  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.
