658 BELL SYSTEM TECHNICAL JOURNAL 



we might have the gradient near the gap less than that at the zero potential. 

 In that case the second term in the brackets would be negative. This means 

 a diminution in drift action because the penetration changes little with 

 energy while the electron travels faster over the distance it has to cover. 

 To show how large this effect of weakening the field near the zero potential 

 point may be, we will consider a specific potential variation, one which 

 approximates the field in a long hollow tubular repeller. The field con- 

 sidered will be that in which 



V{z) = {e' - \)/e^ (fl5) 



We obtain 



{e^ - D' 

 tan-' {e^ - l)' 



F=(e^-l) + . Z^j":,^ - m) 



Now 



F'(0) = e-f (fl7) 



V'(z) = 1 (fl8) 



Hence 



/ 1 \ \V'(0) ' 



This shows clearly how the effective drift angle is increased as the field at 

 the zero potential point is weakened. For instance, if V'(0) = ^, so that 

 the field at the zero potential point is ^ that at the gap, the drift effective- 

 ness for a given number of cycles drift is more than doubled (F = 2.27). 

 There is another approach which is important in that it relates the varia- 

 tions of drift time obtained by varying various voltages. Suppose the gap 

 voltage with respect to the cathode is Fo and the repeller voltage with re- 

 spect to the cathode is — Fh . Now suppose Fo and Vr are increased by a 

 factor a, so that the resonator and repeller voltages become aFoand —aVn. 

 The zero voltage point at which the electrons are turned back will be at the 

 same position and so the electrons will travel the same distance, but at each 

 point the electrons will go a times as fast. If, instead of introducing the 

 factor a, we merely consider the voltages F« and Fn to be the variables, we 

 see that the transit time can be written in the form 



T = Fr/^(F«/Fo) (f20) 



