The ratio of the spectral band intensities of the first negative and second positive spectral systems of molecular nitrogen is a well recognized method for indirect determination of the electric field. It is applied for various plasmas, e.g. barrier and corona discharges for industrial applications or geophysical plasmas occurring in the Earth’s atmosphere. The method relies on the dependence of the intensity ratio R ( E / N ) of selected bands on the reduced electric field strength. Both experimental and theoretical approaches have been used to determine this dependence, yet there still is a rather large spread in the data available in literature. The primary aim of this work is to quantify the overall uncertainty of the theoretical R ( E / N ) dependence and identify the main sources of this uncertainty. As the first step we perform sensitivity analysis on a full N ₂ /O ₂ plasma kinetics model to find a minimal set of processes that are influential for the R ( E / N ) dependence. It is found to be in agreement with simplified kinetic models generally used. Subsequently, we utilize Monte Carlo-based uncertainty quantification to provide a confidence band for the electric field obtained from the theoretical R ( E / N ) dependence. Finally, subsequent steps are proposed to significantly reduce the uncertainty of the method.

An established and widely used method for remote electric field determination is based on the ratio of the spectral band intensities of the first negative and second positive spectral systems of molecular nitrogen which does, however, require theoretically or experimentally obtained dependence R ( E / N ) . The aim of this work is to reduce the overall uncertainty in the theoretical dependence R ( E / N ) calculated in part I of this work. We present an in-depth review of the kinetic and cross section data that are available in literature for the most influential processes. By tracking the historical evolution of the kinetic data, their cross-validation by independent authors and by taking into account advances in the experimental methods, we separate datasets that have not been rendered inaccurate by later works. By doing so, we reduce the uncertainty of the theoretical R ( E / N ) dependence and propose corresponding confidence band to be used by scientific community.

We developed an extension of the spectrometric method to estimate a reduced electric field ( E / N ), which is applicable in nitrogen-containing plasmas. The method is based on the intensity ratio of the emission bands of the first negative system (FNS) of N 2 + and the second positive system (SPS) of N ₂ . It uses the emission occurring in the wavelength interval 375–410 nm, which includes six SPS and two FNS bands. The choice of the spectral window is guided by much simpler acquisition and processing of experimental data than the SPS(0, 0) and FNS(0, 0) pair that is typically used. Following this idea, we construct a kinetic model for pure molecular nitrogen, which determines the population of the upper states responsible for the FNS and SPS emission. Moreover, we perform sensitivity analysis of the kinetic model, which allows us to reveal the most significant processes for the investigated intensity ratios. For these processes, we provide an in-depth review of the kinetic data that are available in the literature. We use the fact that the spectral window investigated contains bands to obtain three independent intensity ratios with sufficient signal-to-noise ratio ((FNS(0, 0)/SPS(0, 2), FNS(0, 0)/SPS(1, 4), FNS(0, 0)/SPS(2, 5)), which are usable for more accurate electric field determination. We also provide analytical formulas representing intensity ratio dependencies on E / N . Furthermore, we focus on different spectrometric representations of FNS and SPS bands, which also affect the precision of E / N determination. We examine the FNS/SPS band profiles in terms of different rotational temperatures and instrumental functions. Finally, we propose a simple procedure that enables the use of bandhead intensities in the intensity ratio dependencies, thus avoiding the need to evaluate integral band intensities from the recorded spectra.

In this work, we examine initial phases of micro-discharges produced in deionised water by high-voltage (HV) pulses of nanosecond duration. We apply opto-electrical diagnostics with extremely high temporal (down to 30 ps) as well as spatial (down to 1 μ m) resolution. Frozen interferometric and shadowgraph images show three distinct events. The first, the subcritical (no-discharge) event, is characterised by periodic perturbations of the index of refraction which depart from the anode surface and are pulled away at the speed of sound as an expanding envelope defined by the shape of the anode tip. One-dimensional hydrodynamic modelling of the subcritical phase under conditions mimicking curvatures of real anode tips reveals basic characteristics of perturbations caused by dynamic balance between the hydrostatic and electrostrictive pressures consistent with experimental observations. The second, the dark or non-luminous discharge event, is characterised by the onset of a few isolated very tiny tree-like structures growing from the anode tip. Depending on the HV amplitude, the initial structures occur with a delay of ∼2–3 ns after onset of the HV pulse and subsequently expand with average velocity of ∼1 × 10 ⁵ –2 × 10 ⁵ m s ⁻¹ , creating very dense bush-like structures made of thin hair-like filaments in a few nanoseconds. The third, the luminous discharge event, follows (nearly simultaneously) the dark discharge event and unveils much simpler tree-like morphology determined by the extension of non-luminous bush-like structures. Characteristic dimensions of observed events range from about 1 μ m (typical diameter of non-luminous filaments) to tens of micrometres (characteristic diameters of luminous filaments). Furthermore, we address a possible role of microbubbles developing in the anode region due to the periodic HV pulses and verify that the UV-vis-NIR spectrometric signatures of the luminous phase notably change when replacing non-degassed deionised water with degassed.

The emission spectra of a streamer discharge in pure nitrogen provide an important tool for investigating the fundamental kinetics of excited electronic states of N₂ and benchmark data for validating advanced kinetic schemes for numerical models. In this work, we characterize a streamer monofilament developed in a dielectric barrier discharge configuration, including electrical characteristics, time-resolved images and N₂/N 2 + emission spectra, all acquired with nanosecond temporal resolution. Time-resolved images and emission characteristics provide clear evidence of the formation of a cathode-directed streamer and allow determining the streamer propagation velocity and the typical E / N values using the intensity ratio of nitrogen spectral bands in the center of the discharge gap. We also measure the vibrational distributions of the N₂(C 3 Π u , v = 0–4) and N 2 + (B 2 Σ u + , v = 0–2) states. The population of N₂(C 3 Π u , v = 0–4) state, initially formed by energetic electrons in the streamer head, changes later significantly due to the decrease in the mean energy and concentration of the streamer channel electrons. After a few tens of nanoseconds, the electron-impact excitation rate of N₂(C 3 Π u ) becomes negligible compared to its population by the N₂( A 3 Σ u + ) + N₂( A 3 Σ u + ) pooling. The experimental findings are supported and consistent with the 0D state-to-state kinetic model results and reveal the participation of high vibrational levels of N₂( A 3 Σ u + ) in the pooling reactions.

We investigate the electric field development in weak microseconds-lasting atmospheric pressure Townsend discharge operated in a barrier discharge arrangement in pure nitrogen. The electric field is determined using four different methods: laser-aided electric field induced second harmonics (EFISH), optical emission-based first negative/second positive systems (FNS/SPSs of molecular nitrogen) intensity ratio, electrical equivalent circuit approach and via determination of the Townsend first coefficient α ( E / N ) from the spatial optical emission profile. The resulting values of the electric field obtained by these respective methods, regardless of the differences in absolute values, lie within a reasonable range. The limitations and advantages of all methods are discussed in detail for the investigated discharge. The EFISH measurements are supported by re-computation of the effective interaction-path of the laser using an electrostatic model. The FNS/SPS method provides systematically higher values compared to other methods. We discuss in detail the potential origin of this discrepancy, as this method is at the limit of its applicability due to the low E/N values and we also consider the impossibility of full verification of the underlying assumptions. The focused discussion addresses best-practice issues and identifies possible future steps to improve each of the four methods under given conditions.