Molten metal flow and crater evolution during cathode spot retrograde motion

A three-dimensional hydrodynamic erosion model is established to analyze molten metal flow and cathode surface evolution along a prescribed cathode spot (CS) retrograde motion trajectory under a transverse magnetic field (TMF). The CS trajectory is determined using a statistical model based on the probability density of TMF-driven CS motion, while molten metal flow and crater evolution are simulated using the volume of fluid method with adaptive mesh refinement. The simulations show that pressure drives molten metal redistribution, whereas craters left by extinguished CS disrupt the axisymmetric evolution of newly ignited CS. This asymmetry promotes molten metal jetting and droplet formation on the previous spot side. For the prescribed CS motion trajectory, at 150 mT, cathode erosion remains localized during the first 150 ns, causing adjacent craters to coalesce into deeper composite erosion craters. Increasing the TMF from 150 to 571 mT strengthens the retrograde motion bias in successive CS ignition, producing a more directional erosion trajectory and reducing localized cathode erosion. Comparison with experimental morphologies shows that the model can effectively simulate molten melt flow under a prescribed retrograde motion trajectory of the CS. These results provide a basis for understanding the retrograde motion and evolution mechanisms of vacuum arc CS.