The process of beam formation in a supersonic expansion into a high pressure (10-2 -1 Torr) expansion chamber, a so-called Campargue-type beam source, has been investigated, using the theoretical frame work of an ideal undisturbed expansion as a reference. Absolute values of the centre-line intensity I(O)expt have been measured as a function of the reservoir pressure po at three different pumping speeds in the range of 25-230 l/s for the gases He, Ne and Ar. These experimental results have been used to determine a model description of the two characteristic features of a Campargue-type expansion, i-e. the nozzle-skimmer distance zam (po) of maximum intensity at each value of the reservoir pressure po and the skimmer transmission probability Ta(zam-I(O)expt/I(0) in this maximum, using the centre-line intensity I(O) of an ideal undisturbed expansion as a reference. A simple model function Ta (zam = q1 expt-q2Kna- (z am) gives a perfect description, when using an inverse skimmer Knudsen number Kna-1 with a mean free path based on the long-range van der Waals interactions that dominate the collisions at the low temperatures of the flow field at the skimmer orifice. The value of zam can be described by a non-dimensional length c which measures the distance zM - Zam. with zM the position of the Mach disk, in units of the viscosity based mean free path. Using the model functions for zam and T3(zam) as input we present scaling laws that predict the performance of a Campargue type beam source as a function of the gas properties (van der waals constant C6, mass m, viscosity based cross section Qvimc), the reservoir conditions (nozzle radius, reservoir pressure po and temperature To) and the parameters of the experimental arrangement (skimmer radius, temperature of the expansion chamber, pumping speed S). Measured values for He and Ne of the maximum maximorum J(O)exptmmm, i.e, the maximum of I (O)expt as a function of po, are well described by the scaling law presented. Preliminary measurements of the dependency of I(O)exptmm on the reservoir temperature To are also in good agreement with our scaling law which predicts I(O)exptmm Toii/g. Heating the nozzle is an inexpensive way of increasing the centre-line intensity, as compared to the expensive approach of increasing pumping speed with a dependency I(O)exptmm S7/9. Typical values of I(O)exptmm at room temperature are 1.5x1020 and 33x1019 s-1 sr--1 for He at S = 230 l s-1 and Ne at S = 180 l s-1, respectively, showing a favourable comparison to conventional low-pressure expansions with oil diffusion pumps in the expansion chamber. Measurements of the virtual source radius, i.e. a mapping of the velocity component perpendicular to the stream lines, provide design rules for the ratio of skimmer radiu s to nozzle radius required for optimum performance. Moreover, they provide qualitative support of our model description of the loss processes at the skimmer orifice.