A theory for the cathode mechanism in low-current vacuum arcs, with application to the calculation of erosion rate

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Abstract
A theory has been proposed which seeks to explain the cathode mechanism in low‐current vacuum arcs. It is shown that the high current density at the cathode surface has been successfully discussed by relating the energy‐balance equation, space‐charge equation, electron‐emission equation, current equation, MHD equation of motion, and the minimum principle of joule heating. When four equations and two limiting conditions combine the five dependent variables, which are temperature of the arc root, electric field at the cathode, total current density, current density carried by electrons, and the radius of the arc root, the current density and temperature at the arc root are obtained as a function of the arc current with the cathode‐fall voltage as a parameter. It is also shown that the relationship between the arc current and the evaporation rate from the arc cathode root can be calculated. The theoretical results are in good qualitative agreement with the experimental data of the current density and the erosion rate.

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