On the self-consistent modeling of a traveling wave sustained nitrogen discharge

Abstract

We present a self-consistent formulation to study low-pressure traveling wave (azimuthally symmetric surface transverse magnetic mode) driven discharges in nitrogen. The theoretical model is based on a self-consistent treatment of the electron and heavy particle kinetics, wave electrodynamics, gas thermal balance, and plasma–wall interactions. The solution provides the axial variation (as a result of nonlinear wave power dissipation along the wave path) of all discharge quantities and properties of interest, such as the electron energy distribution function and its moments, population densities of all relevant excited and charged species [N2(X 1Σg+,ν),N2(A 3Σu+,a′ 1Σu−,B 3Πg,C 3Πu,a 1Πg,w 1Δu), N2+, N4+, e], gas temperature, degree of dissociation [N(4S)]/N, mean absorbed power per electron, and wave attenuation. A detailed analysis of the energy exchange channels among the degrees of freedom of the heavy particles is presented. Particular attention is paid to the axial variation of the gas and wall temperatures, which affect in a complex way the discharge operation. For the high electron densities and reduced electric fields achieved at 2.45 GHz, it is shown that the contribution of exothermic reactions involving excited molecules in metastable states to the total gas heating can be significant. The role of the triplet N2(A 3Σu+) metastable state as an energy “reservoir” that pumps translational modes of gas particles is pointed out. A strong correlation between the degree of dissociation, the concentration of metastable N2(A 3Σu+), N(2D,2P) particles, and surface kinetics is shown to exist. Spatially resolved measurements of the gas and wall temperatures, electron density, and wave propagation characteristics provide a validation of the model’s predictions.

Theoretical insight into Ar–O2surface-wave microwave discharges

“…Clearly a zero-dimensional model solves at each step a given cross section of the discharge tube, but the axial structure can nevertheless be obtained from the additional coupling of the wave-to-plasma power balance equation for the electron density gradient, as detailed in [37]. Herein we do not address the axial structure of the discharge, once we are essentially interested in the region close to the end of the discharge, defining the conditions for the afterglow.…”

“…Take note that an axial description of a surface wave discharge can be achieved by coupling the wave and the electron power equations. Such axial description goes beyond the purpose of the present research, but all details on how to do it can be found in [37], where a study of the axial structure of a surface wave nitrogen discharge was conducted.…”

Relaxation of heavy species and gas temperature in the afterglow of a N2 microwave discharge

“…To shorten this paper to an appropriate length, the reader should refer to references [4][5][6][7]9,11] for more details on collisional data, modelling aspects concerning the electron Boltzmann equation, microwave discharge and post-discharge conditions, to references [1,2,10,11] for additional information on gas heating mechanisms, gas thermal balance equation and energy data, as well as to [1,[13][14][15] for the values of the molar heat capacity and thermal conductivity under non-equilibrium conditions.…”

“…In these calculations, the high-frequency maintenance sustaining electric field in the plasma is self-consistently calculated for a cylindrical tube, imposing the quasi-neutrality condition and the requirement that under steady-state conditions the total rate of ionization must compensate exactly for the rate of electron loss by diffusion to the wall plus the electron-ion recombination. Additionally, as in [9], the gas thermal balance equation is incorporated in the system of equations. This equation determines the radially averaged gas temperature T g assuming a parabolic radial profile for the gas temperature and considering further that heat conduction is the main cooling mechanism.…”

“…This equation determines the radially averaged gas temperature T g assuming a parabolic radial profile for the gas temperature and considering further that heat conduction is the main cooling mechanism. Furthermore, this equation must account for all available energy to gas heating (translational mode) from volume and wall processes, described with detail in [1,2,[9][10][11][12].…”