Center-line intensity of a supersonic helium beam

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 center-line intensity. Several approaches for predicting the center-line intensity exist, with the so-called quitting surface model incorporating the largest amount of physical dependences in a single analytical equation. However, until now only a limited amount of experimental data has been available. Here we present a comprehensive 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 spherical surface from where the particles leave in a molecular flow determined by Maxwell-Boltzmann statistics. We use numerical solutions of the Boltzmann equation to determine the properties of the expansion. The center-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 μm , skimmer diameters ranging from 4 to 390 μm , a source pressure range from 2 to 190 bars, and nozzle-skimmer distances between 17.3 and 5.3 mm. To further support the two analytical approaches, we also perform equivalent ray-tracing simulations. We conclude that the quitting surface model predicts the center-line intensity of helium beams well for skimmers with a diameter larger than 120 μm when using a continuously expanding beam until the skimmer aperture. For the case of smaller skimmers the trend is correct, but the absolute agreement is not as good. We propose several explanations for this and test the ones that can be implemented analytically.