Transverse Fields in Traveling- Wave Tubes 



By J. R. PIERCE 



Traveling-wave tubes will have gain even if the r-f field at the mean position 

 of the electron stream is purely transverse. The addition of a longitudinal mag- 

 netic focusing field reduces the gain due to transverse fields and increases the 

 electron velocity for optimum gain. 



ALL 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 Uttle importance. With weak focusing fields, however, the trans- 

 verse motion of electrons may be important in producing gain. The trans- 

 verse 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.^ This is closely analagous to the action of the longi- 

 tudinal 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 elec- 

 tron speed, and we shall neglect other field components attributable to local 

 space charge. The writer believes the results so obtained to be vaUd at low 

 currents but in error at high currents, and an acceptable guide at currents 

 usually encountered. 



In an earlier paper^ a relation was found between the longitudinal field Ez 

 excited in a mode of propagation of a transmission system and the longitud- 



1 See, for instance, J. R. Pierce and W. G. Shepherd, "Reflex Oscillators," B. S. T. /., 

 Vol. 26, No. 3, pp. 666-670 (Julv, 1947). 



2 J. R. Pierce, "Theory of the Beam-Type Traveling- Wave Tube," Froc. I. R. E., Vol. 

 35, pp. 111-123, Feb. 1947. 



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