Abstract
Based upon Boltzmann's equations, general equations applicable to any phenomena related to beam electrons, gas molecules, and ions or electrons produced by collision are derived. The restrictions imposed are that the acceleration voltage of the electron beams are high enough compared with the ionization potential of the gas and the impressed electrical and magnetic field strengths are not so high as to ionize the gas molecules.
In the latter half, these general equations are applied to the “Gas focussing”. In the first place, longitudinal flows of ions are calculated with the result that about one volt of dip in the axial potential distributions is sufficient to trap the ion. Then, the radial flows of ions are calculated, wherein the information about the probability η of recombinations of ions at the tube wall is required in deriving quantitative results. Relations between pressure, neutrality of beam, beam current and V are calculated and illustrated. It is concluded that the radial flow of ions play an important part in the trapped conditions when axial flow is interrupted.
