434 BELL SYSTEM TECHNICAL JOURNAL 



Let us investigate this for the case b = d = (we have already assumed 

 QC = 0). In this case 



5, = V^/2 - yi/2 



^3 = j 



and we obtain 



F = l-\- (l/2)(4 - 7r)(re/r)(l/C)| {P/2 -V3/2) 



(10.29) ; 

 - i( V3P/2 - 1/2) |2 



p ^ (0^- e.)c (10.30) 



For a given gun transit-angle 0i , the parameter P can be given values 

 ranging from diC to large negative values by increasing the drift angle 

 02 between the gun anode and the beginning of the helix. 



We see that 



F = I -\- (1/2) (4 - t){T,/T){\/C)(P' - VSP + 1) (10.31) 



The minimum value of (P- — \/3P +1) occurs when 



P = Vs/2 (10.32) 



if the product of the gun transit angle and C is large enough, this can be 

 attained. The corresponding value of (P- — V^SP + 1) is \, and the cor- 

 responding noise figure is 



^ = 1 + (1/2)(1 - 7r/4)(r,/r)(l/C) (10.33) 



A typical value for 7\. is 1()20°A', and for a reference temperature of 290° A', 



Tc/T = 3.5 



A typical value of C is .025. For these values 



F = 17 



or a noise figure of 12 db. 



Let us consider cases for no attenuation or space-charge but for other 

 electron velocities. In this case we write, as before 



52 = X2 + jy2 



53 = a-3 + jy:i 

 Let us write, for convenience, 



L = 1 doSiP + 5i + 52 I' (10.34) 



