Note: Design principles of a linear array multi-channel effusive metal-vapor atom source

Atomic beams can easily be produced by allowing atoms to effuse through a channel. In an earlier investigation [A. Majumder et al. , Vacuum 83, 989 (2009)], we had designed, fabricated, and characterized an effusive metal-vapor source using collinear-array of multi-channel. In this note, we describe the theoretical basis of designing the source. Atom density in atomic beam has been estimated using a set of analytical expressions for long-channel operated in transparent mode. Parametric studies on aspect ratio of channel, inter-channel separation, beam width, and vertical distance from the source are carried out. They are useful in providing physical picture and optimizing design parameters.