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 so-called quitting surface model incorporating the largest amount of physical dependencies 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 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 µm, skimmer diameters ranging from 4 µm to 390 µm, a source pressure range from 2 to 190 bar, and nozzleskimmer distances between 17.3 mm and 5.3 mm. To further 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 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 not as good. We propose several explanations for this, and test the ones that can be implemented analytically.

Neutral Helium Microscopy (SHeM): A Review

“…However, note that for low background pressure the shock structure and Mach disc are less pronounced and disappear. Figure reproduced from [34] the beam) [36,42]. The absolute differences between a cold (liquid nitrogen cooled) and a warm source at the same pressure can easily be on the order of 1 • 10 13 counts/s • m 2 [42].…”

“…Figure reproduced from [34] the beam) [36,42]. The absolute differences between a cold (liquid nitrogen cooled) and a warm source at the same pressure can easily be on the order of 1 • 10 13 counts/s • m 2 [42].…”

“…To solve this equation, a velocity distribution, and an interaction potential have to be assumed. The equations needed to solve the expansion are included in [42,7]. As mentioned above for this review, we provide an open-source implementation of the solution to the Boltzmann equation in spherical coordinates [4].…”

Characterisation and modeling of a pulsed molecular beam

“…Ref. [23]) refined this description by making the distribution ellipsoidal, hence defining two internal temperatures in the beam, one in the beam direction (T ) and the other, T ⊥ in the perpendicular direction. Here, T ⊥ = T = T is assumed.…”

Fast resolution change in neutral helium atom microscopy

“…through microskimmers is reduced. 24 The source has been modified as follows: In front of the skimmer, two piezo electrical tables (Attocube, ANPx101/NUM/UHV) are placed on top of each other to provide x and y movements. On the top table, a 8 × 14 mm home made chip (see Figure 3 shows how the piezo tables are mounted in the chamber.…”