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Journal of Physics B Atomic Molecular and Optical Physics

On the evolution of the phase-space distributions of a non-spherical molecular ultracold plasma in a supersonic beam

Markus Schulz-Weiling, Hossein Sadeghi, Jachin Hung, Edward R. Grant

Published Sep 22, 2016• 15 citations
Publisher

Abstract

Abstract This paper offers a toolbox for characterizing the initial conditions and predicting the evolution of the ultracold plasma that forms after resonant laser preparation of a Rydberg gas entrained in a differentially pumped supersonic molecular beam. The conditions afforded by a skimmed free-jet expansion combined with the geometry of laser excitation, determines the phase-space volume of the excited gas. A hydrodynamic shell model, that accounts for the ellipsoidal spatial distribution of this excitation volume in concert with the deforming effects of dissociative recombination, serves to simulate the ambipolar expansion of this molecular ultracold plasma.

DOI
10.1088/0953-4075/49/19/193001

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arXiv:1103.0053•Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 2011•27 citations
Abstract This paper offers a toolbox for characterizing the initial conditions and predicting the evolution of the ultracold plasma that forms after resonant laser preparation of a Rydberg gas entrained in a differentially pumped supersonic molecular beam. The conditions afforded by a skimmed free-jet expansion combined with the geometry of laser excitation, determines the phase-space volume of the excited gas. A hydrodynamic shell model, that accounts for the ellipsoidal spatial distribution of this excitation volume in concert with the deforming effects of dissociative recombination, serves to simulate the ambipolar expansion of this molecular ultracold plasma.
The conditions aforded by a skimmed free-jet expansion intersected by two laser pulses, driving resonant transitions in nitric oxide, determine the phase-space volume of a dense molecular Rydberg ensemble. Spontaneous avalanche to plasma within this system leads to the development of two macroscopic domains. These domains are clearly distinguished by their polarizability as well as their locality within the plasma. The first domain appears at the system core, is polarized by fields exceeding 500 mV/cm and displays an ambipolar expansion character suggestive of initial electron temperatures exceeding 150 Kelvin. The second domain travels with the velocity of the supersonic beam and is robust to the application of several hundred V/cm pulses. It is further distinguished through the apparent arrest of relaxation channels, annealing the domain over a millisecond or more in a state far from thermal equilibrium. Both domains are linked via the spontaneous breaking of ellipsoidal symmetry to form bifurcating arrested volumes.
Abstract Double-resonant transitions excite nitric oxide in a seeded supersonic molecular beam, yielding a state-selected Rydberg gas that evolves to form an ultracold plasma. This plasma propagates in z with the molecular beam over a variable distance as great as 600 mm to strike an imaging detector, which records the charge distribution in the dimensions, x and y . The laser-crossed molecular beam excitation geometry convolutes an axial Gaussian distribution of NO about z with the Gaussian intensity distribution of the laser beam about x to create an ellipsoidal volume of Rydberg gas. Plasma images provide evidence for the relaxation of this Rydberg gas volume in an electron impact avalanche that breaks the ellipsoidal symmetry in x to form repelling plasma volumes. We find that the energy deposited in the recoil velocity of mass transport, V x depends systematically on the initially selected Rydberg gas principal quantum number, n 0 , and the initial density of the Rydberg gas, ρ 0 . These quantities combine to determine ρ e , the initial density of electrons formed by the prompt Penning ionization of closely spaced pairs of Rydberg molecules. Above a threshold density of Penning electrons, we find that V x depends linearly on ρ e . We argue that this bifurcation occurs as a consequence of the initial geometry of the Rydberg gas. Ambipolar electron expansion accelerates initially formed core ions. Resonant charge transfer redistributes this ion energy to the column of Rydberg molecules on the long axis of the ellipsoid. The equalized velocities in each direction give rise to a ± x streaming motion that concentrates density in opposing plasma volumes, causing the symmetric gas volume to split like a rotating liquid drop. Significantly, these dynamics reduce electron temperature with little decrease in the ion density or increase in the ion temperature. This appears to facilitate the formation of a strongly coupled plasma.
A Rydberg gas of xenon, entrained in a supersonic atomic beam, evolves slowly to form an ultracold plasma. In the early stages of this evolution, when the free-electron density is low, Rydberg atoms undergo long-range -mixing collisions, yielding states of high orbital angular momentum. The development of high- states promotes dipole–dipole interactions that help to drive Penning ionization. The electron density increases until it reaches the threshold for avalanche. Ninety μs after the production of a Rydberg gas with the initial state, , a 432 V cm−1 electrostatic pulse fails to separate charge in the excited volume, an effect which is ascribed to screening by free electrons. Photoexcitation cross sections, observed rates of -mixing, and a coupled-rate-equation model simulating the onset of the electron-impact avalanche point consistently to an initial Rydberg gas density of .
We report the spontaneous formation of a plasma from a gas of cold Rydberg molecules. Double-resonant laser excitation promotes nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, to single Rydberg states extending as deep as $80\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$ below the lowest ionization threshold. The density of excited molecules in the illuminated volume approaches $1\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$. This population evolves to produce free electrons and a durable cold plasma of electrons and intact NO+{\mathrm{NO}}^{+}NO+ ions.
The double-resonant laser excitation of nitric oxide, cooled to 1 K in a seeded supersonic molecular beam, yields a gas of $\ensuremath{\approx}{10}^{12}$ molecules per cubic centimeter in a single selected Rydberg state. This population evolves to produce prompt free electrons, and a durable cold plasma of electrons and intact NO+{\text{NO}}^{+}NO+ ions. This plasma travels with the molecular beam through a field-free region to encounter a grid. The atomic weight of the expansion gas controls the beam velocity and hence the flight time from the interaction region to the grid. Monitoring electron production as the plasma traverses this grid measures its longitudinal width as a function of flight time. Comparing these widths to the width of the laser beam that defines the initial size of the illuminated volume allows us to gauge the rate of expansion of the plasma. We find that the plasma created from the evolution of a Rydberg gas of NO expands at a small but measurable rate, and that this rate of expansion accords with the Vlasov equations for an initial electron temperature of ${T}_{e}\ensuremath{\approx}7\text{ }\text{K}$.
Double-resonant photoexcitation of nitric oxide in a molecular beam creates a dense ensemble of 50f(2) Rydberg states, which evolves to form a plasma of free electrons trapped in the potential well of an NO + space charge. The plasma travels at the velocity of the molecular beam and, on passing through a grounded grid, yields an electron time-of-flight signal that gauges the plasma size and quantity of trapped electrons. This plasma expands at a rate that fits with an electron temperature as low as 5 K, colder than typically observed for atomic ultracold plasmas. The recombination of molecular NO + cations with electrons forms neutral molecules excited by more than twice the energy of the NO chemical bond, and the question arises whether neutral fragmentation plays a role in shaping the redistribution of energy and particle density that directs the short-time evolution from Rydberg gas to plasma. To explore this question, we adapt a coupled rate-equations model established for atomic ultracold plasmas to describe the energy-grained avalanche of electron–Rydberg and electron–ion collisions in our system. Adding channels of Rydberg predissociation and two-body, electron–cation dissociative recombination to the atomic formalism, we investigate the kinetics by which this relaxation distributes particle density and energy over Rydberg states, free electrons and neutral fragments. The results of this investigation point to conditions under which such processes can effect the steady-state temperature of plasma electrons.