654 BELL SYSTEM TECHNICAL JOURNAL 



the d.-c. initial conditions being given in the previous section, and the 

 first order initial velocity being the same as that at A. From (43a) 

 we have 



" (- ^J"'(m + 1) f.^. 



The computation of the a.-c. component of acceleration at B is 

 based on the particular property possessed by negative grid tubes 

 that no electrons reach the negative grid. Then, because the velocity 

 at B is the same as that at A it follows that the conduction component 

 of the current is the same at both planes. The total first-order current 

 may be written from (1) 



Ii = (pw)i + e-^ • 



Multiplying through by e/kme we can write 



/ = (? + ^, (70) 



where Q = (pu)ie/kme measures the conduction current, and is the 

 same at planes A and B. Hence at plane A, and since d/dt = p for 

 exponential currents and voltages: 



/o = (2 + pdiA. (71) 



At plane B we have similarly 



/, = (3 + paB. (72) 



From (71) and (72) there results 



pas = Jp — Jc -{- paiA. (73) 



The value of aiA may be obtained from (42a) so that the acceleration 

 at B is given by 



pas = J, -J.- 2 J,. Z (^ + 3) ! • (74) 



All of the initial values at the plane B have been obtained and are 

 expressed in (55), (56), (69) and (74). The potential between B and 

 the plate is now obtained from (41a) and follows, where // = TpjTc'. 



{ Wn - T^.)i _ (J _ J . high + 1) , ^^ (- h^e)"in-\-2) 

 ' KIV ~ ^ " '^ 2/3, "^ ■""" i {n + 4) ! 



