During the HBC fuse working, the fault current implies the initiation of an electric arc which is composed of metallic species vapours mainly, generally silver. This defines the end of the pre-arcing time. This electric arc interacts quickly with the surrounding silica sand grains or quartz sand. Thus a silver plasma is formed around the reduced sections of the fuse element. This silver plasma interacts with the silica sand grains and this interaction gives rise to the ignition of a plasma composed of vapours resulting from the dissociation of the SiO2 molecules. The radiation escaped from the SiO2 plasma can be used to assess experimentally the temperature (T) and the electron density (ne), two fundamental parameters for modelling purposes. T and ne are difficult to interpret because of the strong gradients in pressure, temperature, and material densities from the centre to the surroundings where the measurement is done. We propose a first formulation to calculate this radiation in order to increase the understanding of the radiation measurements.