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Plasma Physics and Controlled Fusion

Theory of phase separation in ultra-cold neutral plasmas

Padma Kant Shukla, K. Avinash

Published Nov 21, 2012• 3 citations
Publisher

Abstract

We present an equation of state for mildly coupled ions in ultra-cold neutral (UCN) plasmas. By introducing the mean field approximation, we obtain expressions for free energy and pressure of ions. It is found that below a critical temperature, the ions undergo a first-order phase transition and exist in a mixed vapor?liquid phase for a range of values of the ion Coulomb coupling parameter ?i (=?the ion Coulomb energy/the ion kinetic energy), and in a mildly coupled liquid state for values of ?i above this range. Our analytical results demonstrate that the phenomena of phase transitions, as reported herein, are relevant for the existing computer simulations and are expected to be observed in the forthcoming UCN laboratory plasma experiments.

DOI
10.1088/0741-3335/54/12/124030

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Journal of Physics Conference Series•Nov 1, 2016•1 citation
We present an equation of state for mildly coupled ions in ultra-cold neutral (UCN) plasmas. By introducing the mean field approximation, we obtain expressions for free energy and pressure of ions. It is found that below a critical temperature, the ions undergo a first-order phase transition and exist in a mixed vapor?liquid phase for a range of values of the ion Coulomb coupling parameter ?i (=?the ion Coulomb energy/the ion kinetic energy), and in a mildly coupled liquid state for values of ?i above this range. Our analytical results demonstrate that the phenomena of phase transitions, as reported herein, are relevant for the existing computer simulations and are expected to be observed in the forthcoming UCN laboratory plasma experiments.
We show the existence of the liquid-vapor phase coexistence and a critical point for strongly coupled ions in ultracold neutral (UCN) plasmas. Expressions for the free energy of UCN plasmas and an equation of state for the ions are obtained in the mean field approximation. A van der Waals-like isotherm shows the existence of a critical point in UCN plasmas. Depending on the ion temperature, the ions are shown to exist in a mixed vapor-liquid phase for a range of the ion Coulomb coupling parameter Γ(i) (defined by the ratio between the ion interaction and the ion kinetic energies), and in a strongly coupled liquid state for values of Γ(i) above this range. The estimates of critical constants show that it may be possible to observe these phenomena in the present day UCN plasmas.
The details of recent calculations of the expansion of ultra-cold, neutral plasmas are given. The calculations are performed at several levels. The simplest level assumes an ansatz for the form of the electron and ion density; the result is a simple, ordinary differential equation which can be easily solved. The medium level of sophistication assumes the electrons are in thermal equilibrium but does not assume a particular form for the ion density; the result is a partial differential equation which is solved numerically. For the highest level of sophistication, a Monte Carlo technique is used to solve for the electron phase space distribution and solve for the ion motion in the resulting mean field. All levels of simulation include three body recombination and electron-Rydberg scattering. This paper contains the results of our simulations and compares them to measurements made on ultra-cold plasmas. Three body recombination is found to be important at very low temperatures since it is a heating mechanism for the electron gas. The collisions between cold electrons and Rydberg atoms are another important source of electron heating and de-excitation of atoms formed in the plasma. The evolution of the distribution of atoms in the plasma is simulated and several counter-intuitive effects that have been observed can be explained. Our simulations show that the plasma coupling constant does not become larger than ∼1/5 for the reported experiments. The behavior of plasma processes are investigated, e.g., ion acoustic waves, spike formation, and electron evaporation. The evolution of a cold Rydberg gas into a plasma is also simulated but certain properties of our simulation do not agree with measurements.
