194 ^ BELL SYSTEM TECHNICAL JO URN A L 



introducing argon at a pressure of about a micron into the tube. The elec- 

 trons are emitted from only two spots of active material located at the op- 

 posite ends of a diameter on the cathode sleeve. In Fig. 3a the line joining 

 the spots is lined up with the magnetic field and in 3b this line is at an angle 

 of about 45° with respect to the field. This arrangement does not reproduce 

 exactly the space charge conditions in the tube as actually used but does 

 serve to give a picture of the electron paths in a qualitative sort of way. 



As shown by the patterns of Fig. 2 above a minimum strength of magnetic 

 field the shape of the focus does not change greatly. An approximate equa- 

 tion may be derived for the beam width in terms of the magnetic field above 

 this minimum value that is useful for predicting the performance of new 

 designs. The electrons that leave the cathode at right angles to the beam 

 require the strongest magnetic field to keep them in focus. Now because of 

 the cylindrical structure the electric field is concentrated near the cathode 

 and we will assume that after leaving the vicinity of the cathode the velocity 

 does not change appreciably. Setting v equal to the component of this 

 velocity at right angles to the magnetic field we have that the radius r of the 

 spiral path is given by the relation 



mv 



where H is the magnetic field-strength and m and e are the mass and charge 

 of an electron. 

 We also write 



'= ]/ 



2eKV 



where K is the fraction of the anode voltage corresponding to v. 



The width of the focus A is approximately equal to the cathode diameter 

 D plus twice the maximum radius of curvature of the spiral paths 



6.7\/KV 



A •= D + 



H 



where A and D are in centimeters and V is in practical volts. By substitu- 

 tion in this formula we have found that the empirical constant K is about 

 0.7 for the tubes that have been made to date. A minimum value for H is 

 obtained, again approximately, by setting the last term in the equation 

 equal to D. 



Unifokm: Electric Field 



As mentioned above the uniform field is obtained by imposing potentials 

 around the anode periphery varying as the sine of the angle. The cathode is 



