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.
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.
Rydberg atom formation is a source of heating in plasmas. The rate of three-body recombination in an ultracold neutral plasma was measured and temperature for the plasma was extracted. With large-scale Monte Carlo and particle-in-cell simulations, we have ab initio calculated the rate of excitation, de-excitation, ionization (and recombination) in electron-Rydberg atom collision and investigated the short-time dynamics of three-body recombination in an ultracold neutral plasma. Comparison with observed rates is quite good. Particular attention is paid to the low-frequency microfield effect on Rydberg state cut-off in the plasma.
Rydberg atom formation is a source of heating in plasmas. The rate of three-body recombination in an ultracold neutral plasma was measured and electron temperature was derived from it using standard equilibrium recombination rates. With large-scale Monte Carlo and particle-in-cell simulations, we have calculated ab initio the rate of excitation, de-excitation, ionization (and recombination) in electron-Rydberg atom collision and investigated the short-time dynamics of three-body recombination in an ultracold neutral plasma. Comparison with observed rates is quite good. Particular attention is paid to the low-frequency microfield effect on Rydberg state cut-off in the plasma.
We report a systematic experimental and numerical study of the expansion of ultracold Rydberg plasmas. Specifically, we have measured the asymptotic expansion velocities,
v0, of ultracold neutral plasmas (UNPs) which evolve from cold, dense samples of Rydberg rubidium atoms using ion time-of-flight spectroscopy. From this, we have obtained values for the effective initial plasma electron temperature,
Te,0=mionv02/kB (where
mion is the
Rb+ ion mass), as a function of the original Rydberg atom density and binding energy,
Eb,i. We have also simulated numerically the interaction of UNPs with a large reservoir of Rydberg atoms to obtain data to compare with our experimental results. We find that for Rydberg atom densities in the range ${10}^{7}--{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$, for states with principal quantum number
n>40,Te,0 is insensitive to the initial ionization mechanism which seeds the plasma. In addition, the quantity
kBTe,0 is strongly correlated with the fraction of atoms which ionize, and is in the range $0.6\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|\ensuremath{\lesssim}{k}_{B}{T}_{e,0}\ensuremath{\lesssim}2.5\ifmmode\times\else\texttimes\fi{}|{E}_{b,i}|$. On the other hand, plasmas from Rydberg samples with $n\ensuremath{\lesssim}40$ evolve with no significant additional ionization of the remaining atoms once a threshold number of ions has been established. The dominant interaction between the plasma electrons and the Rydberg atoms is one in which the atoms are deexcited, a heating process for electrons that competes with adiabatic cooling to establish an equilibrium where
Te,0 is determined by their Coulomb coupling parameter, ${\mathrm{\ensuremath{\Gamma}}}_{e}\ensuremath{\sim}0.01$.