

BEAM FORMATION WITH ELECTRON GUNS 403 



jspreadiug of the beam with distance. This is true because, in microwave 

 beam tubes, the beam from a magnetically shielded Pierce gun normally 

 enters a strong axial magnetic field near a point where the radius is a 

 minimum, so that magnetic focusing forces largely determine the beam's 

 subsequent behavior. The analog computer data has therefore been re- 

 processed to stress the dependence of the beam's minimum diameter and 

 the corresponding axial position of the minimum on the basic design 

 iparameters fdfa , perveance, and s/Va/T. As a first step in this direc- 

 tion, the radius, rgs , of a circle which includes 95 per cent of the beam 



: I current is obtained as a function of axial position along the beam. Such 

 idata are shown graphically in Fig. 12. Finally, the curves of Fig. 12 are 



. lused in conjunction with the tabular data to obtain the "Design Curves" 

 of Fig. 13 where all of the pertinent information relating to the beam 

 at its minimum diameter is presented. 



\D. Example of Gun Design Using Design Charts 



Assume that we desire an electron gun with the following properties : 

 anode voltage Va = 1,080 volts, cathode current Ip = 7.1 ma, and mini- 

 mum beam diameter 2(r95)min = 0.015 inches. Let us further assume a 

 cathode temperature T = 1080° Kelvin, an available cathode emission 

 density of 190 ma per square cm, and an anode lens correction factor 

 of r = 1.1. From these data we find -x/Va/T = 1.0, perveance P = 

 0.2 X 10"^ amps/(volts)^''" and (r95)min/''c = 0.174. Reference to the de- 

 sign chart, Fig. 13, now gives us the proper value for fc/fa : using the 

 upper set of curves in the column for y/Va/T =1.0 we note the point 

 of intersection between the horizontal line for {rgr^^i^/rc = 0.174 and 

 the perveance line P = 0.2, and read the value of fc/fa (= 2.8) as the 

 corresponding abscissa. The convergence angle of the gun, de , is now 

 simply determined fi'om the equation^^ 



de = cos-^ {\ - t|^ X 10^) (37) 



{Qe is found to be 13.7° in this example) and the potential distribution 

 in the region of the cathode can be obtained from (30). 



When this point has been reached, the gun design is complete except 

 for the shapes of the beam forming electrode and the anode, which are 

 determined with the aid of an electrolytic tank in the usual way. The 

 radius of the anode hole which will give a specified transmission can be 

 found by obtaining (re/a)a through the use of Fig. 5, and then choosing 

 the anode radius from Fig. 7. In practical cases where (rf/a)a > 3.0, 



