418 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



ing inininumi position in Curve B. Fortunately, in the gun design stage, 

 one is usually more concerned with the value of (r95)min than with its 

 exact axial location. The principal need for knowing the axial location of 

 the minimum is to enable the axial magnetic field to build up suddenly 

 in this neighborhood. However, since this field is normally adjusted ex- 

 perimentally to produce best focusing, an approximate knowledge of 

 2m in is usually adequate. 



In Fig. 15b we show a similar set of experimental and theoretical beam 

 profiles for another gun. The relative profiles are much the same as in 

 Fig 15a, and all of several other guns measured yield experimental 

 points similarly situated with respect to curves of Type B. 



C. Comparison of Experimental and Theoretical Current Density Dis- 

 tributions where the Minimum Beam Diameter is Reached 



In Fig. 14 we have plotted the current density distribution we would 

 have predicted in a transverse plane at ^min for the example introduced 

 in Section 5Z). Here the experimental and theoretical curves are nor- 

 malized to include the same total currents in their respective beams. 

 The noticeable difference in predicted and measured current densities 

 at the center of the beam does not appreciably alter the properties such 

 a beam would have on entering a magnetic field because so little total 

 current is actually represented by this central peak. 



D. Variation of Beam Profile with T 



All of the design charts have been based on a value of T = 1.1, which 

 is typical of the values obtained by the methods of Section 3. When 

 appreciably different values of F are appropriate, we can get some feel- 

 ing for the errors involved, in using curves based on T = 1.1, by refer- 

 ence to Fig. 16. Here we show beam profiles as obtained by the methods 

 of this paper for three values of F. The calculations are again based on 

 the gun of Section 5D, and a value of just over 1.1 for F gives the ex- 

 perimentally obtained value for (r95)min . 



7. SOME ADDITIONAL REMARKS ON GUN DESIGN 



In previous sections we have not differentiated between the voltage 

 on the accelerating anode of the gun and the final beam voltage. It is 

 important, howovei', that the separate functions of these two voltages 

 be kept clearly in mind: The accelerating anode determines the total 

 current drawn and largely controls the shaping of the beam; the final 

 beam voltage is, on the other hand, chosen to give maximum interaction 

 between the electron beam and the electromagnetic waves traveling 

 along the slow wave circuit. As a consequence of this separation of func- , 



