28 



BELL SYSTEM TECHNICALVOURNAL 



about 640 volts (tan ^l^ = .05), 1,400 volts (.075), 2,500 volts (.1), 5,600 volts 

 (.15), 9,800 volts (.2). 



3.1b The Impedance Parameter (Er/^-P) 



Figure 3.4 shows a plot of a quantity Fiya) vs. ya. This quantity is com- 

 puted from a very complicated expression (Appendi.x II), but it is accurately 

 given over the range shown by the empirical relation 



Fiya) = 7.154 e-''''"" (3.8) 



0.5 10 1.5 2.0 2.5 30 35 4.0 4.5 5.0 55 60 6.5 7.0 7.5 8.0 



ra 



Fig. 3.5 — Factors by which (Z^/S/^P)^'^ on the axis should he muUipiied to give the cor- 

 rect value for hollow and solid beams of radius r. 



For the field on the axis of the helix, 



{Ey^'^pyi' = {i3/0oy"{y/0y"F(ya) 



(3.9) 



We should remember that (3/0o = c/v and that y/0 is nearly unity for veloci- 

 ties small compared with the velocity of light. 



In the expression for the gain parameter C, the square of the field E is 

 multiplied by the current /o (2.28). If we were to assume that two electron 



