BEAM FORMATION WITH ELECTRON GUNS 413 



we find less than 1 per cent anode interception if 



anode hole radius = 0.93 r^a + 2o-a (38) 



Additional information about the axial position of (r95)min and the cur- 

 rent density distribution in the corresponding transverse plane is con- 

 tained in Fig. 13. The second set of curves in the \/Va/T = 1 column 

 gives Zm\n/Tc — 2.42 for this example, so that we would predict 



Zmin = distance from anode to (r95)inin = 0.104'' 



The remaining 3''^ and 4*^^ sets of curves in the ■\/Va/T = 1 column 

 allow us to find o- and re/a- at ^min . In particular we obtain a = 0.0029" 

 and I'e/o = 0.8, and use Fig. 6 to give the current density distribution at 

 2min .* Section VI contains experimental data which indicate a some- 

 what larger value for 2m in than that obtained here. However the pa- 

 rameter of greatest importance, (r95)niin , is predicted with embarrassing 

 precision. 



For those cases in which additional information is required about the 

 beam shape at axial points other than ZnVin , the curves of Fig. 12 or the 

 data of Table II may be used. 



6. COMPARISON OF THEORY WITH EXPERIMENT 



In order to check the general suitability of the foregoing theory and 

 the usefulness of the design charts obtained, several scaled-up versions 

 of Pierce type electron guns, including the gun described in Section 5D, 

 were assembled and placed in the double-aperture beam analyzer de- 

 scribed in Reference 7. 



A. Measurement of Current Densities in the Beam 



Measurements of the current density distributions in several trans- 

 verse planes near Smin were easily obtained with the aid of the beam 

 analyzer. The resulting curve of relative current density versus radius 

 at the experimental 2min is given in Fig. 14 for the gun of Section 52). 

 (This curve is further discussed in Part C below.) For this case, as well 

 as for all others, special precautions were taken to see that the gun was 

 functioning properly : In addition to careful measurement of the size and 

 position of all gun parts, these included the determination that the dis- 

 tribution of transverse velocities at the center of the beam was smooth 



* When j'c/o- < 0.5, the current density distribution depends almost entirely on 

 a, and, in only a minor way, on the ratio Te/a- so that in such cases this ratio need 

 not be accurately known. 



