Modelling of plasma generation and expansion in a vacuum arc: application to the vacuum arc remelting process

As part of a complete theoretical description of the behaviour of the electric arc in the vacuum arc remelting process, a model has been developed for the column of plasma generated by a single cluster of cathode spots. The model combines a kinetic approach, taking into account the formation of the plasma in the cathodic region, and a hydrodynamic approach, describing the expansion of the plasma in the vacuum between the electrodes. The kinetic model is based on a system of Boltzmann-Vlasov-Poisson equations and uses a particle-type simulation procedure, combining the PIC (particle in cell) and FPM (finite point set method) methods. In the two-dimensional hydrodynamic model, the plasma is assimilated to a mixture of two continuous fluids (the electrons and the ions), each described by a system of coupled transport equations. Finally, a simplified method has been defined for calculating the electric current density and the energy flux density transmitted by the plasma to the anode. The results of the numerical simulation presented are consistent with a certain number of experimental data available in the literature. In particular, the model predicts a percentage of the electric power of the cluster transmitted to the anode (25%) in good agreement with the value indicated in the literature.