Accurate spectroscopic studies of streamer discharges. 2. Theoretical background and analysis

For pt.1 see ibid., p.589-592, (2005). Theory for diagnostics of the positive primary streamer has been described for providing validation and explanation of the experimental results is presented. Rates and rate constants of electronic processes in primary streamer plasma have been calculated by numerical solution of the steady-state spatially-uniform Boltzmann's kinetic equation for the electron energy distribution function. Principally, they all are the functions only of the local reduced electric field, which is unique free independent parameter for all other variables. Conceptual spatial profile of the reduced electric field within and nearby the streamer head has been constructed based on continuity equations for electrons and positive and negative ions coupled with Poisson's equation in invariant forms. A corresponding profile of the electron number density has been calculated for case of stationary stage of primary streamer propagation. Using nul-dimensional solutions for the population number densities are derived, conjugate one-dimensional spatial profiles for the (0, 0) band luminosities of the first negative both the second positive nitrogen systems versus longitudinal (on-axis) coordinate have been calculated. Just these theoretical luminosity profiles are used for determination of the actual reduced electric field and electron number density by fitting to experimental profiles. Its peak value to first approximation is determined using aggregated graphical nomograms versus the reduced electric field.