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Physical Review A

Dissociative recombination slows the expansion of a molecular ultracold plasma

Hossein Sadeghi, Edward R. Grant

Published Nov 2, 2012• 13 citations
Publisher

Abstract

A fluid model for the expansion of a molecular ultracold plasma composed of NO${}^{+}$ ions and electrons shows that fast dissociative recombination (DR) flattens the charged-particle density distribution, effectively freezing the expansion of the plasma core. However, a much greater fraction of the plasma mass exists at lower density in the wings of the plasma, where dissociative recombination has little effect, and ion motion is driven by a Gaussian charge-density gradient. Here, expansion proceeds as the collisionless acceleration of the ions under the radial pressure of the expanding electron gas. Even though DR flattening dramatically suppresses the radial velocity of ions in the densest part of the plasma, the measured evolution of the overall plasma width remains dominated by the expansion of the outer shells. Thus, despite its frozen core, a dissociating plasma with an initial electron temperature ${T}_{e}(0)$ exhibits a time-evolving width that differs only slightly from a Vlasov expansion with the same ${T}_{e}(0)$.

DOI
10.1103/physreva.86.052701

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A fluid model for the expansion of a molecular ultracold plasma composed of NO+{}^{+}+ ions and electrons shows that fast dissociative recombination (DR) flattens the charged-particle density distribution, effectively freezing the expansion of the plasma core. However, a much greater fraction of the plasma mass exists at lower density in the wings of the plasma, where dissociative recombination has little effect, and ion motion is driven by a Gaussian charge-density gradient. Here, expansion proceeds as the collisionless acceleration of the ions under the radial pressure of the expanding electron gas. Even though DR flattening dramatically suppresses the radial velocity of ions in the densest part of the plasma, the measured evolution of the overall plasma width remains dominated by the expansion of the outer shells. Thus, despite its frozen core, a dissociating plasma with an initial electron temperature Te(0){T}_{e}(0)Te​(0) exhibits a time-evolving width that differs only slightly from a Vlasov expansion with the same Te(0){T}_{e}(0)Te​(0).
Using state-selected double-resonant excitation, we create a Rydberg gas of NO molecules excited to the principal quantum number n = 50 of the f-series converging to the ion rotational level, N(+) = 2. This gas evolves to form an ultracold plasma, which expands under the thermal pressure of its electrons, and dissipates by electron-ion recombination. Under conditions chosen for this experiment, the observed rates of expansion vary with selected plasma density. Electron temperatures derived from these expansion rates vary from T(e) = 12 K for the highest density up to 16 K at four-fold lower density. Over this range, the apparent electron coupling parameter, defined as Γ(e) = e(2)/4πε(0)ak(B)T(e), falls from nearly three to about one. The decay of charged-particle density fits with a kinetic model that includes parallel paths of direct two-body and stepwise three-body dissociative recombination. The overall recombinative decay follows a second-order rate law, with an observed rate constant that fits with established scattering-theory estimates for elementary two-body dissociative recombination. A small residual increase in this rate constant with decreasing charged-particle density suggests a growing importance of the three-body recombination channel under conditions of decreasing electron correlation.
The results of a theoretical investigation of an ultracold, neutral plasma composed only of equal mass positive and negative charges are reported. In our simulations, the plasma is created by the fast dissociation of a neutral particle; each dissociation leads to one positive ion and one negative ion with the same mass as the positive ion. The temperature of the plasma is controlled by the relative energy of the dissociation. We studied the early time evolution of this system where the initial energy was tuned so that the plasma is formed in the strongly coupled regime. In particular, we present results on the temperature evolution and three body recombination. In the weakly coupled regime, we studied how an expanding plasma thermalizes and how the scattering between ions affects the expansion. Because the expansion causes the density to drop, the velocity distribution only evolves for a finite time with the final distribution depending on the number of particles and initial temperature of the plasma.
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.
Double-resonant photoexcitation of nitric oxide in a molecular beam creates a dense ensemble of 51f(2) Rydberg states, which evolves to form a plasma of free electrons trapped in the potential well of an NO + spacecharge. 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. Dissociative recombination of NO + ions with electrons provides the primary dissipation mechanism for the plasma. We have identified three dissociation pathways, and quantified their relative contributions to the measured rate: Two-body dissociative recombination competes with direct three-body recombination to neutral dissociation products, and with a process in which three-body recombination and electron-impact ionization form an equilibrium population of high-Rydberg states that decays by predissociation. Using available collision-theory rate constants for three-body recombination and ionization, together with quantum mechanical estimates of predissociation rates, we predict that the relaxation of the plasma to a high-Rydberg equilibrium outpaces direct three-body dissociative recombination, and, among second-order processes, the rate of two-body electron-cation dissociative recombination substantially exceeds the rate at which the high-Rydberg equilibrium dissociatively relaxes. The rate constant for dissociative recombination extracted from these data conforms with predictions drawn from theory for isolated electron-ion collisions. Methods based on the dissipation of molecular ultracold plasmas may provide a means for estimating rates of dissociative recombination for a variety of complex molecules.
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 ${T}_{e}\ensuremath{\approx}7\text{ }\text{K}$.
Spontaneous avalanche to plasma splits the core of an ellipsoidal Rydberg gas of nitric oxide. Ambipolar expansion first quenches the electron temperature of this core plasma. Then, long-range, resonant charge transfer from ballistic ions to frozen Rydberg molecules in the wings of the ellipsoid quenches the ion-Rydberg-molecule relative velocity distribution. This sequence of steps gives rise to a remarkable mechanics of self-assembly, in which the kinetic energy of initially formed hot electrons and ions drives an observed separation of plasma volumes. These dynamics adiabatically sequester energy in a reservoir of mass transport, starting a process that anneals separating volumes to form an apparent glass of strongly coupled ions and electrons. Short-time electron spectroscopy provides experimental evidence for complete ionization. The long lifetime of this system, particularly its stability with respect to recombination and neutral dissociation, suggests that this transformation affords a robust state of arrested relaxation, far from thermal equilibrium.