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arXiv:2012.14577 · Physics of Plasmas

Expansion of ultracold neutral plasmas with exponentially decaying density distributions

M. K. Warrens, Grant M. Gorman, S. J. Bradshaw, T. C. Killian

Published Feb 1, 2021• 11 citations
arXivHTMLPDF

Abstract

We present a study of the expansion of an ultracold neutral plasma (UCNP) with an initial density distribution that decays exponentially in space, created by photoionizing atoms shortly after their release from a quadrupole (or biconic cusp) magnetic trap. A characteristic ion acoustic timescale is evident in the evolution of the plasma size and velocity, indicating that the dynamics are reasonably well described by a model of hydrodynamic expansion of a quasi-neutral plasma. However, for low plasma density and high initial electron temperature, excess ion kinetic energy in the vicinity of the central density peak suggests significant local non-neutrality at early times. Observations are compared to the well-understood self-similar expansion of a UCNP with an initial Gaussian density distribution, and a similar scaling law describes the evolution of plasma size for both cases.

DOI
10.1063/5.0042460

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Ultracold neutral plasmas (UNPs), which are formed by photoionizing a cloud of cold atoms, have been a powerful platform for studying a wide variety of plasma phenomena. Two areas of interest include expansion into vacuum and the development of shockwaves. Previous UNP experiments have used plasmas with an initial Gaussian density distribution. UNPs with a radially exponentially decaying density distribution, or exponential UNPs, can be formed by photoionizing atoms out of a purely magnetic trap. This dissertation studies the expansion in free space of exponential UNPs as well as the development and characterization of shockwaves in exponential UNPs. The free space expansion of an exponential UNP is compared to the well-known self-similar hydrodynamic expansion of a Gaussian plasma. Similar scaling laws describe the size evolution well for both cases. The evolution of the plasma size and velocity show a characteristic ion acoustic time scale, indicating that the plasma is generally well-described by a hydrodynamic description. While the exponential UNP is predominantly in the hydrodynamic regime, heating at the central peak for low-density, high-electron temperature suggests significant local non-neutrality at early times. This thesis presents the first observation of a shockwave in a UNP. The evolution of the density and velocity for exponential UNPs show signs of wave steepening. A significant density and velocity jump over a narrow region develops. These occur at the same location in the plasma. Additionally, a large spike in the ion temperature occurs at this front. The relative ion velocity across the front modestly surpasses the local sound speed. The initial conditions were varied to characterize the development of shockwaves. Varying the density and electron temperature did not impact shock formation for the ranges used. Changing the shape caused the shocks to disappear as the density gradient decreased. This suggests that the electron thermal pressure gradient plays a significant role in the shock formation. The establishment of shock formation in UNPs opens a new avenue of research for UNPs.

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In strongly magnetized neutral plasmas, electron motion is reduced perpendicular to the magnetic field direction. This changes dynamical plasma properties such as temperature equilibration, spatial density evolution, electron pressure, and thermal and electrical conductivity. In this paper we report measurements of free plasma expansion in the presence of a strong magnetic field. We image laser-induced fluorescence from an ultracold neutral Ca^{+} plasma to map the plasma size as a function of time for a range of magnetic field strengths. The asymptotic expansion velocity perpendicular to the magnetic field direction falls rapidly with increasing magnetic field strength. We observe that the initially Gaussian spatial distribution remains Gaussian throughout the expansion in both the parallel and perpendicular directions. We compare these observations with a diffusion model and with a self-similar expansion model and show that neither of these models reproduces the observed behavior over the entire range of magnetic fields used in this study. Modeling the expansion of a magnetized ultracold plasma poses a nontrivial theoretical challenge.

