Transverse Fields in Traveling-Wave Tubes

LL slow electromagnetic waves have both longitudinal and transverse electric field components. Sometimes either the longitudinal or the transverse field may go to zero along a line or plane parallel to the direction of propagation. For instance, for the slow mode of propagation there is no transverse field on the axis of a helically-conducting sheet. Still, over any plane normal to the direction of propagation there are bound to be both longitudinal and transverse field components. If a very strong longitudinal magnetic field is used in connection with a traveling-wave tube, the transverse motions of electrons may be so restricted as to be of little importance. With weak focusing fields, however, the transverse motion of electrons may be important in producing gain. The transverse fields can force the electrons sidewise, and thus change the longitudinal fields acting on them in such a way as to abstract energy from the electron stream. 1 This is closely analagous to the action of the longitudinal fields in displacing electrons forward or backward into regions of greater or lesser longitudinal field. The purpose of this paper is to analyze the behavior of traveling-wave tubes in which transverse fields are important. The attack will be similar to that used previously. 1. CIRCUIT THEORY In this paper we shall consider only the electric field associated with the slow mode of propagation along the circuit having a speed close to the electron speed, and we shall neglect other field components attributable to local space charge.