KEFLEX OSCILLATORS 663 



The shapes for electrodes to realize this field may be obtained analytically 

 by known means or experimentally by measurements in a water tank. The 

 general appearance of such electrodes and their embodiment in a reflex 

 oscillator are shown in Fig. 138. Here C is the thermionic cathode forming 

 part of an electron gun which shoots an electron beam through the apertures 

 or gap in a resonator R. The beam is then reflected in the drift field formed 

 by the resonator wall, zero potential electrode I and negative electrode II, 

 which give substantially the axial potential distribution shown in Fig. 137. 

 Small apertures in the resonator wall and in electrode I allow passage of the 

 electron beam without seriously distorting the drift field. Voltage sources 

 Vi and V-i maintain the electrodes at proper potentials. Either suitable 

 convergence of the electron beam passing through the resonator from the 

 gun or axial magnetic focusing will assure return of reflected electrons 

 through the resonator aperture. In addition, the aperture in electrode I 

 forms a converging lens which tends to offset the diverging action of the 

 fields existing between the resonator wall and I, and between I and II. 

 R-f power is derived from resonator R by a. coupling loop and line L. 



APPENDIX VIII 

 Electronic Gap Loading 



If a measurement is made of gap admittance in the presence and in the 

 absence of the electron beam passing across it once, it will be found that the 

 electron stream gives rise to an admittance component Y. The susceptance 

 is unimportant, but the conductance G can have a noticeable effect on the 

 efficiency of an oscillator. 



Petrie, Strachey and Wallis have provided an important expression for 

 this gap conductance due to longitudinal fields when the r-f voltage is small 

 compared with the beam voltage Vo-f In this analysis it is presumed that 

 the fields in the beam are due to the voltages on the electrodes only and not 

 to the space change in the beam.' This analysis is of such importance that 

 it is of interest to reproduce it in a slightly modified form. We will first 

 consider the general cases of interaction with longitudinal fields and will 

 then consider transverse fields also. 



A. Longitudinal Field 



Assume a stream of electrons flowing in the positive x direction, constitut- 

 ing a current — /o , bunched to have an a-c convection current component 



2' These expressions were communicated to the writers through unpubUshed but widely 

 circulated material by D. P. R. Petrie, C. Strachey and P. J. Wallis of Standard Tele- 

 phones and Cables Valve Laboratory. 



28 The expressions are valid in the presence of space charge, but as the field is not known, 

 they cannot be evaluated. 



