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Physical Review A

Cooling and slowing in high-pressure jet expansions

Wolfgang Christen, Klaus Rademann

Published Jan 4, 2008• 20 citations
Publisher

Abstract

The mathematical term for the mean flow velocity in supersonic beams of ideal gases is extended to include real gas properties. This procedure yields an explicit dependence of the flow velocity on pressure, as observed in recent experiments of free jet expansions. Applied to stagnation conditions slightly above the critical point, the model suggests that seeded high-pressure jet expansions might be suitable for slowing down virtually any molecule with maximum efficiency. Moreover, we discuss the consequence of a pressure-dependent flow velocity ${v}_{0}$ for the speed ratio $S={v}_{0}/\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ with respect to collisional cooling and suggest to use the velocity spread $\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ as a more nonambiguous measure of translational temperature in high-pressure jet expansions.

DOI
10.1103/physreva.77.012702

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The mathematical term for the mean flow velocity in supersonic beams of ideal gases is extended to include real gas properties. This procedure yields an explicit dependence of the flow velocity on pressure, as observed in recent experiments of free jet expansions. Applied to stagnation conditions slightly above the critical point, the model suggests that seeded high-pressure jet expansions might be suitable for slowing down virtually any molecule with maximum efficiency. Moreover, we discuss the consequence of a pressure-dependent flow velocity v0{v}_{0}v0​ for the speed ratio S=v0/\ensuremathΔv\ensuremath∥S={v}_{0}/\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}S=v0​/\ensuremathΔv\ensuremath∥​ with respect to collisional cooling and suggest to use the velocity spread \ensuremathΔv\ensuremath∥\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}\ensuremathΔv\ensuremath∥​ as a more nonambiguous measure of translational temperature in high-pressure jet expansions.
Supersonic expansions of pure and seeded rare gases have been investigated experimentally, measuring the translational and rotational temperatures. The lowest achievable translational temperature in the jet depends on both gas properties as well as on experimental boundary conditions like nozzle shape and nozzle–skimmer distance. We show that there is a limit to the lowest temperature achieved, under practical conditions, set by condensation in the jet. A large cluster binding energy enhances the formation of clusters and they release their condensation energy into the beam. The spatial confinement of the jet extends to long distances, and is sensitive to the shape of the nozzle. The confined jet forms a narrow cone of high intensity, and results in increased collision probability and cluster formation.
We have obtained substantial alignment of I2(X 1Σ+g;v″=0;J″=13,15) seeded in supersonic beams of light carrier gases. Laser-induced fluorescence and a variant of the magnetic precession technique were used to measure the ratio n⊥/n∥ of molecules with the rotational angular momentum vector J perpendicular to the beam axis z to those with J parallel (or antiparallel) to z. As the nozzle stagnation pressure P0 is increased, this ratio increases markedly, reaches a maximum, and then decreases steadily. At the maximum, n⊥/n∥=1.6, 1.7, and 2.2, respectively, for He, D2, and H2 as the carrier gases; this occurs at different pressures of the order of 103 Torr for nozzle diameter d=50 μm and temperature T0=315 K and corresponds to nearly the same rotational temperatures of about 6–8 K. We compare the observed dependence of alignment on P0⋅d with a J-dependent model that invokes two mechanisms for alignment, macroscopic gas transport, and anisotropic rotational cooling. The transport processes involve reorientation of J and give rise to alignment with n⊥/n∥>1; this dominates the initial increase with P0⋅d up to the maxima. The anisotropic cooling processes do not in our model involve reorientation of J but are fostered by the anisotropy of the rotational relaxation cross section; the alignment arises from different Boltzmann weights for molecules with J⊥z and J∥z due to their slightly different rotational temperatures (about 5%). At high P0⋅d the net alignment is dominated by the anisotropic cooling term. At the correspondingly low rotational temperatures, this term counteracts the effect of gaseous transport, so the net alignment can reverse. Indeed, at high P0⋅d we do observe n⊥/n∥<1. For a higher rotational state (J″=39,41) we find lower alignment that peaks at a higher rotational temperature (about 27 K), as predicted by the model.
The flow velocity of gas emerging from a supersonic nozzle mounted on a high-speed rotor can be largely canceled by the rotor velocity, thereby producing an intense beam of molecules traveling in a vacuum with translational speeds slowed to a few tens of meters per second. Centrifugal action significantly enhances the supersonic character of the gas flow from the rotating nozzle, further narrowing the spread of velocities in the emerging beam. These features are demonstrated by model calculations and experimental results for beams of Xe and for O 2 and CH 3 F seeded in Xe.
We have found recently that, in a supersonic expansion of a mixture of two monoatomic gases, the parallel temperatures of the two gases can be very different. This effect is large if the seeded gas is highly diluted and if its atomic mass is considerably smaller than the one of the carrier gas. In the present paper, we present a complete derivation of our theoretical analysis of this effect. Our calculation is a natural extension of the existing theory of supersonic cooling to the case of a gas mixture, in the high dilution limit. Finally, we describe a set of temperature measurements made on a beam of lithium seeded in argon. Our experimental results are in very good agreement with the results of our calculation.
The paper reports on calculations of the flow properties in low-temperature He free-jet expansions by means of the Lennard-Jones potential and the recently appearing He-He van der Waals potential based on perturbation theory. The calculated speed ratios are compared with both the values we measured in the 20--80 K source temperature range and data which were already reported. The comparison points out a better agreement of our experimental results with the speed ratio values obtained by the recent potential whenever the parallel temperature of the beam decreases below ${10}^{\ensuremath{-}2} \mathrm{K}.$ In the same temperature range the light He-cluster size is analyzed.
We describe a pulsed rotating supersonic beam source, evolved from an ancestral device [M. Gupta and D. Herschbach, J. Phys. Chem. A 105, 1626 (2001)]. The beam emerges from a nozzle near the tip of a hollow rotor which can be spun at high-speed to shift the molecular velocity distribution downward or upward over a wide range. Here we consider mostly the slowing mode. Introducing a pulsed gas inlet system, cryocooling, and a shutter gate eliminated the main handicap of the original device in which continuous gas flow imposed high background pressure. The new version provides intense pulses, of duration 0.1-0.6 ms (depending on rotor speed) and containing ∼10(12) molecules at lab speeds as low as 35 m/s and ∼10(15) molecules at 400 m∕s. Beams of any molecule available as a gas can be slowed (or speeded); e.g., we have produced slow and fast beams of rare gases, O(2), Cl(2), NO(2), NH(3), and SF(6). For collision experiments, the ability to scan the beam speed by merely adjusting the rotor is especially advantageous when using two merged beams. By closely matching the beam speeds, very low relative collision energies can be attained without making either beam very slow.