Using high-resolution laser-induced fluorescence spectroscopy, ion dynamics in\nan expanding ultracold neutral plasma (UNP) have been studied in unprecedented\ndetail. The evolution of the ion temperature is of great interest because the ions in\nan ultracold neutral plasma are strongly coupled, meaning their Coulomb interaction\nenergy exceeds the thermal energy. This leads to novel plasma properties that are\nhard to describe theoretically. Understanding all the factors that contribute to ion\ntemperature evolution is critical for designing schemes to cool the ions and achieve\neven stronger Coulomb coupling.\nThis work has also observed several phenomena that have not previously been\nstudied in ultracold plasmas. Ion adiabatic cooling has been observed in a UNP for\nthe first time, resulting in ion temperatures as low as 100mK and up to a tripling of\nthe Coulomb coupling parameter. The importance of electron-ion energy transfer is\ndemonstrated with the first observations of electron-ion collisional heating. Inclusion\nof this effect into existing numerical models provides better agreement with experimental\nresults. Results of molecular dynamics simulations of equilibrating plasmas\nhave been compared to early time experimental data, which provides a new method\nof density determination that is much less sensitive to experimental systematics and\nis accurate to within 10%. This improved certainty in the density allows accurate\ncomparison between data and a theoretical model of the plasma dynamics. The\nagreement is excellent, but on a hydrodynamic time scale a small amount of extra\nheat (on order of 100mK), not ascribable to electron-ion collisions or other sources in\nthe model, is detected in the ion component. Potential sources are discussed within\nas well as proposals for further studies and improvements.
By photoionizing samples of laser-cooled atoms with laser light tuned just above the ionization limit, plasmas can be created with electron and ion temperatures below 10 K. These ultracold neutral plasmas have extended the temperature bounds of plasma physics by two orders of magnitude. Table-top experiments, using many of the tools from atomic physics, allow for the study of plasma phenomena in this new regime with independent control over the density and temperature of the plasma through the excitation process. Characteristic of these systems is an inhomogeneous density profile, inherited from the density distribution of the laser-cooled neutral atom sample. Most work has dealt with unconfined plasmas in vacuum, which expand outward at velocities of order 100 m/s, governed by electron pressure, and with lifetimes of order 100 μs, limited by stray electric fields. Using detection of charged particles and optical detection techniques, a wide variety of properties and phenomena have been observed, including expansion dynamics, collective excitations in both the electrons and ions, and collisional properties. Through three-body recombination collisions, the plasmas rapidly form Rydberg atoms, and clouds of cold Rydberg atoms have been observed to spontaneously avalanche ionize to form plasmas. Of particular interest is the possibility of the formation of strongly coupled plasmas, where Coulomb forces dominate thermal motion and correlations become important. The strongest impediment to strong coupling is disorder-induced heating, a process in which Coulomb energy from an initially disordered sample is converted into thermal energy. This restricts electrons to a weakly coupled regime and leaves the ions barely within the strongly coupled regime. This review will give an overview of the field of ultracold neutral plasmas, from its inception in 1999 to current work, including efforts to increase strong coupling and effects on plasma properties due to strong coupling.
We measured the velocity distribution of ions in the ultracold neutral plasma (UNP) during its early evolution by the technique of velocity map imaging. The ion temperature during the phase of ion equilibrium was obtained experimentally through this method. The Coulomb coupling parameter of ions in the UNP after disorder-induced heating was also determined to be 2.1, which agreed well with the prediction from a charged particle tracing simulation. In addition, the ion expansion during the ion equilibration phase was observed. Notably, the experimentally observed expansion speed is larger than the value obtained from the self-similar expansion model, indicating the involvement of additional mechanisms, besides the electron thermal pressure, in driving the ion expansion. We have also discussed the contributions of ion–ion correlations and charge imbalance to the plasma expansion.
Phase diagrams for the "shelf Coulomb" and the modified pseudopotential plasma models developed in our previous works are compared. Qualitative agreement is observed between gas-liquid phase transition region of "shelf Coulomb" model and liquid-gas structure region of modified pseudopotential one. The possibility of experimental finding of the phase transition in nonequilibrium ultracold Rydberg plasma is considered. Parameters (density, temperature, levels of Rydberg atoms) for such a transition are estimated. Conclusion is made that "shelf Coulomb" model phase transition is practically impossible to observe in equilibrium strongly coupled plasmas due to high neutral atoms density at low temperatures: T crit ≈ 0.076.