Two dimensional imaging of the virtual source of a supersonic beam: helium at 125 K

Here we present the first two-dimensional images of the virtual source of a supersonic helium expansion. The images were obtained using a free-standing Fresnel zone plate with an outermost zone width of 50 nm as imaging lens and a beam cooled to around 125 K. The nozzle diameter was 10 μm. The virtual source diameter was found to increase with stagnation pressure from 140 ± 30 μm at po = 21 bar up to 270 ± 25 μm at po = 101 bar. The experimental results are compared to a theoretical model based on the solution of the Boltzmann equation by the method of moments. The quantum mechanical cross sections used in the model have been calculated for the Lennard-Jones (LJ) and the Hurly-Moldover (HM) potentials. By using a scaling of the perpendicular temperature that parametrizes the perpendicular velocity distribution based on a continuum expansion approach, the LJ potential shows a good overall agreement with the experiment. However, at higher pressures the data points lie in between the two theoretical curves and the slope of the trend is more similar to the HM curve. Real gas corrections to enthalpy are considered but they affect the results less than the experimental errors.