Regular Article

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

¹ Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
² Departamento de Engenharia Física, Faculdade de Engenharia, Universidade do Porto, R. Dr. Roberto Frias, 4200-465 Porto, Portugal

^* e-mail: cdp@fe.up.pt

Received: 21 June 2017
Received in final form: 12 September 2017
Accepted: 25 September 2017
Published online: 13 October 2017

Abstract

In this paper we present a self-consistent kinetic model to study the temporal variation of the gas temperature in the afterglow of a 440 Pa microwave nitrogen discharge operating at 433 MHz in a 3.8 cm diameter tube. The initial conditions in the afterglow are determined by a kinetic model that solves the electron Boltzmann equation coupled to the gas thermal balance equation and a system of rate-balance equations for N₂(X ¹∑_g⁺, v) molecules, electronically excited states of N₂, ground and excited states of atomic nitrogen and the main positive ions. Once the initial concentrations of the heavy species and gas temperature are known, their relaxation in the afterglow is obtained from the solutions to the corresponding time-dependent equations. Modelling predictions are found to be in good agreement with previously measured values for the concentrations of N(⁴S) atoms and N₂(A ³∑_u⁺) molecules, and the radially averaged gas temperature T_g along the afterglow of a microwave discharge in N₂ under the same working conditions. It is shown that gas heating in the afterglow comes essentially from the energy transfer involving non-resonant vibration–vibration (V–V) collisions between vibrationally excited nitrogen molecules, as well as from energy exchanges in vibration–translation (V–T) on N₂–N collisions.