Functional dependence of the V-I characterstic of an arc on the thermal parameters

Numerical and analytical results of a self-consistent analysis of the voltage-current (V-I) characteristic of an electrical discharge are presented. The dependences of the critical current density for the onset of the arc and the peak voltage drop on the exponent n characterizing the dependence of conductivity on temperature are examined. They are found empirically to be proportional to (n - 3/2)-(n+1)/2(n-1) and (n - 3/2)-1/2, respectively.