CIRCUIT DESCRIBED IN TERMS OF NORMAL MODES 237 



CHAPTER VI 



THE CIRCUIT DESCRIBED IN TERMS OF 

 NORMAL MODES 



Synopsis of Chapter 



IN CHAPTER II, the field produced by the current in the electron stream, 

 which was assumed to vary as exp {—Tz), was deduced from a simple 

 model in which the electron stream was assumed to be very close to an ar- 

 tificial line of susceptance B and reactance X per unit length. Following 

 these assumptions, the voltage per unit length was found to be that of 

 equation (2.10) and the field E in the z direction would accordingly be V 

 times this, or 



E = ^f~f2 i (6.1) 



Here we will remember that Fi is the natural propagation constant of 

 the line, and K is the characteristic impedance. 

 We further replaced K hy a. quantity 



£2//32p = 2K (6.2) 



where E is the field produced by a power flow P, and /3 is the phase constant 

 of the line. For a lossless line, Fi is a pure imaginary and 



&■= -Vl (6.3) 



From (6.1) and (6.2) we obtain 



2(rf - F^) ' ^^-^^ 



To the writer it seems intuitively clear that the derivation of Chapter 

 II is correct for waves with a phase velocity small compared with the 

 velocity of light, and that (6.4) correctly gives the part of the field asso- 

 ciated with the excitation of the circuit. However, it is clear that there are 

 other field components excited; a bunched electron stream will produce a 

 field even in the absence of a circuit. Further, many legitimate questions 

 can be raised. For instance, in Chapter II capacitive coupling only was 

 considered. What about mutual inductance between the electron stream 

 and the inductances of the line? 



