A unified theory of free burning arcs, cathode sheaths and cathodes

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Abstract
A theoretical method of predicting properties of free burning arcs and their cathodes is presented in a unified treatment. The method combines a one-dimensional model of the non-equilibrium plasma sheath adjacent to the cathode and a two-dimensional model for the arc column and the solid cathode. Two internal boundaries divide the arc-cathode domain into an arc region, a sheath region and a cathode region. The internal boundary conditions are adjusted during the iteration procedure to satisfy the energy conservation and current continuity equations. The effective resistance of the cathode sheath region is obtained from the sheath calculation assuming charge transport using an ambipolar diffusion approximation. No assumptions are made as to the distributions of, current density and temperature at the cathode surface. The model accounts for cathode surface effects and assumes that the cathode is a thermionic emitter. Material functions such as the thermal and electrical conductivities of the arc plasma and cathode are required as input parameters. Predictions are made, for any given arc current and cathode configuration, of the temperature and current density distributions in the arc and the cathode. Information is also provided about sheath properties. The results from a calculation for 200 A arc burning in argon with a thoriated tungsten cathode are in good agreement with the experimental measurements of the arc column and cathode surface temperatures and the arc voltage.