On the axial structure of a nitrogen surface wave sustained discharge: Theory and experiment

Abstract

A model for a surface wave sustained nitrogen discharge accounting in a self-consistent way for electron and heavy particles kinetics and discharge electrodynamics has been developed. The system under analysis is a plasma column produced by a traveling, azimuthally symmetric (m=0 mode) surface wave. The model is based on a set of coupled equations consisting of the electron Boltzmann equation and the rate balance equations for the most important excited species—vibrationally, N2(X 1Σg+, ν), and electronically excited states, N2(A 3Σu+, a′ Σu−, B 3Πg, C 3Πu, a 1Πg)—and charged particles (e, N2+, N4−) in the discharge. Electron collisions with nitrogen molecules of the first and the second kind and electron–electron collisions are accounted for in the Boltzmann equation. The field strength necessary for steady-state operation of the discharge is obtained from the balance between the total rates of ionization (including direct, stepwise, and associative ionization) and of electronic losses (due to diffusion to the wall and bulk recombination). The transfer of wave power to the discharge occurs through collisional processes, thus the set of equations is closed by an ordinary differential equation (stemming from basic electrodynamical relations) which associates the axial gradient of the electron density to the wave attenuation. As a result, a self-consistent interdependence between wave propagation and discharge characteristics is obtained over the whole plasma column. The axial profile of the gas temperature and the initial value of the electron density at the position of the wave launcher are used as input parameters. The model determines the axial structure of the discharge—axial variations of the electron energy distribution function and its moments, the vibrational distribution function of the electronic ground state, and the densities of the most important electronically excited states and positive ions—consistently with the electric field and the surface wave dispersion characteristics. A spatially resolved experimental investigation of the electron energy distribution function, the gas and the vibrational temperatures, and the population densities of some electronically excited states along with wave propagation characteristics measurements provides a verification of the model. Strong correlation between different plasma balances, governing the discharge production, and discharge electrodynamics—the basis of surface-wave discharge physics—has been demonstrated both theoretically and experimentally.