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Physical Review A

Brightness and virtual source size of a supersonic deuterium beam

Thomas J.G. Reisinger, Martin Greve, Sabrina D. Eder, G. Bracco, Bodil Holst

Published Oct 3, 2012• 13 citations
Publisher

Abstract

Supersonic beams have numerous applications in research fields ranging from spectroscopy with nanodroplets to surface science and matter-wave microscopy. Thus, measurement and prediction of their properties is of considerable interest. In this paper we present measurements of the virtual-source size and its brightness, as well as the terminal speed and terminal speed ratio of a supersonic deuterium (D${}_{2}$) beam. The speed distribution data were measured with time-of-flight experiments and Fresnel zone-plate imaging was used to measure virtual source size. The point-spread function of the zone plate was simulated based on the measured wavelength distribution and used to extract the width of the virtual source and its brightness from the focus measurement. The experiments were carried out with a 10-$\ensuremath{\mu}$m-diameter nozzle and a source temperature of ${T}_{0}=310$ K in the pressure range ${p}_{0}=3$--171 bars and for ${T}_{0}=106$ K in the pressure range ${p}_{0}=3$--131 bars. We found that using deuterium as opposed to helium results in a virtual source that is about a factor 2 brighter under similar stagnation conditions. A comparison between the measured data and the predictions from a theoretical model based on the Boltzmann equation, which explicitly include the coupling between translational and rotational degrees of freedom as well as the real-gas properties of D${}_{2}$, resulted in good correspondence for the two different interaction potentials we tried. A careful comparison with the experimental results shows that the potential by Buck et al. [J. Chem. Phys. 78, 4439 (1983)] is moderately better than the Lennard-Jones potential at describing the expansion dynamics.

