Cathode Fall in Helium and Argon 5 



is considered to be the sole source of ions. In the negative glow 

 where the positive and negative currents are equal the horizontal 

 portion of the curves represents the value of the current due to 

 either type of ions. If X^ is assumed as the source of ions, then 

 at one ionizing interval toward the cathode, X'^, the negative cur- 

 rent will have dropped to one-half its original value, or one-fourth 

 the total current, and the positive current will be three-fourths the 

 total current. At two ionizing intervals the negative current will 

 be one-eighth the total current, while the positive current will be 

 seven-eighths, and so on until the positive ions are carrying practi- 

 cally all the current. 



Assuming the negative glow to be the sole source of ions leads 

 to the development of a relatively simple theory of the potential at 

 different points in the gas, between the cathode glow and the nega- 

 tive glow. The results of the theory obtained agree very closely 

 with the experimental measurements made. 



THEORY OF THE POTENTIAL FALL 



If we assume the source of positive ions, X^^, to be an infinite 

 equipotential plane surface, and that between it and the polariza- 

 tion region, Xg, of an infinite plane cathode, there is a uniform 

 current density, /, of positive ions, with the potential gradient 

 8V/8X at X,, equal to zero, Poisson's Law for density of charge, 

 since the planes are parallel, gives 



0^2 = ~ 47r«e, (l) 



where n is the numl)er of positive ions per c.c. and e the ionic 

 charge. From the law of the mobility of the ions we have the 

 current density 



- . dV ■ 



J ^ — ^eU-^' (2) 



where U is the mobility, or velocity of the ions in cm. per sec. for 

 a potential gradient of one volt per cm. 



If the source of ions and the polarization region are infinitely 

 long, concentric cylindrical surfaces, the Poisson equation becomes 



