Conversion efficiency in axial monotrons

Abstract

Abstract~A comparative st udy is given on the bunching mechanisms which develops in transit-time tubes with RF-field bunching, often referred to as monotrons. Uniform and stepped wise longitudinal electric-field profiles are discussed, and it is shown that the two-fold enhancement in the conversion efficiency of a monotron operating in the 7t mode--instead of the longitudinally uniform TM olO mode for which the efficiency is limited to 20 percent-arises from a phase synchronization process due to the action of RF electric fields of reversed signs in each partition of the bisected cavity dp =qEof(z)cos(OJt+¢o) dt in which the electron position is given by equation(1) the trajectory (2) In the calculation which follows , we normalize the motion variables according to p= p / me , == zOJ/ c, t = OJ t whereby the force equation becomes nondimensionalized, 0.0 0.5 1.0 1.5 2.0 2.5 3.0 normalized axial distance zw/c Fig. 1. Stepped field profile repres ented by the function f ei) = -tanh[l 00(= -d/2) with d = 2.90 . OJ -0 E 0 rn .!!! <+= o 0.. -1 where p is the electron momentum, q= -I e I and m are the electronic charge and the electron rest mass, OJ is the angular frequency of the RF field of amplitude Eo, and ¢o denotes the electron entrance phase. In the force equation j{z) specifies the electric-field axial distribution. For the TM olO mode the field is uniform,j{z) = 1, and to describe the axial distribution of the 1t mode we use the analytical function profile fez) = -tanh[100(z-d / 2)] as illustrated in Fig. 1. (4) (3) [511+Wo(keV)]2 -511 2 p(O) = 511 .dP-= = -g f(z)cos(t + ¢o) dt where g = qEo / tome. First, using f (z)=l and g =0.045 (to be justified later), the force and trajectories equations are numerically solved subject to the initial conditions =(¢o) =0, p(¢o) =Po with the initial momentum Po corresponding to the injection energy W o =1O keY, through