656 BELL SYSTEM TECHNICAL JOURNAL 



order theory are ordinarily rather small even for the first two modes of 

 operation, and are quite negligible for higher modes. 



APPENDIX VI 



General Potential Variation in the Drift Space 



Suppose that the potential of the drift space is given by V{x), where 

 ^ = at zero potential and ar = / at the gap. Then the transit time from 

 the gap to zero potential and back again is 



Imagine now that the entire drift space is raised by a very small amount 

 AF. The zero potential point will now occur at 



X = -AF/F'(0) (f2) 



where 



F'(.t) = dV/dx (f3) 



Hence the new transit time will be 



TO + Ar = (2/^2^) f PTV ^^l at/v (f"^) 



J-^vlv'm [V(x) + AF> 



Now let 



z= x-^ AF/F'(0) (f5) 



Then, including first order terms only, if V{x) can be expanded in a Taylor's 

 series about 0, 



To + At 



[F(2) - [F'(z)/F'(0)]AF + AF]^ 



(2/V27?) I 

 Jo 



-n/-./i-\(t^ ^' -±- Av [^ KF-(.)/F-(0)) - l]dz 



AF \ 



+ F'(0)[F(/)]V 



Whence 



, At ,,, ,-. I 1 ^ rq( r(.)/F-(0)) - \\dz 



In computing F it should be noted that by definition the gap voltage pre- 



