Direct images of the virtual source in a supersonic expansion

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.