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New Journal of Physics

Collisional microwave heating and wall interaction of an ultracold plasma in a resonant microwave cavity

M. A. W. van Ninhuijs, Job Beckers, O.J. Luiten

Published Jun 1, 2022• 4 citations
Publisher

Abstract

Abstract Recently, we introduced a resonant microwave cavity as a diagnostic tool for the study of ultracold plasmas (UCPs). This diagnostic allows us to study the electron dynamics of UCPs non-destructively, very fast, and with high sensitivity by measuring the shift in the resonance frequency of a cavity, induced by a plasma. However, in an attempt to theoretically predict the frequency shift using a Gaussian self-similar expansion model, a three times faster plasma decay was observed in the experiment than found in the model. For this, we proposed two causes: plasma–wall interactions and collisional microwave heating. In this paper, we investigate the effect of both causes on the lifetime of the plasma. We present a simple analytical model to account for electrons being lost to the cavity walls. We find that the model agrees well with measurements performed on plasmas with different initial electron temperatures and that the earlier discrepancy can be attributed to electrons being lost to the walls. In addition, we perform measurements for different electric field strengths in the cavity and find that the electric field has a small, but noticeable effect on the lifetime of the plasma. By extending the model with the theory of collisional microwave heating, we find that this effect can be predicted quite well by treating the energy transferred from the microwave field to the plasma as additional initial excess energy for the electrons.

