Stability of direct current transfer to thermionic cathodes: I. Analytical theory

Stability of different modes of steady-state current transfer to cathodes of high-pressure arc discharges is investigated in the framework of the model of nonlinear surface heating. An eigenvalue problem governing perturbations has been formulated and its properties analysed. It is shown that the spectrum of this problem is real, therefore the change of stability can occur only at bifurcation points, in which different modes of steady-state current transfer join each other. Analytical expressions describing behaviour of the increment in the vicinity of bifurcation points have been derived. A general pattern of stability of the diffuse mode of current transfer to axially symmetric cathodes and of 3D spot modes branching off from the diffuse mode is established. Theoretical predictions are found to be in agreement with trends observed in the experiment and it is shown that the recently published comparison of the theory and the experiment on the spot mode needs to be revisited.