BEAM FORMATION WITH ELECTRON GUNS 



397 



8 



10 



12 



14 



16 



I Fig. 8 — A curve showing the effect of a quantity related to the space charge 

 • force (in the drift region) on a thermal electron with standard deviation a. (See 

 'equation 28.) 



which are related by the mutual dependence of Fr^ and Fa on re/a. F„ 

 and Frjve are plotted in Figs. 8 and 9. 



We may summarize the treatment of the drift region, then, as follows: 

 1 (a) The input values of r^ and rgJ at the entrance to the anode lens 

 jare obtained from the Pierce gun parameters r^ and 6, while the value 

 of a and aJ at the lens entrance can be obtained as mentioned above 

 by integrating (15) from the cathode, where Mc = and (dfx/dt)c = 1, 

 to the anode plane. (The minus subscripts on r' and a' indicate that 

 these slopes are being evaluated on the gun side of the lens; a plus sub- 

 script will be used to indicate evaluation on the drift region side of the 

 lens.) The values of Ve and a on leaving the lens will of course be their 

 entrance values in the drift region, and the effect of the lens on r/ and 

 a' is simply found in terms of the anode lens correction factor T by use 

 of (20). The value of a at the anode can be obtained from (17) if n is 

 known there. In this regard, (15) can be integrated once to give 



= 1_/M dt 



" " r\dt)c{r,/r,y 



(29) 