Physical review. E•Apr 6, 2022•20 citations
We present a study of the expansion of an ultracold neutral plasma (UCNP) with an initial density distribution that decays exponentially in space, created by photoionizing atoms shortly after their release from a quadrupole (or biconic cusp) magnetic trap. A characteristic ion acoustic timescale is evident in the evolution of the plasma size and velocity, indicating that the dynamics are reasonably well described by a model of hydrodynamic expansion of a quasi-neutral plasma. However, for low plasma density and high initial electron temperature, excess ion kinetic energy in the vicinity of the central density peak suggests significant local non-neutrality at early times. Observations are compared to the well-understood self-similar expansion of a UCNP with an initial Gaussian density distribution, and a similar scaling law describes the evolution of plasma size for both cases.
Ultracold neutral plasmas (UNPs), which are formed by photoionizing a cloud of cold atoms, have been a powerful platform for studying a wide variety of plasma phenomena. Two areas of interest include expansion into vacuum and the development of shockwaves. Previous UNP experiments have used plasmas with an initial Gaussian density distribution. UNPs with a radially exponentially decaying density distribution, or exponential UNPs, can be formed by photoionizing atoms out of a purely magnetic trap. This dissertation studies the expansion in free space of exponential UNPs as well as the development and characterization of shockwaves in exponential UNPs. The free space expansion of an exponential UNP is compared to the well-known self-similar hydrodynamic expansion of a Gaussian plasma. Similar scaling laws describe the size evolution well for both cases. The evolution of the plasma size and velocity show a characteristic ion acoustic time scale, indicating that the plasma is generally well-described by a hydrodynamic description. While the exponential UNP is predominantly in the hydrodynamic regime, heating at the central peak for low-density, high-electron temperature suggests significant local non-neutrality at early times. This thesis presents the first observation of a shockwave in a UNP. The evolution of the density and velocity for exponential UNPs show signs of wave steepening. A significant density and velocity jump over a narrow region develops. These occur at the same location in the plasma. Additionally, a large spike in the ion temperature occurs at this front. The relative ion velocity across the front modestly surpasses the local sound speed. The initial conditions were varied to characterize the development of shockwaves. Varying the density and electron temperature did not impact shock formation for the ranges used. Changing the shape caused the shocks to disappear as the density gradient decreased. This suggests that the electron thermal pressure gradient plays a significant role in the shock formation. The establishment of shock formation in UNPs opens a new avenue of research for UNPs.
We demonstrate magnetic confinement of an ultracold neutral plasma (UCNP) created at the null of a biconic cusp, or quadrupole magnetic field. Initially, the UCNP expands due to electron thermal pressure. As the plasma encounters stronger fields, expansion slows and the density distribution molds to the field. UCNP electrons are strongly magnetized over most of the plasma, while ion magnetization is only significant at the boundaries. Observations suggest that electrons and ions are predominantly trapped by magnetic mirroring and ambipolar electric fields, respectively. Confinement times approach 0.5 ms, while unmagnetized plasmas dissipate on a timescale of a few tens of microseconds.
This work describes the evolution of an ultracold neutral plasma as it expands freely in vacuum. It presents a comprehensive study of the electron temperature evolution under different initial conditions. Ultracold neutral plasmas are created by photoionizing laser-cooled neutral atoms in ultrahigh vacuum. The ions are typically at a temperature of ∼ 1K while the electron temperature can be set from 1--1000 K. After photoionization, some of the highly energetic electrons escape from the cloud, leaving a net positive charge in the cloud. This creates a Coulomb well which traps the rest of the electrons, and a plasma is formed. Since the electrons have a lot of kinetic energy, they tend to leave the cloud, however, the Coulomb force from the ion pulls the electrons back into the cloud. This exerts a recoil force on the ions, and the whole plasma starts expanding radially outwards. Since the expansion is caused by the thermal pressure of the electrons, a study of the plasma expansion unravels the complicated electron temperature evolution, under different initial conditions. Many collisional processes become significant as a plasma expands. These physical processes tend to heat or cool the ions and electrons, leading to very different kinds of evolution depending on the initial conditions of the plasma. This work demonstrates three different regions of parameter space where the degree of significance of these physical processes is different during the ultracold neutral plasma evolution. The experimental results are verified by theoretical simulations, performed by Thomas Pohl, which untangle the complicated electron temperature evolution.
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] .
We present observations of wave steepening and signatures of shock formation during expansion of ultracold neutral plasmas formed with an initial density distribution that is centrally peaked and decays exponentially with distance. The plasma acceleration and velocity decrease at large distance from the plasma center, leading to central ions overtaking ions in the outer regions and the development of a steepening front that is narrow compared to the size of the plasma. The density and velocity change dramatically across the front, and significant heating of the ions is observed in the region of steepest gradients. For a reasonable estimate of electron temperature, the relative velocity of ions on either side of the front modestly exceeds the local sound speed (Mach number M≳1). This indicates that by sculpting steep density gradients, it is possible to create the conditions for shock formation, or very close to it, opening a new avenue of research for ultracold neutral plasmas.
In strongly magnetized neutral plasmas, electron motion is reduced perpendicular to the magnetic field direction. This changes dynamical plasma properties such as temperature equilibration, spatial density evolution, electron pressure, and thermal and electrical conductivity. In this paper we report measurements of free plasma expansion in the presence of a strong magnetic field. We image laser-induced fluorescence from an ultracold neutral Ca^{+} plasma to map the plasma size as a function of time for a range of magnetic field strengths. The asymptotic expansion velocity perpendicular to the magnetic field direction falls rapidly with increasing magnetic field strength. We observe that the initially Gaussian spatial distribution remains Gaussian throughout the expansion in both the parallel and perpendicular directions. We compare these observations with a diffusion model and with a self-similar expansion model and show that neither of these models reproduces the observed behavior over the entire range of magnetic fields used in this study. Modeling the expansion of a magnetized ultracold plasma poses a nontrivial theoretical challenge.