Three-dimensional heat transfer equation was used to discuss the circular region of high temperature formed on the surface of the tubular tungsten cathode

the cathode surface temperature in the region becomes uniform gradually (except that at the point of the cathode arc root) when the cathode arc root of the secondary arc is rotating on surface of the tungsten cathode and the rotating frequency of the secondary arc root is increasing. And the necessary condition of the cathode surface temperature is provided to form the model of the multi-arc-root or diffusive arc root. At the same time

the cathode surface temperature at the point of the cathode arc root decreases and reaches a constant when the rotating frequency increases.