BEAM FORMATION WITH ELECTRON GUNS 



381 



and cathode at zero potential and Ai at potential B, and (3) Vsc(f, r) is 

 the soUition when space charge is present but when Ax , A^ , and cathode 

 are all grounded. 



If the configuration of charge which contributes to Vs<-(f, r) is that 

 corresponding to ideal Pierce type flow, then we can use the principle 

 of superposition to give the Langmuir potential, VL(r, r): 



VUr, r) = Vcif, r) + V,{f, r) + V..{f, r) 



(2) 



Furthermore, the potential configuration for the case where ^i and A2 

 are at potentical C can be written 



V =V.-\-^V, + F(.c)' 



(3) 



where the functional notation has been dropped and F(sc)' is the po 

 icntial due to the new space charge when Ai and A2 are grounded. 

 We are now ready to use the fact that F(sc)' may be well approximated 

 1)3' Fsc which is easily obtained from (2). This substitution may be 

 justified by noting that the space charge distribution in a gun using a 

 \'oltage C for Ai does not differ significanth^ from the corresponding dis- 

 tribution when Ai is at voltage B except in the region near and beyond 

 A-i where the charge density is small anyway (because of the high electron 

 velocities there). Substituting Fsc as given by (2) for F(sc)' in (3) then 

 gives 



V 



Vi 



1 



B, 



V, 



(4) 



We have thus obtained an expression, (4), for the potential at an arbi- 



ANODE A2 



v=c 



ANODE A, 

 V = B 



CATHODE 



Fig. 1(a) — ■ Electrode configuration for anode lens evaluation in Section 2>A. 



