TRANSVERSE MOTION OF ELECTRONS 



627 



These values are chosen because there is a longitudinal field tube which 

 operates at 7.5 cm with a value of C (which corresponds to D) of about .03. 

 The table below shows the ratio of the maximum value of Xi to the maximum 

 value of Xi for no magnetic focusing field. 



A field of 50 to 100 gauss should be sufiicient to give useful focusing action. 

 Thus, it may be desirable to use magnetic focusing fields in transverse- 



0.2 0.4 0.6 



0,6 1.0 1.2 1.4 t.6 1.8 2.0 2.2 2.4 

 PROPORTIONAL TO MAGNETIC FIELD, f 



2.6 2.8 3.0 3.2 



Fig. 13.11 — Here Xi , the x for the increasing wave, is plotted vs/, which is proportional 

 to the strength of the focusing field. The velocity parameter b has been chosen to maxi- 

 mize Xi . The ordinate Xi is proportional to gain per wavelength. 



field traveling-wave tubes. This will be more especially true in low-voltage 

 tubes, for which D may be expected to be higher than .03. 



13.5 Mixed Fields 



In tubes designed for use with longitudinal fields, the transverse fields 

 far off the axis approach in strength the longitudinal fields. The same is true 

 of transverse field tubes far off the axis. Thus, it is of interest to consider 

 equation (13.26) for cases in which a is neither very small nor very large, 

 but rather is of the order of unity. 



If the magnetic field is very intense so that P is large, then the term con- 

 taining a^, which represents the effect of transverse fields, will be very small 

 and the tube will behave much as if the transverse fields were absent. 