DOI
10.1088/1367-2630/ac6c46

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Abstract Recently, we introduced a resonant microwave cavity as a diagnostic tool for the study of ultracold plasmas (UCPs). This diagnostic allows us to study the electron dynamics of UCPs non-destructively, very fast, and with high sensitivity by measuring the shift in the resonance frequency of a cavity, induced by a plasma. However, in an attempt to theoretically predict the frequency shift using a Gaussian self-similar expansion model, a three times faster plasma decay was observed in the experiment than found in the model. For this, we proposed two causes: plasma–wall interactions and collisional microwave heating. In this paper, we investigate the effect of both causes on the lifetime of the plasma. We present a simple analytical model to account for electrons being lost to the cavity walls. We find that the model agrees well with measurements performed on plasmas with different initial electron temperatures and that the earlier discrepancy can be attributed to electrons being lost to the walls. In addition, we perform measurements for different electric field strengths in the cavity and find that the electric field has a small, but noticeable effect on the lifetime of the plasma. By extending the model with the theory of collisional microwave heating, we find that this effect can be predicted quite well by treating the energy transferred from the microwave field to the plasma as additional initial excess energy for the electrons.
We present an in situ study of the electron dynamics of an ultracold 85Rb^{85}\mathrm{Rb}85Rb plasma using microwave cavity resonance spectroscopy with submicrosecond temporal resolution and vastly improved sensitivity. We observe a three times faster plasma decay than predicted by a self-similar Gaussian expansion model, which might be attributed to collisional microwave heating and plasma-wall interactions. The demonstrated sensitivity enables nondestructive probing of other (nearly) ionized media of fundamental importance as well, such as cold Rydberg gases and antihydrogen plasmas.
Ultracold plasmas (UCPs) are created by photo-ionization of a cloud of laser-cooled atoms, and have initial electron temperatures in the range 1-100 K and initial ion temperatures in the range 0.001-1 K. As a consequence UCPs can be in the strongly coupled regime, where the typical Coulomb interaction between the particles exceeds the thermal energy of the particles; a clear distinction with conventional plasmas. UCPs are not stable systems and the electron and ion temperature will rise during their evolution. The introduction of a disturbing rf-field to the plasma is expected to speed up the heating of the plasma.In this thesis the intrinsic electron heating mechanisms are studied as well as the heating mechanisms induced by an external rf field. Numerical simulations were performed with the General Particle Tracer code and compared to analytical theories.Two intrinsic heating mechanisms were studied: disorder-induced heating (DIH) and heating by three-body recombination (TBR). DIH arises due the random initial positions of the electrons. An excess of potential energy exists in the electron distribution which is rapidly converted into thermal energy. The time scale of DIH was found to be on the order of the inverse Mie-frequency, confirming analytical theories. TBR was identified in the simulations and the TBR heating rate was found to agree well with analytical models. Two rf-induced heating mechanisms were studied: collisionless energy absorption and collisional absorption. The first of these processes was found to depend strongly on the ratio between the rf field frequency and the oscillation frequency of the electrons in the plasma. Collisional absorption was studied in a regime that collisionless absorption is negligible. Absorption arises because the electrons, which are oscillating at the rf field frequency, are deflected by the Coulomb fields of the ions. The amount of collisional absorption was found to depend strongly on the amplitude of the rf field. It was found that the rf field effectively suppresses the electron-ion collision frequency as a function of increasing field amplitude, confirming analytical theories. For low to moderate amplitudes the amount of energy absorption increases, but less than one might intuitively expect due to the decrease in collision frequency. For very strong field amplitudes the energy absorption even decreases as a function of field amplitude.The understanding achieved, provides new roads to control these type of plasmas experimentally. Ultracold plasmas (UCPs) are created by photo-ionization of a cloud of laser-cooled atoms, and have initial electron temperatures in the range 1-100 K and initial ion temperatures in the range 0.001-1 K. As a consequence UCPs can be in the strongly coupled regime, where the typical Coulomb interaction between the particles exceeds the thermal energy of the particles; a clear distinction with conventional plasmas. UCPs are not stable systems and the electron and ion temperature will rise during their evolution. The introduction of a disturbing rf-field to the plasma is expected to speed up the heating of the plasma.In this thesis the intrinsic electron heating mechanisms are studied as well as the heating mechanisms induced by an external rf field. Numerical simulations were performed with the General Particle Tracer code and compared to analytical theories.Two intrinsic heating mechanisms were studied: disorder-induced heating (DIH) and heating by three-body recombination (TBR). DIH arises due the random initial positions of the electrons. An excess of potential energy exists in the electron distribution which is rapidly converted into thermal energy. The time scale of DIH was found to be on the order of the inverse Mie-frequency, confirming analytical theories. TBR was identified in the simulations and the TBR heating rate was found to agree well with analytical models. Two rf-induced heating mechanisms were studied: collisionless energy absorption and collisional absorption. The first of these processes was found to depend strongly on the ratio between the rf field frequency and the oscillation frequency of the electrons in the plasma. Collisional absorption was studied in a regime that collisionless absorption is negligible. Absorption arises because the electrons, which are oscillating at the rf field frequency, are deflected by the Coulomb fields of the ions. The amount of collisional absorption was found to depend strongly on the amplitude of the rf field. It was found that the rf field effectively suppresses the electron-ion collision frequency as a function of increasing field amplitude, confirming analytical theories. For low to moderate amplitudes the amount of energy absorption increases, but less than one might intuitively expect due to the decrease in collision frequency. For very strong field amplitudes the energy absorption even decreases as a function of field amplitude.The understanding achieved, provides new roads to control these type of plasmas experimentally.
We present the design and commissioning of a resonant microwave cavity as a novel diagnostic for the study of ultracold plasmas. This diagnostic is based on the measurements of the shift in the resonance frequency of the cavity, induced by an ultracold plasma that is created from a laser-cooled gas inside. This method is simultaneously non-destructive, very fast (nanosecond temporal resolution), highly sensitive, and applicable to all ultracold plasmas. To create an ultracold plasma, we implement a compact magneto-optical trap based on a diffraction grating chip inside a 5 GHz resonant microwave cavity. We are able to laser cool and trap (7.25 ± 0.03) × 107 rubidium atoms inside the cavity, which are turned into an ultracold plasma by two-step pulsed (nanosecond or femtosecond) photo-ionization. We present a detailed characterization of the cavity, and we demonstrate how it can be used as a fast and sensitive probe to monitor the evolution of ultracold plasmas non-destructively. The temporal resolution of the diagnostic is determined by measuring the delayed frequency shift following femtosecond photo-ionization. We find a response time of 18 ± 2 ns, which agrees well with the value determined from the cavity quality factor and resonance frequency.
Several mechanisms by which an external electromagnetic field influences the temperature of a plasma are studied analytically and specialized to the system of an ultracold plasma (UCP) driven by a uniform radio-frequency (rf) field. Heating through collisional absorption is reviewed and applied to UCPs. Furthermore, it is shown that the rf field modifies the three-body recombination process by ionizing electrons from intermediate high-lying Rydberg states and upshifting the continuum threshold, resulting in a suppression of three-body recombination. Heating through collisionless absorption associated with the finite plasma size is calculated in detail, revealing a temperature threshold below which collisionless absorption is ineffective.
Applying a short electric field pulse to an ultracold plasma induces an electron plasma oscillation. This manifests itself as an oscillation of the electron center of mass around the ion center of mass in the ultracold plasma. In general, the oscillation can damp due to either collisionless or collisional mechanisms, or a combination of the both. To investigate the nature of oscillation damping in ultracold plasmas, we developed a molecular dynamics model of the ultracold plasma electrons. Through this model, we found that depending on the neutrality of the ultracold plasma and the size of an applied DC electric field, there are some parameter ranges where the damping is primarily collisional and some primarily collisionless. We conducted experiments to compare the measured damping rate with theory predictions and found them to be in good agreement. Extension of our measurements to different parameter ranges should enable studies for strong-coupling influence on electron-ion collision rates.
We have experimentally demonstrated both heating and cooling of electrons in an ultracold neutral plasma (UNP) by embedding Rydberg atoms into the plasma soon after its creation. We have determined the relationship between the initial electron temperature, Te,i{T}_{e,i}Te,i​, and the binding energy of the added Rydberg atoms, Eb{E}_{b}Eb​, at the crossover between heating and cooling behaviors (that is, the binding energy of the atoms, which, when they are added to the plasma, neither accelerate nor slow down the plasma expansion). Specifically, this condition is $|{E}_{b}|\ensuremath{\approx}2.7\ifmmode\times\else\texttimes\fi{}{k}_{B}{T}_{e,i}$ when the diagnostic used is the effect of the Rydberg atoms on the plasma asymptotic expansion velocity. Additionally, we have obtained experimental estimates for the amount of heating or cooling which occurs when the Rydberg binding energy does not satisfy the crossover condition. The experimental results for the crossover condition, and the degree of heating or cooling away from the crossover, are in agreement with predictions obtained from numerical modeling of the interactions between Rydberg atoms and the plasma. We have also developed a simple intuitive picture of how the Rydberg atoms affect the plasma, which supports the concept of a ``bottleneck'' in the Rydberg state distribution of atoms in equilibrium with a coexisting plasma.