416 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



12 

 11 



10' 



z 



UJ 



o 



5 

 UJ 



> 



01 23456789 



RADIUS IN MILS 



Fig. 14 — Current density distribution in a transverse plane located where the 

 95 per cent radius is a minimum. The predicted and measured curves are normal- 

 ized to contain the same total current. (The corresponding prediction from the 

 universal beam spread curve would show a step function with a constant relative 

 current density of 64.2 for r < 1.2 mils and zero beyond.) The gun parameters are 

 given in Section 5D. 



and generally Gaussian in form, thereby indicating uniform cathode 

 emission and proper boundary conditions at the edge of the beam near 

 the cathode. The ejffect of positive ions on the beam shape was in every I 

 case reduced to negligible proportions, either by using special pulse 

 techniques, or by applying a small voltage gradient along the axis of 

 the beam. 



B. Comparison of the Experiinentally Measured Spreading of a Beam with 

 that Predicted Theoretically 



From the experimentally obtained plots of current density versus 

 radius at several axial positions along the beam, we have obtained at 

 each position (by integrating to find the total current within any radius) 

 a value for the radius, rgs , of that circle which encompasses 95 per cent 

 of the beam. For brevity, we call the resulting plots of rgs versus axial 

 distance, "beam profiles". The experimental profile for the giui de- 

 scribed in Section 5D is shown as curve A in Fig. 15(a). Curve B shows 

 the profile as predicted by the methods of this paper and obtained from 

 Fig. 12. Curve C is the corresponding profile which one obtains by the 

 Hines-Cutler method, and Curve D represents Tq^ as obtained from the 



