Analysing bifurcations encountered in numerical modelling of current transfer to cathodes of dc glow and arc discharges

摘要

Bifurcations and/or their consequences are frequently encountered in numerical modelling ofcurrent transfer to cathodes of gas discharges, also in apparently simple situations, and afailure to recognize and properly analyse a bifurcation may create difficulties in the modellingand hinder the understanding of numerical results and the underlying physics. This work isconcerned with analysis of bifurcations that have been encountered in the modelling ofsteady-state current transfer to cathodes of glow and arc discharges. All basic types ofsteady-state bifurcations (fold, transcritical, pitchfork) have been identified and analysed. Theanalysis provides explanations to many results obtained in numerical modelling. In particular,it is shown that dramatic chapges in patterns of current transfer to cathodes of both glow andarc discharges, described by numerical modelling, occur through perturbed transcriticalbifurcations of first- and second-order contact. The analysis elucidates the reason why themode of glow discharge associated with the falling section of the current-voltagecharacteristic in the solution of von Engel and Steenbeck seems not to appear in 2D numericalmodelling and the subnormal and normal modes appear instead. A similar effect has beenidentified in numerical modelling of arc cathodes and explained.