120 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



We shall assume in considering (2.28) and (2.29) that the beam is 

 sufficiently wide for the transit of an electron from one side to the other 

 to take a few RF cycles. The number of cycles is in fact, coz/o/ttwi , and, 

 hence, from the definition of z, we see that for values of A: less than 2, 

 perhaps, z is certainly positive. 



Let us consider (2.29) first since it proves to be the simpler case. If we 

 transfer the term ttz to the right hand side, it follo^^•s from the observa- 

 tion that z is positive (for modest values of h), that it is necessary to 

 make the sum negative. The sum may be studied qualitatively by sketch- 

 ing in the k^ — d' plane the lines on which the individual terms go to 

 infinity, given by 



[(n + 3^)^ - k'f 



8' = 



(n -f K)' + k' 



(2.30) 



3.5 



Fig. 3 



