NONLINEAR SURFACE HEATING OF A PLANE SAMPLE AND MODES OF CURRENT TRANSFER TO HOT ARC CATHODES

A hypothesis is suggested that nonuniqueness of multidimensional therm al balance of a finite sample heated by a nonlinear external energy fl ux may be a reason for the existence of multiple modes of current tran sfer to hot are cathodes. In order to check this hypothesis, bifurcati on analysis has been carried out of the equation of heat conduction in the body of a thermionic cathode supplemented with a boundary conditi on describing hearing by the adjacent plasma. Multiple solutions have been found, one of them describing a diffuse mode and others describin g various spot modes. Solutions describing spot modes have been calcul ated 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 avai lable experimental information. [S1063-651X(98)00711-9].