Brightness and virtual source size of a supersonic deuterium beam

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) 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-μm-diameter nozzle and a source temperature of T₀=310 K in the pressure range p₀=3--171 bars and for T₀=106 K in the pressure range p₀=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, 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.