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Physical Review A

Testing the validity of supersonic molecular beam modeling in the high-throughput range using an Even-Lavie valve

Simen K. Hellner, Sabrina D. Eder, G. Bracco, Bodil Holst

Published Mar 19, 2024• 1 citation
Publisher

Abstract

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 ${p}_{0}d=400--2000\phantom{\rule{0.28em}{0ex}}\mathrm{mbar}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$, where ${p}_{0}$ is the reservoir stagnation pressure and $d$ 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 ${p}_{0}d$ regime up to 190 $\text{mbar}\phantom{\rule{0.16em}{0ex}}\text{cm}$, showing good agreement.

DOI
10.1103/physreva.109.032813

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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-\textmum-diam\textmu{}\text{m-diam}\textmum-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.
We describe a generally applicable method for the experimental determination of stationary flow conditions in pulsed supersonic beams, utilizing time-resolved electron induced fluorescence measurements of high pressure jet expansions of helium. The detection of ultraviolet photons from electronically excited helium emitted very close to the nozzle exit images the valve opening behavior-with the decided advantage that a photon signal is not affected by beam-skimmer and beam-residual gas interactions; it thus allows to conclusively determine those operation parameters of a pulsed valve that yield complete opening. The studies reveal that a "flat-top" signal, indicating constant density and commonly considered as experimental criterion for continuous flow, is insufficient. Moreover, translational temperature and mean terminal flow velocity turn out to be significantly more sensitive in testing for the equivalent behavior of a continuous nozzle source. Based on the widely distributed Even-Lavie valve we demonstrate that, in principle, it is possible to achieve quasi-continuous flow conditions even with fast-acting valves; however, the two prerequisites are a minimum pulse duration that is much longer than standard practice and previous estimates, and a suitable tagging of the appropriate beam segment.
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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.
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.
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-$\ensuremath{\mu}$m-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.