Method of matched asymptotic expansions versus intuitive approaches: calculation of arc cathode spots

A model of steady-state solitary spots with a step-function dependence of the density of the energy flux from the plasma to the cathode surface on the surface temperature is suggested. While being simple and clear cut, this model, nevertheless, reflects essential features of the physics involved. It is found that a solution obtained by means of the method of matched asymptotic expansions is close to exact numerical results, in contrast to a solution obtained with the use of Steenbeck's principle of minimum power.