to slightly below the ionization threshold—spontaneously evolve into ultracold plasmas. Thomas Gallagher at the University of Virginia and Pillet and coworkers have shown that strong attractive interactions between the highly polarizable Rydberg atoms lead to ionizing collisions, which produce electrons that ionize other Rydberg atoms. Once electrons begin to get trapped by Coulomb attraction to the ions, they ionize even more atoms, and the resulting avalanche creates a plasma.

The avalanche ionization approach to forming an ultracold plasma has recently been applied to molecules—specifically, nitrogen monoxide molecules in a supersonic beam. ¹² Such molecular plasmas are orders of magnitude more dense than those made from laser-cooled atoms. Their electrons, unlike those in atomic systems, appear to be cold enough (a few kelvin) to be strongly coupled, as estimated through plasma expansion studies. What exactly is different about the molecular plasma that allows strongly coupled electrons is an open question.

Antimatter plasmas

Most ultracold plasmas are produced by lasers. A notable exception is the antimatter plasmas at the heart of low-energy antihydrogen research. Precision tests of CPT symmetry (charge conjugation, parity, and time reversal) and the gravitational acceleration of antimatter require cold antihydrogen, preferably confined to a trap. To achieve that goal, experimenters at the antiproton decelerator facility at CERN capture antiprotons and positrons in separate Penning traps, in which they are subject to a large magnetic field (see the Quick Study by Gerald Gabrielse on page 68 of this issue). Through cyclotron radiation or thermalization with trapped electrons, the samples cool to about 4 K. The two oppositely charged single-component plasmas are then overlapped to create an ultracold neutral antimatter plasma, still subject to a magnetic field on the order of a few tesla.

It was recognized in 1988 that three-body recombination, with its T^-9/2 scaling, might be an efficient mechanism for antihydrogen formation in ultracold antimatter plasmas. ¹³ In 2002 two collaborations, ATHENA and ATRAP, observed low-energy antihydrogen. (Antihydrogen formed at high energies in a beam had been detected six years earlier.) ATHENA detected the antihydrogen from its annihilation on trap walls—neutral antihydrogen atoms are not confined by the fields of the Penning trap. (See Physics Today, November 2002, page 17 .) ATRAP observed antihydrogen by field ionization and detection of the resulting charged particles, which had the added benefit of confirming that the atoms were formed in the expected Rydberg states. (See Physics Today, January 2003, page 14 .) The ATRAP result was both good news and bad news—good in that antihydrogen did indeed form by recombination, but bad because the atoms were stuck in high-lying quantum states and could not immediately be used in precision spectroscopic measurements. Much effort has focused on understanding and harnessing the recombination dynamics to make ground-state antihydrogen atoms, but the process is quite complex and is further complicated by the strong magnetic field.

In zero field, recombination involves not a single collision but a series of collisions. An atom is formed with a small binding energy and is buffeted by electrons, which may reionize the atom or increase or decrease the binding energy. If the atom reaches a low enough principal quantum number, further collisions and radiation will probably drive it to the ground state. In a 5-T magnetic field, positrons are tightly bound to the magnetic field lines, and atoms that form are not the simple highly excited Bohr atoms familiar from quantum textbooks. Rather, they are so-called guiding-center atoms, in which the positrons slowly drift around the antiprotons while rapidly circling with small Larmor radii, as shown in figure 3. Collisions also look much different: When a guiding-center atom collides with a free positron, the free positron and the bound positron tend to switch places. As a result of such radically altered dynamics, the overall three-body collision rate may be about an order of magnitude slower than the field-free rate. ¹⁴ The ATRAP field-ionization results showed that the antihydrogen atoms were traveling faster than expected and that the number of atoms ionized scaled with the ionizing field in an unanticipated way. Further theoretical work revealed the complexity of atom formation in high fields. Monte Carlo simulations showed that a significant charge-exchange process was occurring and the guiding-center atom approach was starting to break down, with the electron orbits becoming chaotic for more tightly bound atoms. ¹⁵

One can wonder whether it would make more sense to study the recombination physics of magnetized plasmas using matter—protons and electrons—rather than the much more expensive antimatter. Although hard to come by, antimatter does have certain advantages, such as easy detection through the annihilation products. Although no one has yet made a proton—electron ultracold plasma, Georg Raithel and colleagues have produced a rubidium ultracold plasma in nested Penning traps at high magnetic field. Their system may provide a recombination testing ground that can be of use to the antihydrogen community.

Future directions

As the relatively young field of ultracold plasmas continues to grow, work continues on many fronts. Ultracold plasmas are a good system for studying heat transport and global thermal equilibration in strongly coupled plasmas. Recent experiments with molecular plasmas demonstrate new phenomena such as dissociative recombination and suggest that thermalization of ions with the cold background gas in the supersonic expansion could yield larger values of the coupling constant Г. Ultracold plasmas are also being investigated as a bright electron or ion source for applications such as ion milling, microscopy, and seeding free-electron lasers. ¹⁶ Although ultracold plasmas are in many ways extremely simple systems, they display a broad range of phenomena of interest to many sectors of physics. Researchers have learned a tremendous amount by studying classical plasma concepts and by probing the effects of correlations and strong coupling. As experiment and theory explore this new playground at the boundary of plasma physics, many more discoveries will surely come.