The Cathode Fall of an Arc

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Abstract
The distribution of energy of electrons at the boundary of the cathode fall of an arc is worked out for the thermionic arc and for the high field arc upon both the classical Schottky theory, and the quantum mechanical theory of high field emission. For the same value of cathode fall, the electrons from the thermionic arc have energies several volts greater than those from the high field arc. To give the positive ions necessary for space charge purposes, the cathode fall of the high field arc consequently must be several volts greater than that of the thermionic arc, if the mechanism of production of positive ions is the same in the two arcs. The minimum value of the difference in cathode fall is 4 to 6 volts. Tests are thus suggested for Langmuir's high field theory of cold cathode arcs. Data for the mercury arc indicate that electrons, in sufficient number to produce the necessary positive ions, have energies certainly less than 7 volts at the boundary of the cathode fall. Either the field theory does not apply to the mercury arc, or positive ions are produced by a cumulative process or other complicated means.

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