472 BELL SYSTEM TECHNICAL JOURNAL 



distribution of the emitted electrons must be made. The simplest 

 assumption is that the electrons are emitted from the cathode with 

 zero velocity. From this assumption and the assumption discussed 

 in the preceding paragraph it follows that the potential maximum 

 always occurs at the cathode surface and the emitted electrons are 

 accelerated everywhere in their path between cathode and anode. The 

 current to the anode is determined by the potential distribution in 

 the space. 



A better assumption is that the electrons are emitted with a Max- 

 wellian velocity distribution. For this case the potential maximum 

 occurs at some distance from the cathode. The position and value of 

 the maximum depends upon the work function and temperature of the 

 cathode, the geometry of the electrodes and the applied potential. 

 In order that an electron shall reach the anode, its initial velocity 

 normal to the surface must correspond to an energy which is equal 

 to or greater than the potential maximum. 



For parallel plates and cylindrical electrodes the following solutions 

 have been obtained for the two assumptions in regard to the velocity 

 distribution of the emitted electrons. 



Electrons Emitted with Zero Velocity 

 For infinite parallel plates: 



i = (Af2/97r)(e/m)KF^/x-') = 2.33 X 10-«(FVx-), (81) 



where i is the current to the anode in amp. per cm.^ ; x the distance in 

 cm. between cathode and 'anode; and V is the applied potential in 

 volts corrected for the contact potential; e and m are the charge and 

 mass of the electron, respectively. 

 For long coaxial cylinders: 



i = (2V2/9)(g/m)Hl^V^i3') = 1-48 X lO-^FV^?^-), i^l) 



(3 is a function of Rjr^ where R and r^ are the radii of anode and cathode, 

 respectively. Table Y shows a few values of jS^ as a function of i?/ro 



TABLE V 

 Values of /S^ 



taken from a table given by Langmuir and Blodgett.'^ 



