Formation of self-organized anode patterns in arc discharge simulations

Pattern formation and self-organization are phenomena commonly observed experimentally in diverse types of plasma systems, including atmospheric-pressure electric arc discharges. However, numerical simulations reproducing anode pattern formation in arc discharges have proven exceedingly elusive. Time-dependent three-dimensional thermodynamic non-equilibrium simulations reveal the spontaneous formation of self-organized patterns of anode attachment spots in the free-burning arc, a canonical thermal plasma flow established by a constant dc current between an axi-symmetric electrode configuration in the absence of external forcing. The number of spots, their size and distribution within the pattern depend on the applied total current and on the resolution of the spatial discretization, whereas the main properties of the plasma flow, such as maximum temperatures, velocity and voltage drop, depend only on the former. The sensibility of the solution to the spatial discretization stresses the computational requirements for comprehensive arc discharge simulations. The obtained anode patterns qualitatively agree with experimental observations and confirm that the spots originate at the fringes of the arc-anode attachment. The results imply that heavy-species-electron energy equilibration, in addition to thermal instability, has a dominant role in the formation of anode spots in arc discharges.