THERMIONIC VACUUM TUBES 



37 



and, as he shows, the effect of the space charge is to create a region of 

 negative potential immediately around the emitter. Let Fig. 5 

 represent the value of the potential as one proceeds from the cathode 

 in the direction x, and V' represent the minimum value of the poten- 

 tial. Assuming indefinitely large emission from the cathode, V 

 (which is a function of E p ) , determines the space current corresponding 



Fig. 5 



to any particular value of E p . The lower the value of V the fewer 

 the electrons with initial velocities sufficient to carry them past the 

 equipotential surface V' into the region where they are attracted by 

 the anode. Assuming the average initial velocity to be 0.3 volts 

 (roughly a temperature of 2400° K), Fry finds an appreciable deviation 

 from the 3/2 power law for E^,<30 volts, but initial velocities need be 

 considered only in tubes which operate at low E p . 



Another factor which, for low E p causes an appreciable deviation 

 from the 3/2 power law, is the potential gradient in a filament cathode 

 due to the heating current. Whereas velocity of emission tends to 

 make r? <3/2, the potential gradient in the filament has the reverse 

 effect. In general, the latter more than overbalances the former and 

 for small anode voltages ??>3/2. The value of r? when the cathode 

 potential gradient is considered, but initial velocities are neglected, 

 has been given by W. Wilson, 10 who finds that when E p is less than 

 the potential drop across the filament 7? = 5/2, while for higher E p it 

 gradually approaches the limiting value 3/2. 



10 For discussion of the 5/2 power relation, see Van der Bijl, The Thermionic 

 Vacuum Tube, p. 64. 



