Diffusion Cooling of Electrons in an A.C. Field

Abstract

Boundaries affect the measured values of transport coeffcients in all drift tube experiments, to a greater or lesser extent, and nowhere is this more apparent than in the experiment first devised by Cavalleri (1969) and subsequently adapted by Crompton and coworkers in the 1970s. The phenomenon of ‘diffusion cooling’ is particularly striking and arises essentially from a penetration of the ‘boundary layer’ (of thickness of the order of the mean free path for energy exchange) throughout a significant portion of the gas chamber. Although this is something of an obstacle to extracting the classical diffusion coefficient from experimental data, it is of great interest in its own right from a theoretical point of view, and the Crompton et al. experiments motivated several theoretical treatments which successfully explained diffusion cooling, albeit for zero applied field and on the basis of the ‘two-term’ spherical harmonic representation of the velocity distribution function. The present paper puts these theories in the context of the modern, generalised eigenvalue theory, which may be used as a basis for describing all swarm experiments. In addition, the earlier zero-field studies are generalised to the extent that an a.c. heating field is included, as was the case for the original Cavalleri experimental set-up. This field is found to enhance diffusion cooling effects for a simple model cross section.