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.