Analysis of Multivelocity Electron Beams by the DensityFunction Method
Abstract
Some mathematical techniques are presented which assist in the analysis of onedimensional multivelocity accelerated electron streams by the densityfunction method. These techniques include methods for removing mathematical singularities from the equations. The correspondence between the densityfunction method and the usual singlevelocity analysis is discussed; and a new definition of the equivalent ac voltage in terms of the density function is given. This definition is meaningful even for large velocity spread. The densityfunction method and the singlevelocity theory agree for small velocity spread while, for a strongly multivelocity beam, no simple transmissionline type of equations are to be found. Because of the latter fact, a common assumption about the noise conservation properties of the lowvoltage region of an electron gun is not valid, and the beam's ``noisiness'' is not invariant with distance in this region. These conclusions are verified by detailed noise calculations reported in an accompanying paper.
 Publication:

Journal of Applied Physics
 Pub Date:
 October 1957
 DOI:
 10.1063/1.1722593
 Bibcode:
 1957JAP....28.1132S