Subnanosecond spectral diagnostics of streamer discharges: II. Theoretical background

Abstract

In this second of two papers, we have developed a fully self-consistent method of diagnostics of streamer discharge plasmas based on the analysis of absolute intensities of the second positive (SPS) and first negative (FNS) systems of molecular nitrogen. The theory of the method combines a spectroscopic technique for the calculation of temporal waveforms of the nitrogen absolute SPS and FNS (0, 0)-band emission and a self-consistent semi-analytical parametric axially symmetric 1.5D model of the filamentary streamer head. The spectroscopic technique takes into account characterizations of all units of the measuring spectro-optical channel, including spatiotemporal resolution and resolution in wavelength. Also, chromatic aberrations of the focusing lighting lens, errors in the adjustment of the object image onto the input slit as well as the correction of the slit function at the non-uniformly illuminated input slit of the monochromator on width are taken into account. The model of the streamer head is characterized by some trial-consistent allowable parametric on-axis profile of the electric field combined with the electron and total space charge number density profiles fully self-consistent with each other and with the trial electric field. Additionally, the corresponding 2D configuration for the field and the electron number density is constructed via special ellipse-like geodesic lines. The absolute values and the synchronous ratio of the 1L spatially and time-resolved cross-correlated temporal waveforms of the SPS to the FNS (0, 0)-bands, the ratio of their altitudes and the total emission power for both the waveforms measured in paper I have been taken into account to reconstruct the 2D structure of the streamer head. With a procedure fitting the directly computed output voltage waveforms to the experimental ones, the peak values of the electric field and the electron number density within the streamer head at mid-gap distances have been found to be 430–500 Td and (2–3) × 1014 cm−3, respectively. And the corresponding absolute electric field is thus 70–80 kV cm−1 at the initial gas temperature within the repetitive streamer region of 450 K.