6>2 BELL SYSTEM TECHNICAL JOURNAL 



If we assume 3.75 cycles of drift, then from (2.4) the magnitude of the small 

 signal electronic admittance is 



y, = ^'hO/lV, (h57) 



- 4.71 h/Vo . 



Thus, in this example, the gap loading is about 1/10 of the small signal elec- 

 tronic admittance. 



D . Bunching in the Gap 



An unbunched stream will become bunched due to a single transit across 

 an excited gap. Expression (hlO) gives us a means for calculating the ex- 

 tent of this bunching. As an example, we will consider the case of fine 

 parallel grids separated by a distance (. Then the gradient is given by 



V'(xr) = V/f. (h58) 



from Xi = to Xj = X2 = A and by zero elsewhere. Thus 



2Vaf Jo 



klV = (/o/Fo)(l/2)[l - UMi^ - e^'^W^. (h59) 



It should be noted that for large values of 7 ^ 



i<,IV = (l/2)(/o/Fo)r^'"^. (h60) 



For our previous example, if 7 ^ = tt, 



i^lV = .592 (/o/Fo)r''''". (h61) 



If the current is referred to the center of the gap instead of the second 

 grid, we obtain a current i such that 



ijY = .592 {h/Vo)e-''-'\ (h62) 



Now, the electrons constituting current / will drift 3.75 cycles and will 

 return across the gap in the opposite direction. To get the induced circuit 

 current / we take this into account and multiply by ^ 



I/V = -^{i/V)e-'''^'-''^ 



(1^63) 

 = -.375(/o/Fo)r^'''. 



This is very nearly of the same size as the electronic gap loading. 



The general conclusion seems to be that for typical conditions encoun- 

 tered in reflex oscillators, gap loading and bunching in the gap are small 

 and probably less important than various errors in the theory. 



