The current and velozity distributions in a velocity modulated, brillouin-focused electron beam

Abstract

Radio-frequency current distributions in a Brillouin-focused electron beam that has been velocity-modulated by a gridless-gap cavity are described. A review is presented of the small signal theory of ideal Brillouin beams in addition to small- and large-signal experimental results. An approximation is made to predict the RF current contours in a Brillouin beam whose d-c current- density profile resembles a trapezoid. The predictions of this theory are found to agree well with actual beam behavior in that both the thickness and the amplitude of the RF current density ring around the beam vary with the depth of modulation alpha when alpha is very small. The large-signal results show that an average non linear force is present, which causes the average diameter of the modulated beam to be smaller at some axial positions than the diameter of the d- c Brillouin beam. In addition, the large-signal results show that at least two- second- and two third-harmonic waves are present on the beam. One of these in each case is the component arising from the square-wave current-density wave at the edges of the beam. The other wave in each case is thought to have arisen from the nonlinear drive in the high alternating fields in the cavity gap.