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

Abstract

Theory for diagnostics of the positive primary streamer has been described for providing validation and explanation of the experimental results presented in part 1. Rates and rate constants of electronic processes in primary streamer plasma have been calculated by numerical solution of the steadystate 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 derived in part #1, 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.

Sliding discharge optical emission characteristics

“…for the FNS spectral band head (0,0). In air at atmospheric pressure, the excitation process only comes from direct electron impact [13]. Thus, the reaction rates are directly proportional to the electron density, while the rate constants are strongly dependent on the electric field value.…”

“…The local continuity equations for the excitation of the FNS and SPS by direct electron impact and their successive collisional quenching in a steady-state approximation can be written as follows [13]:…”

“…where [ ] ν , q B ν are the corresponding quenching rates. For atmospheric air density, the quenching rates are [13]:…”

“…Once the E/N value is determined, the plasma density can be obtained using the atomic model [13] if the absolute line intensity is known. This procedure was employed to estimate the streamer head density for the SD [9].…”