REFLEX OSCILLATORS 483 



The work tells us that, considering longitudinal iields only, the electron 

 flow produces a small signal conductance component across the gap 



7 = -- (6.2) 



Here ^ is the modulation coefficient and Uo is the electron speed. 7o and 

 Vq are beam current and beam voltage. If the gap has a length d, the 

 transit angle across it is 6g = yd and (6.1) may be rewritten 



It is interesting to compare this conductance with the magnitude of the 

 small-signal electronic admittance, ye ■ In doing so, we should note that 

 the current crosses the gap twice, and on each crossing produces an elec- 

 tronic conductance. Thus, the appropriate comparison between loss con- 

 ductance and electronic admittance is IGehlje ■ Using (6.3) we obtain 



Usually, the drift angle Q is much larger than the gap transit angle Qg . 

 Further, if we examine the curves for mcdulation coefficient /? which are 

 given in Appendix II, we find that {dl3^/ddg)/l3''^ will not be very large. Thus, 

 we conclude that in general the total loss conductance for longitudinal fields 

 will be small compared with the electronic admittance. An example in 

 Appendix VIII gives {IGehlj^ as about 1/10. It seems that this effect 

 will probably be less important than various errors in the theory of the reflex 

 oscillator. 



Even though this electronic gap leading is not very large, it may be in- 

 teresting to consider it further. We note, for instance, that the conductance 

 GeL is positive when jQ" decreases as gap transit angle increases. For paral- 

 lel fine grids this is so from Qg = to ^^ = 27r (see Fig. 119 of Appendix II). 

 At Qg = Itt, where /3 = 0, dfS'^/ddg = 0, and the gap loading is zero. In a 

 region beyond dg — 2x, d^'^/ddg becomes positive and the gap conductance 

 is negative. Thus, for some transit angles a single gap can act to produce 

 oscillations. For still larger values of dg , Gcl alternates between positive 

 and negative. Gap transit angles of greater than lir are of course of little 

 interest in connection with reflex oscillators, as for such transit angles /3 is 

 very small. 



For narrow gaps with large apertures rather than fine grids, d^^/ddg 



