THE NATURE OF TEE WAVES 411 



vs. QC. In Fig. 8.13, this has been done for b chosen to make Xi a maximum. 

 We see that a small loss dd causes more reduction of gain as QC is increased 

 (more space charge). 

 Let us now differentiate (7.13) with respect to QC 



25 ^5 = f A Z^- f ^ ^.^. - 4 d{QC) (8.32) 



{-h -\- J d + jbf 



By using (7.13) with QC = we obtain 



In Fig. 8.14, dx/d{QC) has been plotted vs. d iox b ^ 0. 



We see that the reduction of gain for a small amount of space charge 

 becomes greater, the greater the loss is increased {d increased). 



Both Fig. 8.13 and Fig. 8.14 indicate that for large values of QC or d the 

 gain will be overestimated if space charge {QC) and loss {d) are considered 

 separately. 



