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Anomalous cooling of the parallel velocity in seeded beams: theory and experiments

Alain Miffre, Marion Jacquey, M Büchner, G. Trénec, J. Vigué

Published Jun 25, 2004• 0 citations
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Abstract

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.

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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.
Supersonic expansion is a very powerful tool to produce an atomic beam with a well defined velocity and, by seeding a test gas in such an expansion, the energy of the test gas can be transferred, at least partially, to the very-low-temperature carrier gas. The case usually studied is the one of a heavy gas seeded in a light carrier gas and, in this case, the parallel temperature of the seeded gas is always larger than the one of the carrier gas. In the present paper, we study the opposite case which has received less attention: when a light gas is seeded in a heavier carrier gas, the parallel temperature can be substantially lower for the seeded gas than for the carrier gas. This effect has been first observed by Campargue and co-workers in 2000, in the case of atomic oxygen seeded in argon. In the present paper, we develop a theoretical analysis of this effect, in the high dilution limit, and we compare our theoretical results to several experimental observations, including a set of measurements we have made on a beam of lithium seeded in argon. The agreement between theory and experiments is good.
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 $S={v}_{0}/\ensuremath{\Delta}{v}_{\ensuremath{\parallel}}$ 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.
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.
Supersonic molecular beams are used in many applications ranging from spectroscopy and matter wave optics to surface science. The experimental setup typically includes a conically shaped, collimating aperture, the skimmer. It has been reported that microskimmers with diameters below 10 μm produce beams with significantly broader velocity distributions (smaller speed ratios) than larger skimmers. Various explanations for this phenomenon have been proposed, but up till now, only a limited amount of data has been available. Here we present a systematic study of the velocity distribution in microskimmer supersonic expansion helium beams. We compare a 4 μm diameter skimmer with a 390 μm diameter skimmer for room temperature and cooled beams in the pressure range 11-181 bars. Our measurements show that for properly aligned skimmers, the only difference is that the most probable velocity for a given pressure and temperature is slightly lower for a microskimmed beam. We ascribed this to the comparatively narrow and long geometry of the microskimmers which can lead to local pressure variations along the skimmer channel. We compare our measurements to a model for the supersonic expansion and obtain good agreement between the experiments and simulations.
We have produced a pulsed supersonic expansion of helium with an effective pre-expansion temperature below 100 K. This low initial gas temperature is achieved by cooling a pulsed gas valve and gas channel with liquid nitrogen. The resulting supersonic helium beam has a translational velocity that is approximately 55% that of the room-temperature source and an internal temperature of 270 mK. The increased Mach number for a cold supersonic expansion agrees with theoretical predictions and reflects the increased cross section of helium at low collision energies.