TRANSVERSE MOTION OF ELECTRONS 621 



Here ijB is the cyclotron radian frequency and /3„, is a corresponding propa- 

 gation constant. 

 Now 



y = dy/di - {dy/dz){dz/di) (13.19) 



y = uoij^e - T)y (13.20) 



From (13.20) and (13.17) we obtain 



y = OT' \( -Q T-N2 I o2t (13,21) 



2T oKjiSe - r) + |8J 



It is easily shown that the equation for p can be obtained exactly as in 

 Chapter II. From (2.22) and (2.18) we have 



^"^'*^' (13.22) 



13.3 Combined Equation 



From the circuit equation (13.10) and the baUistical equations (13.21) 

 and (13.22) we obtain 



1 = 





(13.23) 



The voltage at the beam is $ times the circuit voltage, so the effective 

 impedance of the circuit at the beam is $^ times the circuit impedance. 

 Thus 



a = $2^/o/4n (13.24) 



It will be convenient to define a dimensionless parameter / specifying ^^ 

 and hence the magnetic field 



/ = /3.//3.C (13.25) 



We will also use b and b as defined earlier 



-r = -j^e + ^eCb 



-Fi = -j^e-j^eCb 



After the usual approximations, (13.23) yields 



i^ - * = ,U (^) (13.26) 



«2 = (<J>V/3e$)' (13.27) 



It is interesting to consider the quantity (4>'/j3e$)^ for typical fields. For 



