A REVIEW OF THE AC SPACE-CHARGE EFFECT IN ELECTRON CIRCUIT INTERACTIONS

This paper provides a critical examination of traditional theoretical treatments of alternating current (ac) space-charge effects in vacuum electronic devices. By treating several simple examples, it is found that the commonly made decomposition of the first-order field into a "circuit part" and a "space-charge part" is ambiguous and misleading. In at least one case, this terminology has led to a formulation that double counts the effect of space charge in the beam-circuit interaction. In other cases, the "space-charge term" in the dispersion relation-equivalently Pierce's space-charge parameter (QC)-has been improperly or incompletely evaluated. The implications for gyrotrons, peniotrons, free-electron lasers, Smith-Purcell-type generators, and crossed-field devices are addressed. The space-charge effects are briefly discussed in nonlinear theories and in particle simulations. For the models examined, it is found that the most useful and convenient representation for the ac fields is one based on an eigenfunction expansion of the ac magnetic field, even when that field is not itself important to the electron dynamics.