620 BELL SYSTEM TECHNICAL JOURNAL 



So that 



In (13.7), it is assumed that$ = 1. If $ 5^ 1, we should replace p in (13.7) 

 by the a-c component of effective charge. The total effective charge pe is 



PB = Hp + Po) (13.8) 



The term pn is included because ^ will vary if the y-position of the charge 

 varies. To the first order, the a-c component pg of the effective charge is, 



Pe = $p + po^'y (13.9) 



PE = ^P - (lo/tioWy (13.9) 



Here y is the a-c variation in position along the y coordinate. Thus, if $ 5^ 0, 

 we have instead of (13.7) 



V = (p2 _ p2^ . (13.10) 



This is the circuit equation we shall use. 



13.2 Ballistic Equations 



We will assume an unperturbed motion of velocity uq in the z direction, 

 parallel to a uniform magnetic focusing field of strength B. As in Chapter 

 II, products of a-c quantities will be neglected. 



In the X direction, perpendicular to the y and z directions 



