IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 41 (2008) 015210 (9pp) doi:10.1088/0022-3727/41/1/015210 Self-consistent spatio-temporal simulation of pulsed microwave discharge Z Bonaventura, D Trunec, M Meˇ sko, P Vaˇ sina and V Kudrle Department of Physical Electronics, Faculty of Science, Masaryk University, Kotl´ aˇ rsk´ a 2, 611 37 Brno, Czech Republic E-mail: zbona@physics.muni.cz Received 24 April 2007, in final form 17 October 2007 Published 19 December 2007 Online at stacks.iop.org/JPhysD/41/015210 Abstract A spatio-temporal theoretical model of pulsed microwave discharge was developed. This model is based on the macroscopic continuity equation for electrons and on the wave equation for an electromagnetic wave passing through the discharge plasma. These equations were solved together and in a self-consistent manner. For simplicity, the continuity equation was solved in one dimension only and the electromagnetic wave was assumed to be plane and transversal. Both equations were solved numerically and the spatio-temporal dependences of electron concentration and the amplitude of the microwave electric field were obtained. It was found that the discharge development depends, significantly, on the initial spatial distribution of electron concentration. Two different cases were studied: the discharge development during the first microwave pulse only and after several successive pulses. The calculations were performed particularly for the discharge in nitrogen. The results were compared with experimental data from our previous work. M Animations of the time development of figures 7, 8 and 9 are available in the online edition at http://stacks.iop.org/JPhysD/41/015210 1. Introduction Pulsed microwave discharges have already been studied by our group both experimentally and theoretically. In the experiment [1] the time dependences of electron concentration, transmitted microwave power and selected nitrogen band intensities were measured for pulsed microwave discharge in nitrogen. The electron distribution function and macroscopic parameters (mean energy, ionization and diffusion coefficients, etc) were obtained from the solution of the Boltzmann equation [2, 3] for the conditions corresponding to the experiment. It was found that microwave power is significantly absorbed and/or reflected by the discharge plasma. To take into account this effect, it is necessary to solve the wave equation for the electromagnetic wave passing through the plasma. The influence of plasma on the wave propagation is described by complex conductivity. Solving the wave equation, the spatial distribution of electric field strength amplitude, E 0 , is obtained and this quantity is used to determine the ionization and diffusion coefficients and the complex conductivity. These coefficients are dependent on E 0 . The time development of electron concentration is described by the continuity equation with corresponding source and loss terms. Since the electromagnetic wave influences the electron concentration and the propagation of the wave is influenced by the electron concentration, it is necessary to solve the wave equation and the continuity equation together in a self-consistent manner. During our experimental work [1] several interesting questions arose. Where and when exactly is the discharge ignited? Is the observed stratification caused by the wave reflection from plasma? The model presented in this paper was developed in particular to answer these questions and consequently to gain a better understanding of temporal behaviour in this type of plasma. For simplicity, the calculations were performed in one spatial dimension only and the electromagnetic wave was assumed to be plane and transversal. Pulsed microwave discharge in nitrogen was studied experimentally and theoretically by Baeva and co-workers [4, 5] and Repsilber et al [6]. However, the theoretical models in these studies were not self-consistent; they were based on the numerical solution of the Boltzmann equation 0022-3727/08/015210+09$30.00 1 © 2008 IOP Publishing Ltd Printed in the UK