SPATIALLY DEPENDENT ENERGY DISTRIBUTIONS FOR ELECTRONS DRIFTING THROUGH A GAS IN A UNIFORM ELECTRIC FIELD.

摘要

The steady state distribution function is obtained for electrons initially emitted from a point source into a neutral gas and which subsequently drift under the influence of a uniform dc electric field while undergoing elastic collisions with the gas atoms. The usual approximations are retained of regarding the distribution function as almost spherical in velocity space and of regarding the fractional energy gain or loss by an electron upon collision as small. However,the terms in the Boltzmann transport equation involving spatial derivatives of the distribution,which are usually assumed small in comparison to the field and collision terms,are treated exactly. The distribution function is given as a sum of energy modes,each of which decay with distance from the source. The lowest of these modes is the far-distant distribution,while the higher ones,which decrease more rapidly with distance,describe the decay of the initial source energy distribution. The complete distribution is obtained in terms of known functions in the case of an energy independent collision frequency,whereas in the energy independent cross section case,only the lowest mode is obtained.