Calculation of Electron-be am Divergence at Medium Gas Pressuresf

In the calculation of the divergence of long electron beams, perfect vacuum conditions aro generally assumed to exist. However, in all practical cases, the presence of gas within the tube cannot be avoided; its effect is to reduce the dispersive forces on the beam. Because of the large number of variables involved, the effect of gas on beam divergence has not thus far been susceptible to analytic solution; however, a numerical approach based on the use of universal curves and step-by-step integration is found to be capable of giving a reasonable estimate of the beam profile in the presence of gas. Three examples of electron beams of various perveances and entrance angles are solved using this method over a range of pressures from perfect vacuum to full neutralization. A study of these cases enables us to give a rational picture of tho behaviour of electron streams in the presence of gas and several interesting conclusions are drawn regarding the position of the minimum, cross-over, and tho condition for parallel beam. Indications are that pressures better than 10−8 mm Hg are required before one can truly assume perfect vacuum conditions to prevail.