Electrode patterns in arc discharge simulations: effect of anode cooling

Self-organized electrode patterns are often observed experimentally in diverse types of electrical discharges, including atmospheric-pressure electric arcs, but rarely captured in general-purpose computational plasma dynamics simulations. Time-dependent three-dimensional thermodynamic non-equilibrium (two-temperature) simulations reveal the spontaneous formation of self-organized anode attachment spot patterns in the free-burning arc, a canonical direct-current (dc) discharge with an axisymmetric electrode configuration and in the absence of external forcing. The simulations are based on a monolithic fluid-electromagnetic plasma flow model numerically implemented within a second-order-accurate in space and time variational multiscale finite element framework. Simulation results show the gradual emergence of spot patters with increasing levels of anode cooling: from a single diffuse spot for low cooling levels to the eventual coverage of the anode region by small spots for intense cooling. The characteristics of the patterns, such as the number, size and location of the spots, markedly depend on the imposed total current. Furthermore, the patterns transition from steady to dynamic with decreasing total current for high cooling levels. The pattern dynamics show the formation of new spots by the splitting of old ones occurring in the center of the plasma, as well as the movement and eventual extinction of spots at the plasma boundaries. The different types of anode patterns (from diffuse to self-organized spots) have a significant effect on the total voltage drop across the plasma column, but a minor effect on other plasma characteristics away from the anode region. The results indicate that thermal instability together with equilibration between heavy-species and electron energy have a dominant role in the formation of anode patterns in arc discharges.