Center-line intensity of a supersonic helium beam

Abstract

Supersonic helium beams are used in a wide range of applications, for example surface scattering experiments and, most recently, microscopy. The high ionization potential of neutral helium atoms makes it difficult to build efficient detectors. Therefore, it is important to develop beam sources with a high centre line intensity. Several approaches for predicting the centre line intensity exist, with the quitting surface model incorporating the largest amount of physical dependencies. However, until now only a limited amount of experimental data has been available. Here we present a study where we compare the quitting surface model with an extensive set of experimental data. In the quitting surface model the source is described as a sphere from where the particles leave in a molecular flow determined by Maxwell-Boltzmann statistics. We use numerical solutions of the Boltzmann equation to determine its properties. The centre-line intensity is then calculated using an analytical integral. This integral can be reduced to two cases, one which assumes a continuously expanding beam until the skimmer aperture, and another which assumes a quitting surface placed before the aperture. We compare the two cases to experimental data with a nozzle diameter of 10 micron, skimmer diameters ranging from 4 micron to 390 micron, a source pressure range from 2 to 190 bar, and nozzle-skimmer distances between 17.3 mm and 5.3 mm. To support the two analytical approaches, we have also performed equivalent ray tracing simulations. We conclude that the quitting surface model predicts the centre line intensity well for skimmers with a diameter larger than 120 micron when using a beam expanding until the skimmer aperture. For the case of smaller skimmers the trend is correct, but the absolute agreement not as good. We propose several explanations for this, and test the ones that can be implemented analytically.