j540 



BELL SYSTEM TECHNICAL JOURNAL 



such that the stream flow is reversed and caused to retraverse the gap. 

 The round trip transit time, Tq , in the retarding field when a signal exists 

 across the gap is then given by 



2 \/277(Fo + &V sinoih) 



(cl) 



C "7 It 



where 77 = - X 10 = 1.77 X 10 in practical units and h is the time of 

 m 



first entry of the gap. The time of return to the gap will be 



h= h^- Ta (c2) 



More accurately /i and h are measured from the central plane of the gap in 

 which case a second term should be added to (cl) corresponding to motion at 



RESONATOR 



Fig. 126.— Diagram of a. reflex oscillator showing quantities used in the treatment ol 

 bunching. 



constant velocity. This term is, however, very small and will be neglected 

 here. If ii is the current returning to the gap and 7o the uniform current 

 entering the gap on its first transit, then from conservation of charge one may 

 write 



h dh = /.. dh (c3) 



In what follows it will be first assumed that /? and h are related by a single 

 valued function. At the end of this appendix it will be shown that the 

 analysis is also valid where the relating function is multiple valued. 



\Vc now make a Fourier series analvsis of ;'•) in order to determine the 



