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Journal of Physics A Mathematical and Theoretical

The King model for electrons in a finite-size ultracold plasma

D. Vrinceanu, Gouthaman S. Balaraman, Lee A. Collins

Published Sep 29, 2008• 5 citations
Publisher

Abstract

A self-consistent model for a finite-size non-neutral ultracold plasma is obtained by extending a conventional model of globular star clusters. This model describes the dynamics of electrons at quasi-equilibrium trapped within the potential created by a cloud of stationary ions. A random sample of electron positions and velocities can be generated with the statistical properties defined by this model.

DOI
10.1088/1751-8113/41/42/425501

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A self-consistent model for a finite-size non-neutral ultracold plasma is obtained by extending a conventional model of globular star clusters. This model describes the dynamics of electrons at quasi-equilibrium trapped within the potential created by a cloud of stationary ions. A random sample of electron positions and velocities can be generated with the statistical properties defined by this model.
Electrons in a spherical ultracold, quasi-neutral plasma at temperature in the Kelvin range can be created by laser excitation of an ultracold, laser-cooled atomic cloud. The dynamical behaviour of the electrons is similar to the one described by conventional models of star cluster dynamics. The single mass component, the spherical symmetry and no star evolution are here accurate assumptions. The analogue of binary star formations in the cluster case is a three-body recombination in Rydberg atoms in the plasma case with the same Heggie's law: soft binaries get softer and hard binaries get harder. We demonstrate that the evolution of such an ultracold plasma is dominated by Fokker—Planck kinetics equations formally identical to the ones controlling the evolution of a star cluster. The Virial theorem leads to a link between the plasma temperature and the ions and electron numbers. The Fokker—Planck equation is approximate using gaseous and fluid models. We found that the electrons are in a Kramers—Michie—King type quasi-equilibrium distribution as stars in clusters. We suggest that the evaporation rate can be used to determine the temperature. As an example, knowing the electron distribution and using forced fast electron extraction, in a ‘violent extraction’ way, we are able to determine the plasma temperature knowing the trapping potential depth.
Electrons in a spherical ultracold quasineutral plasma at temperature in the Kelvin range can be created by laser excitation of an ultra-cold laser cooled atomic cloud. The dynamical behavior of the electrons is similar to the one described by conventional models of stars clusters dynamics. The single mass component, the spherical symmetry and no stars evolution are here accurate assumptions. The analog of binary stars formations in the cluster case is three-body recombination in Rydberg atoms in the plasma case with the same Heggie's law: soft binaries get softer and hard binaries get harder. We demonstrate that the evolution of such an ultracold plasma is dominated by Fokker-Planck kinetics equations formally identical to the ones controlling the evolution of a stars cluster. The Virial theorem leads to a link between the plasma temperature and the ions and electrons numbers. The Fokker-Planck equation is approximate using gaseous and fluid models. We found that the electrons are in a Kramers-Michie-King's type quasi-equilibrium distribution as stars in clusters. Knowing the electron distribution and using forced fast electron extraction we are able to determine the plasma temperature knowing the trapping potential depth.
In the last decade, ultracold plasmas have been created in the laboratory by photo-ionizing laser-cooled atoms. To understand the overall dynamics of ultracold plasmas, one needs to understand Rydberg collisional processes at ultracold temperatures. The two kinds of problems addressed in this thesis are: study of Rydberg atomic processes at ultracold temperatures, and a study of the overall dynamics of \nthe ultracold plasmas. \nTheoretical methods based on quantal-classical correspondence is used to understand Rydberg atomic processes such as radiative cascade, and radiative recombination. A simulation method suitable for ultracold collisions is developed and tested. \nThis method is then applied to study collisional-Stark mixing in Rydberg atoms. \nTo study the dynamics of the ultracold plasmas, a King model for the electrons in plasmas is proposed. The King model is a stationary, finite sized electron distribution for the electrons in a cloud of fixed ions with a Gaussian distribution. A Monte-Carlo method is developed to simulate the overall dynamics of the King distribution.
We have studied the behavior of cold Rydberg atoms embedded in an ultracold plasma. We demonstrate that even deeply bound Rydberg atoms are completely ionized in such an environment, due to electron collisions. Using a fast pulse extraction of the electrons from the plasma we found that the number of excess positive charges, which is directly related to the electron temperature Te{T}_{e}Te​, is not strongly affected by the ionization of the Rydberg atoms. Assuming a Michie-King equilibrium distribution, in analogy with globular star cluster dynamics, we estimate Te{T}_{e}Te​. Without concluding on heating or cooling of the plasma by the Rydberg atoms, we discuss the range for changing the plasma temperature by adding Rydberg atoms.
Abstract The electron component of an ultracold neutral plasma (UCP) is modelled based on a scalable method using a self-consistently determined mean-field approximation. Representative sampling of discrete electrons within the UCP is used to project the electron spatial distribution onto an expansion of orthogonal basis functions. A collision operator acting on the sample electrons is employed in order to drive the distribution toward thermal equilibrium. These equilibrium distributions can be determined for non-zero electron temperatures even in the presence of spherical symmetry-breaking applied electric fields. This is useful for predicting key macroscopic UCP parameters, such as the depth of the electrons’ confining potential given other plasma parameters. Dynamics such as electron oscillations in UCPs with non-uniform density distributions can also be treated by this model.
We report on the self-induced electron trapping occurring in an ultracold neutral plasma that is set to expand freely. At the early stages of the plasma, the ions are not thermalized which follow a Gaussian spatial profile, providing the trapping to the coldest electrons. In the present work, we provide a theoretical model describing the electrostatic potential and perform molecular dynamics simulations to validate our findings. We show that in the strong confinement regime, the plasma potential is of a Thomas-Fermi type, similar to the case of heavy atomic species. The numerically simulated spatial profiles of the particles corroborate this claim. We also extract the electron temperature and coupling parameter from the simulation, so the duration of the transient Thomas-Fermi is obtained.