Molecular beams and effusive flows

Molecular flux emanating from an aperture in a beam oven and incident on a point on the beam axis is discussed. The vector flux density is characterized by its vector-velocity (rather than speed) probability distribution. As a consequence, the integrals of the velocity components orthogonal to the beam axis yield the observed dependences of beam intensity upon aperture area and distance from the aperture. Both rectangular and circular apertures are considered. The velocity integrals for the circular aperture are exact and demonstrate how the velocity distribution of the flux density gradually changes from that of the Maxwell flux at the aperture to that of a beam flux at large distances from the aperture. (This cannot be shown with the speed distribution.) An expression then is obtained for the flux from a circular aperture incident on an off-axis point by making use of the concept of a virtual aperture which simplifies the problem considerably. This expression then is used to calculate both the normal flux density distribution and the total flux incident on a finite plane collector. These treatments may be applied to systems with apertures and collectors of almost any shape and/or size