A General Theory of the Plasma of an Arc

The conception of random positive ion velocities corresponding to ion temperatures in a plasma has serious theoretical difficulties and is lacking in direct experimental verification. It is more reasonable to assume that each ion starts from rest and subsequently possesses only the velocity which it acquires by falling through a static electric field which is itself maintained by the balance of electron and ion charges. This new viewpoint thus ascribes motions to the positive ions which, for long free paths, are ordered rather than chaotic, each negative body in contact with the discharge collecting ions from a definite region of the plasma and from it only. The resulting integral ? the plasma-sheath potential distribution have been set up for plane, cylindrical, and spherical plasmas, for long, short and intermediate length ion free paths, and for both constant rate of ionization throughout the plasma and rate proportional to electron density, and these equations have been solved for the potential distribution in the plasma in all important cases. The case of short ion free paths in a cylinder with ion generation proportional to electron density gives the same potential distribution as found for the positive column by Schottky using his ambipolar diffusion theory, with the advantages that ambipolarity and quasineutrality need not appear as postulates. The calculated potential distribution agrees with that found experimentally. The potential difference between center and edge of plasma approximates $\frac{T_e}{11,600}$ volts in all long ion free path cases. The theory yields two equations. One, the ion current equation, simply equates the total number of ions reaching the discharge tube wall to the total number of ions generated in the plasma, but it affords a new method of calculating the density of ionization. The second, the plasma balance equation, relates rate of ion generation, discharge tube diameter (in the cylindrical case), and electron temperature. It can be used to calculate the rate of ion generation, the resulting values checking (to order of magnitude) those calculated from one-stage ionization probabilities. The potential difference between the center of the plasma and a non-conducting bounding wall as calculated from the ion current equation agrees with that found experimentally.