Phenomenological description and modelling of vacuum breakdown

The first stage of vacuum breakdown is modelled using a phenomenological approach to the description of field emission. The field enhancement factor is calculated from the current and voltage measurements during the onset of breakdown, available in the literature. The calculation is based on the Murphy and Good formalism coupled with all the other relevant equations, including equations describing the plasma production and the equation of heat conduction in the cathode body. It is found that the field enhancement factor is not constant, but instead undergoes a gradual increase in time. The sheath voltage does not play a role in the onset of breakdown, but it is a determining factor in whether the ignited arc can be sustained or not. The field emission centre radius is found to be around 1 micrometre. Field emission centres larger than this either require unreasonably high field enhancement factor values, or they cannot lead to sufficient heating. On the other hand, smaller field emission centres produce a current that is much lower than the experimental values. The more advanced stages of breakdown will be studied in the future with account of all relevant physical processes, such as melting of the electrode material, hydrodynamics of the melt motion, and surface deformation, expanding on the previous work on the modelling of cathode spots in low-voltage vacuum arcs.