BEAM FORMATION WITH ELECTRON GUNS 



419 



0.006 



0.02 



0.18 



0.20 



0.22 



0.04 0.06 0.08 0.10 0.12 0.14 0.16 



Z, DISTANCE FROM IDEAL ANODE IN INCHES 



Fig. 16 — Beam profiles as obtained by the methods of this paper for the gun 

 parameters given in Section bD. Curves are shown for three values of the anode 

 lens correction, viz. T = 1.0, 1.1, and 1.2. 



tions, it is fouiicl that some beams which are difficult or impossible to 

 obtain with a single Pierce-gun acceleration to final beam voltage may 

 be obtained more easily by using a lower voltage on the gun anode. The 

 acceleration to final beam voltage is then accomplished after the beam 

 has entered a region of axial magnetic field. 



Suppose, for example, that one wishes to produce a 2-ma, 4-kv beam 

 with (rgs/rc) = 0.25. If the cathode temperature is 1000°K, and the gun 

 anode is placed at a final beam voltage of 4 kv, we have \^Va/T = 2 

 and P = 0.008. From the top set of curves under \^Va/T = 2 in Fig. 

 13, we find (by using a fairly crude extrapolation from the curves shown) 

 that a ratio of fc/fa'^ 3.5 is required to produce such a beam. The value 

 of {ve/o-) at Zmin IS therefore less than about 0.2 so that there is little 

 x'mblance of laminar flow here. On the other hand we might choose 

 r, = 250 volts so that a/fT^ = 0.5 and P = 0.51. From Fig. 13* 

 we than obtain fc/fa = 2.6 and (re/o-)min = 0.8 for the same ratio of 

 '■'joAc(= 0.25). While the flow could still hardly be called laminar, it is 

 (•(jnsiderably more ordered than in the preceding case. Here we have in- 

 cluded no correction for the (convergent) lens effect associated with the 

 post-anode acceleration to the final beam voltage, F = 4 kv. 



Calculations of the Hines-Cutler type will always predict, for a given 

 set of gun parameters and a specified anode lens correction, a minimum 

 beam size which is larger than that predicted by the methods of this 

 ])aper. Nevertheless, in many cases the difference between the minimum 

 sizes predicted by the two theories is negligible so long as the same anode 

 lens correction is used. The extent to which the two theories agree ob- 



