MAGNETRON AMPLIFIER 



655 



At any y — position we can write 



Ad 



-jTa^V 



-jTv 



- Be 



jVv 



Ae-'^« + Be'^v 



(15.3) 

 (15.4) 



If r is purely imaginary, a is purely real, and as F will have only a small real 

 component, a will be considered as a real number. We see that a can range 

 from + CO to — =0 . For instance, consider a circuit consisting of opposed two- 

 dimensional slotted members as shown in Fig. 15.2. For a field with a cosh 

 distribution in the y direction, a is positive above the axis, zero on the axis 

 and negative below the axis. For a field having a sinh distribution in the y 



//// 



Fig. 15.2 — K the circuit is as shown, the ratio between longitudinal and transverse field 

 will be different in sign above and below the axis. This can have an important effect on th 

 operation of the ampUfier. 



direction, <x is infinite on the axis, positive above the axis and negative below 

 the axis. 



We find then, that, (13.10) becomes 



V = 



-jcoTi^Kip + i«(/o/wo)ry) 



p2 _ p2 



15.2 Ballistic Equations 

 The d-c electric field in the y direction will be taken as —Eq. Thus 

 dy 



(15.5) 



dt 



= V 



£, + '-^ - B(z + „.)] 



In order to maintain a rectilinear unperturbed path 



£e = Buo 

 so that (15.6) becomes 



dy ^ d(^V) _ ^^z 

 dt dy 



(15.6) 



(15.7) 

 (15.8) 