DOI
10.1103/physreva.86.043804

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Supersonic beams have numerous applications in research fields ranging from spectroscopy with nanodroplets to surface science and matter-wave microscopy. Thus, measurement and prediction of their properties is of considerable interest. In this paper we present measurements of the virtual-source size and its brightness, as well as the terminal speed and terminal speed ratio of a supersonic deuterium (D2{}_{2}2​) beam. The speed distribution data were measured with time-of-flight experiments and Fresnel zone-plate imaging was used to measure virtual source size. The point-spread function of the zone plate was simulated based on the measured wavelength distribution and used to extract the width of the virtual source and its brightness from the focus measurement. The experiments were carried out with a 10-\ensuremathμ\ensuremath{\mu}\ensuremathμm-diameter nozzle and a source temperature of T0=310{T}_{0}=310T0​=310 K in the pressure range p0=3{p}_{0}=3p0​=3--171 bars and for T0=106{T}_{0}=106T0​=106 K in the pressure range p0=3{p}_{0}=3p0​=3--131 bars. We found that using deuterium as opposed to helium results in a virtual source that is about a factor 2 brighter under similar stagnation conditions. A comparison between the measured data and the predictions from a theoretical model based on the Boltzmann equation, which explicitly include the coupling between translational and rotational degrees of freedom as well as the real-gas properties of D2{}_{2}2​, resulted in good correspondence for the two different interaction potentials we tried. A careful comparison with the experimental results shows that the potential by Buck et al. [J. Chem. Phys. 78, 4439 (1983)] is moderately better than the Lennard-Jones potential at describing the expansion dynamics.
Direct images of the virtual source in a supersonic expansion of helium are presented. The images were obtained using a Fresnel zone plate with free-standing zones, 540 microm in diameter and with an outermost zone width of 50 nm. The general method can be extended to other beams, including seeded beams. Measurements were carried out at absolute source pressures ranging from 11 to 171 bar using a 10 microm nozzle with a source temperature of 320 K. The size of the virtual source was found to be strongly dependent on pressure, changing from a diameter of 67+/-6 microm at an absolute nozzle pressure of 11 bar to 180+/-9 microm at 171 bar. The virtual-source brightness displays a maximum at an absolute nozzle pressure of around 30 bar. This phenomenon occurs because of two competing effects: As the pressure increases, the total flux also increases, but at the same time the virtual source broadens. We modeled the expansion process by calculating the velocity distribution with solutions from the Boltzmann equation to estimate the location of the quitting surface where the frequency of interatomic collisions is assumed negligible. Realistic potentials have been used to calculate the cross section for atomic collisions and, for the velocity distribution perpendicular to the center streamline, a proper scaling with distance derived from the continuum expansion model has been introduced. A good agreement between experiments and model has been found and we discuss its approximation limits. For instance, backscattering effects are not included in the calculations and at present we cannot exclude that they also contribute to a broadening of the virtual-source size for the highest pressure regime. The results presented here are important for improving the understanding of the supersonic expansion process. The experimental method might eventually be used as a new way to test molecular and atomic interaction potentials.
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Supersonic molecular beams are used in several scientific fields ranging from surface science to the spectroscopy of molecules, nanoparticles, and even viruses. It is therefore of interest to understand the fundamental properties of the expansion and resulting beam. Here, we present a study of the change in the most probable velocity with reservoir pressure, using a so-called Even-Lavie pulsed source with a 200-$\textmu{}\text{m-diam}$ nozzle. Experiments were carried out in the throughput range p0d=400−−2000mbarcm{p}_{0}d=400--2000\phantom{\rule{0.28em}{0ex}}\mathrm{mbar}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}p0​d=400−−2000mbarcm, where p0{p}_{0}p0​ is the reservoir stagnation pressure and ddd is the nozzle diameter. Experiments were done on both neutral and metastable helium beams. A two-detector measurement setup was used to account for the valve opening delay. The measurements are modeled with theory which has hitherto only been applied to a p0d{p}_{0}dp0​d regime up to 190 mbarcm\text{mbar}\phantom{\rule{0.16em}{0ex}}\text{cm}mbarcm, showing good agreement.
Low energy (thermal) free jet (supersonic) molecular beams are used in a range of applications from surface science and surface deposition to quantum coherence and gas kinetics experiments. A free jet molecular beam is created by a gas expansion from a high pressure reservoir through a small aperture (nozzle). The nozzle typically has a diameter of 2-20 μm. The central part of the beam is selected using a skimmer, typically up to 500 μm in diameter. Recent years have seen the introduction of highly spatially confined beam sources based on micrometer skimmers and micrometer or even sub-micrometer nozzles. Such sources have been applied, for example, in the investigation of superfluidity and in neutral helium microscopy. However, up till now no source design allowing the precise positioning of the micro-skimmer relative to the nozzle has been available. This is an important issue because the relative position of skimmer and nozzle can influence the beam properties considerably. Here we present the design and implementation of a new molecular beam source, which allows an automatized, 50 nm precision positioning of the skimmer relative to the nozzle. The source is liquid nitrogen cooled and the temperature can be controlled between 110 K and 350 K with a temperature fluctuation of less than ±0.1 K over several hours. Beam intensity measurements using a 5 μm nozzle and a skimmer 5 μm in diameter are presented for stagnation pressures po in the range 3-180 bars. A 2D beam profile scan, using a 9.5 μm skimmer and a 5 μm nozzle is presented as a further documentation of the versatility of the new design and as an illustration of the influence of the relative skimmer-nozzle position on the beam properties.
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.
Micrometer-sized nozzles and skimmers made from drawn glass tubes are described and tested for the production of highly monoenergetic He atom beams. Glass nozzles with diameters between 1 μm and 4 μm when operated at He source stagnation pressures of up to 1000 atm provide intense beams with measured speed ratios of S=50–100, in good agreement with the predicted behavior scaled from nozzles with larger openings. Miniature glass skimmers with diameters as small as 3 μm were also successfully tested with conventional 10 μm diameter nozzles. These miniature nozzle-beam sources can be used to greatly reduce the size of present-day He-atom surface-scattering time-of-flight spectrometers and to reduce the number of vacuum stages and the size of vacuum pumps. They also open up new experimental possibilities as illustrated by measurements of the spatial profiles of seeded nozzle beams.