Nonlinear surface heating of a plane sample and modes of current transfer to hot arc cathodes

A hypothesis is suggested that nonuniqueness of multidimensional thermal balance of a finite sample heated by a nonlinear external energy flux may be a reason for the existence of multiple modes of current transfer to hot arc cathodes. In order to check this hypothesis, bifurcation analysis has been carried out of the equation of heat conduction in the body of a thermionic cathode supplemented with a boundary condition describing heating by the adjacent plasma. Multiple solutions have been found, one of them describing a diffuse mode and others describing various spot modes. Solutions describing spot modes have been calculated in the vicinity of bifurcation points and analyzed qualitatively outside this vicinity. Qualitative conclusions concerning a transition between the diffuse discharge and the first spot mode conform to available experimental information.