Generation and focusing of electron beams with initial transverse-longitudinal correlation

In charged particle beams, one of the roles played by space charge is to couple the transverse and longitudinal dynamics of the beam. This can lead to very complex phenomena which are generally studied using computer simulations. However, in some cases models based on phenomenological or analytic approximations can provide valuable insight into the system behavior. In this paper, we employ such approximations to investigate the conditions under which all the slices of a space charge dominated electron beam with slowly varying current could be focused to a waist with the same radius and at the same location, independent of slice current, and show that this can be accomplished approximately if the initial transverse-longitudinal correlation introduced onto the beam by the electron gun is chosen to compensate for the transverse-longitudinal correlation introduced onto the beam in the drift section. The validity of our approximations is assessed by use of progressively more realistic calculations. We also consider several design elements of electron guns that affect the initial correlations in the beams they generate.