BEAM FORMATION WITH ELECTRON GUNS 



395 



Fig. 6 — Curves showing the current density variation with radius in a beam 

 I which has been dispersed by thermal velocities. Here r« is the nominal beam radius, 

 I r is the radius variable, and <t is the standard deviation defined in equation 17. 



A family of curves with this ratio, Fr , as parameter has been reproduced 

 : from the Hines-Cutler paper and appears here as Fig. 7. Using this no- 

 tation, (25) becomes 



dV ^ Vr,/{2V.) j^ Fr 

 di^ 27reo r 



or 



d r 

 dz^ 



jn_ lo Fr^ Fr 



27r€0 (27,7a)3/2 J. J. 



(27) 



where we have made use of the dc electron drift velocity to make dis- 

 tance the independent variable instead of time, and have defined a 

 quantity K which is proportional to gun perveance. We can now apply 

 (27) to the motion of both the outer (edge) non-thermal electron and 

 the cr-electron. From (26) we see that Fr, and Fg depend only on re/a] 



