t668 BELL S]fjm3M\nmM!fICXi\Ek^0URNAL 



zero at Xa = .ri . Changing the order of integ?^rb)i^ro(iio|«biiw \Bm aw 



(h33) 



From (h29) and (h30) we see that the total power is 



^ = > 47, £ £ (^), (^)>(- - -'^""■"'■' "- '- ■ *^*' 



By the same means resorted to in connection with (hi 2) we find 



Real^-^T^J/J-' (h35) 



B = f'—e''^ dx. (h36) 



J- 00 dy 



We can go a step further. We have 



A 



= f — e^'^^'dx. (h37) 



J- 00 ox 



Now 



Integrating by parts 



dy dy 



^= r P^e^'"" dx. (h38) 



dy J- 00 oxdy 



f "^ ^ e^>- dx. (h39) 



J- 00 OV 



ar 



dy 

 The first term is zero, and we see that 



I iJ I' = (I dA/ay IVt') (1,40) 



Reai^J. ^'l^^/fl'/^r (h4,) 



C. Electronic Gap Loading 



In (hl9) and (h41) we have expressed the power flow from the electron 

 stream to the circuit in rather general terms. What we want immediately 

 is the quantity (conductance) giving the power flow from the circuit to the 

 stream for a single gap. Assume we have a single gap with unit peak r-f 

 voltage across it. The power absorbed by the electron stream can be 



