TRAVELING-WAVE TUBES 737 



We now make the approximation that 



-r=-i/3 + 5. (40) 



Where | 5 | <<C | jS | . Neglecting higher order terms, 



4. Purely Transverse Field Along the Path 

 We can imagine a case in which a approaches infinity and the quantity 



(42) 



(43) 



(44) 



Here J is a parameter describing the difference in speed between the electrons 



and the unperturbed wave and dis a. loss parameter. 



Assuming bD « 1 and dD <^1, and letting ^D{x + jy) = 5, (45) 



we find 



(^2 _ y + /2) (y-i- b) + 2xyix + d) = -1 (46) 



ix' - y2 + /2) {x + d) - 2xy{y + b) = (47) 



where 



f' = A- (^«) 



If would be difficult to work with all of the parameters by f and d. How- 

 ever, it scarcely seems that the attenuation parameter d should enter into 

 any unusual phenomena due to the presence of the magnetic field. Accord- 

 ingly, let us investigate (46) and (47) for J = 0. We then obtain 



x\2,y -\-b)-Y (P -f)iy+b)=-l (46a) 



x[x' + (f- f) - 2y(y + b)] = 0. (47a) 

 From the a; = solution of (47a) we obtain 



x==0 (49) 



