644 BELL SYSTEM TECHNICAL JOURNAL 



Thus 



Ae/e = Aco/w + At/t 



(d2) 



= Aw/W + ((dT/dV)/T)AV 



As shown in Appendix VT, the derivative of t with respect to repeller 

 voltage, dr/dVK , is always negative, while the derivative of t with respect 

 to resonator voltage, dr/dVo , may be either negative or positive. For a 

 linear variation of potential in the drift region, dr/dVo is zero when V^ = 

 Vo and negative for smaller values oi Vr . 



APPENDIX V 

 Electronic Admittance — Non-Simple Theory 



A closer treatment of the drift action in the repeller space follows, in 

 which are considered the changes which occur as the voltage on the cavity 

 becomes large. 



The additional terms to be considered come from an evaluation in series 

 of the higher-order terms of (c7), which were neglected in Appendix III. 

 Only the fundamental component of current will be considered, although 

 other terms could be included if desired. The integrals of interest may be 

 rewritten from (c7), using the relation ip = —0, as follows: 



ai = - [ cos (d, -I- X sin 01 - i ^ sin' di 



IT J-TT \ ^ W 



+ :; — T sm 6i -f 

 2 6- 



'^=^/-/^"t 



I X' . 2 



1 + X sm 01 — - — sm di 



2 



I ^ X • 3 „ I 



-f - — - sm 6i -\- 



Jddi 

 jddi 



(el) 



(e2) 



We shall hereinafter neglect terms of higher order in ^ than those explicitly 



u 



shown here. With this neglect, we can expand the trigonometric functions, 

 obtaining 



di 



-' j cos (dr + X sin e,) jl - ^ -^ sin' 0i -f • • • 1 i0i 



- - [ sin (0, -f X sin di) (e3) 



. _ ^ ^. sin' di -\- l~ sin' 0i + • • • \ ddi 



