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Physics of Plasmas

Numerical simulation of ultracold plasmas

S. G. Kuzmin, Thomas M. O’Neil

Published Aug 30, 2002• 101 citations

Abstract

In recent experiments ultracold plasmas were produced by photoionizing small clouds of laser cooled atoms. This paper presents the results of molecular dynamic simulations for the early time evolution of such plasmas. Contrary to earlier speculation, no evidence of strong electron–electron correlations is observed in the simulations even if the initial value of the coupling parameter (Γe=e2/akTe) is much larger than unity. As electron–electron correlations begin to develop, the correlation energy is released to heat the electrons, raising the electron temperature to the point where Γe∼1 and limiting further development of correlation. Further heating of the electrons occurs as a by-product of three-body recombination. When a model of laser cooling is added to the simulation, the formation of strong ion–ion correlation is observed. Contrary to earlier suggestion, the rate of three-body recombination is observed to be in reasonable agreement with the traditional formula, R=3.9×10−9 s−1[n(cm−3)]2[Te(K)]−9/2, but care must be taken to use the correct temporally evolving temperature, Te. The simulations are challenging because it is necessary to follow three-body recombination into weakly bound (high n quasiclassical) Rydberg states, and the time scale for such states is short compared to that for the plasma dynamics. This kind of problem was faced earlier in computational astrophysics when studying binary star formation in globular clusters and the simulation method used here is adapted from such studies.

DOI: 10.1063/1.1497166

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In recent experiments ultracold plasmas were produced by photoionizing small clouds of laser cooled atoms. This paper presents the results of molecular dynamic simulations for the early time evolution of such plasmas. Contrary to earlier speculation, no evidence of strong electron–electron correlations is observed in the simulations even if the initial value of the coupling parameter (Γe=e2/akTe) is much larger than unity. As electron–electron correlations begin to develop, the correlation energy is released to heat the electrons, raising the electron temperature to the point where Γe∼1 and limiting further development of correlation. Further heating of the electrons occurs as a by-product of three-body recombination. When a model of laser cooling is added to the simulation, the formation of strong ion–ion correlation is observed. Contrary to earlier suggestion, the rate of three-body recombination is observed to be in reasonable agreement with the traditional formula, R=3.9×10−9 s−1[n(cm−3)]2[Te(K)]−9/2, but care must be taken to use the correct temporally evolving temperature, Te. The simulations are challenging because it is necessary to follow three-body recombination into weakly bound (high n quasiclassical) Rydberg states, and the time scale for such states is short compared to that for the plasma dynamics. This kind of problem was faced earlier in computational astrophysics when studying binary star formation in globular clusters and the simulation method used here is adapted from such studies.

We present the first large-scale simulations of an ultracold neutral plasma, produced by photoionization of laser-cooled xenon atoms, from creation to initial expansion, using classical molecular-dynamics methods with open boundary conditions. We reproduce many of the experimental findings such as the trapping efficiency of electrons with increased ion number, a minimum electron temperature achieved on approach to the photoionization threshold, and recombination into Rydberg states of an anomalously low principal quantum number. In addition, many of these effects establish themselves very early in the plasma evolution ( similar ns) before the present experimental observations begin.

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 present simulations of some of the early time properties of ultracold neutral plasmas. We focus on three aspects of this system. First, we study the earliest electron dynamics when the initial temperature of the electrons would place them in the strongly coupled regime. We focus on times out to ∼10 plasma periods of the electron but also present results out to ∼85 plasma periods. In particular, we study how the formation of Rydberg atoms leads to heating and how the mass of the ion could enter the dynamics. Second, we study how the ions behave when the electrons are at high temperatures by comparing simulations that treat the electrons as a fluid and simulations that simultaneously include the electrons and ions. For light ions, the electron–ion scattering transfers substantial energy from the electrons to the ions. Finally, we study the ion motion at early times and at low temperatures where the electron evolution and ion motion could be at comparable time scales. This allows a test of electron–ion scattering when the electron plasma is nearly strongly coupled and we find that the recent values for the electron–ion scattering rate underestimate the ion heating in our calculations.