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arXiv:1510.05743 · Journal of Physics B Atomic Molecular and Optical Physics

A scalable theoretical mean-field model for the electron component of an ultracold neutral plasma

John Guthrie, Jacob Roberts

Published Jan 25, 2016• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/49/4/045701

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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.
Ultracold plasmas (UCPs) are created under conditions of near but not perfect neutrality. In the limit of zero electron temperature, electron screening results in non-neutrality manifesting itself as an interior region of the UCP with both electrons and ions and an exterior region composed primarily of ions. The interior region is the region of the most scientific interest for 2-component ultracold plasma physics. This work presents a theoretical model through which the time evolution of non-neutral UCPs is calculated. Despite Debye screening lengths much smaller than the characteristic plasma spatial size, model calculations predict that the expansion rate and the electron temperature of the UCP interior is sensitive to the neutrality of the UCP. The predicted UCP dependence on neutrality has implications for the correct measurement of several UCP properties, such as electron temperature, and a proper understanding of evaporative cooling of the electrons in the UCP.
Electrons in an expanding ultracold plasma are expected to be in quasiequilibrium since the collision times are short compared to the plasma lifetime, yet electron evaporation is observed as the ion density decreases during expansion. A small electric field that shifts the electron cloud with respect to the ions increases the evaporation rate. Treating the electrons as a zero-temperature fluid, their spatial distribution is calculated as a function of the applied field strength and the ion density. The zero-temperature approximation gives the maximum number of electrons the plasma can hold in the absence of evaporation. By applying this calculation at all times during expansion, the flux of cold electrons from the plasma is predicted and found to be in good agreement with the observed electron signal.
The expansion of ultracold neutral plasmas (UCP) is driven primarily by the thermal pressure of the electron component and is therefore sensitive to the electron temperature. For typical UCP spatial extents, evaporative cooling has a significant influence on the UCP expansion rate at lower densities (less than 108/cm3). We studied the effect of electron evaporation in this density range. Owing to the low density, the effects of three-body recombination were negligible. We modeled the expansion by taking into account the change in electron temperature owing to evaporation as well as adiabatic expansion and found good agreement with our data. We also developed a simple model for initial evaporation over a range of ultracold plasma densities, sizes, and electron temperatures to determine over what parameter range electron evaporation is expected to have a significant effect. We also report on a signal calibration technique, which relates the signal at our detector to the total number of ions and electrons in the ultracold plasma.
Ultracold neutral plasmas (UNPs) are created in a vacuum by photoionizing laser-cooled atoms. The expansion of UNPs begins as a non-equilibrium system that quickly relaxes to a local equilibrium state [1] . We aim to quantify and compare the transport processes that govern the relaxation to equilibrium in the expanding UNP. Using a 1D-1V kinetic code in spherical coordinates, we model the radial expansion of an UNP. We compare our simulation results against analytic expressions to determine where the expansion of the UNP is adiabatic or isothermal. We carry out simulations for various initial density distributions such as an exponentially decaying density distribution [2] . We ultimately aim to extend this approach to a 1D-3V multi-component kinetic code that incudes collisions [3] .
Electron evaporation plays an important role in the electron temperature evolution and thus the expansion rate of low-density ultracold plasmas. In addition, evaporation is useful as a potential tool for obtaining colder electron temperatures and characterizing plasma parameters. A theoretical treatment of evaporation has been developed for atomic gases and has been applied to a one-component plasma system. We numerically investigate whether such an adapted theory is applicable to ultracold neutral plasmas. We find that it is not due to the violation of fundamental assumptions of the model. The details of our calculations and a discussion of the implications for a simple description of the electron evaporation rate in ultracold plasmas are presented.