Characteristics of Radiation-Dominated Electric Arcs

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Abstract
Temperature profiles of arcs when radiation is the principal energy transfer process have been derived from material functions. Arcs which are optically thin are approximately isothermal or constricted depending on whether εN/σ is an increasing or decreasing function of temperature; εN is the net emission coefficient and σ the electrical conductivity. Arcs which are optically thick have a temperature profile similar to conduction dominated arcs. Theoretically predicted examples of these three types of arcs are a 2000‐A arc at 30 atm in air, a low current arc in the vapor of a rare‐earth metal at 20 Torr, and a 4000‐A arc at 1000 atm in air. For arcs which are nearly isothermal, it is possible at any value of current and radius to make approximate calculations of (1) the temperature of the arc core, (2) the electric field strength, (3) the thickness of the outer arc sheath, and (4) the fraction of the input energy carried to the wall by conduction. Such calculations are made for arcs in air and are compared with the results of exact calculations which take into account the details of the self‐absorption of radiation. Approximate calculations show that when εN/σ has a maximum as a function of temperature, multiple solutions for the temperature profile are possible for some values of arc current and radius.

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