INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 34 (2001) 1474–1478 www.iop.org/Journals/jd PII: S0022-3727(01)20122-3 Propagation characteristics of electromagnetic waves along a dense plasma filament H Nowakowska 1 , Z Zakrzewski 1 and M Moisan 2 1 Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-952 Gda ´ nsk, Poland 2 D´ epartement de Physique, Universit´ e de Montr´ eal, Montr´ eal, Qu´ ebec, Canada H3C 3J7 Received 15 December 2000, in final form 2 March 2001 Abstract The characteristics of electromagnetic waves propagating along dense plasma filaments, as encountered in atmospheric pressure discharges, are examined in the microwave frequency range; they turn out to be surface waves. Results of numerical calculations of the dependence of the phase and attenuation coefficients on the plasma parameters are presented. In the limit of large electron densities, this guided wave is akin to a Sommerfeld wave and the propagation can be described in an analytical form. 1. Introduction This presentation deals with the propagation characteristics of electromagnetic waves, in the microwave frequency range, along a small diameter, dense plasma filament. Our interest in this subject stems from its relation to the modelling of microwave plasmas sustained at atmospheric pressure by travelling waves. It has been shown that the axial structure of discharges sustained by travelling waves is solely determined by the attenuation characteristics of the wave (see the detailed review and discussion in [1]). Therefore, when modelling such discharges, a knowledge of the propagation properties becomes of the utmost importance. When undertaking the present work, we had mainly in mind the constricted plasma column of a surface-wave-sustained discharge and also the plasma flame of a microwave plasma torch. Microwave discharges at atmospheric pressure are often radially constricted, i.e. they do not fully fill the discharge tube cross section [2, 3]. A similar effect can also occur at sub- atmospheric pressures exceeding a few Torr [4]. Depending on the operating conditions, these discharges generally take the form of one, or more, axially oriented plasma filaments. When sustained at atmospheric pressure by a travelling surface wave and in a tube with a small enough radius to ensure that they are wall-stabilized, these discharges appear as a bright, axially centred plasma filament [3, 5]. The microwave-plasma torch, in turn, yields a flame-like structure at the end of a metal electrode (usually the inner conductor of a coaxial waveguiding structure), directly in the surrounding atmosphere. It consists, in general, of a bright plasma filament, surrounded by a low intensity plasma shell and terminated by a tenuous plasma plume [6]. As for the discharge mechanism, it was suggested, almost half a century ago ([7], later followed by [8]), that the plasma flame is sustained by an electromagnetic wave guided along the filamentary discharge and dissipating energy within it. However, a definite conclusion on this matter is still pending since it requires the determination of the wave phase and attenuation characteristics and an appropriate experimental verification. This paper is organized as follows. First, the equations describing the propagation of a wave guided along a dense plasma are considered in the very general case: this wave will prove to be a surface wave. The corresponding results, from numerical calculations, of the dependence of the phase and attenuation coefficients on plasma parameters are presented. Second, it is shown that, in the limit of large electron densities, the surface wave acquires the character of a Sommerfeld-type wave [9] while the phase and attenuation coefficients can be expressed in an analytical form. Finally, results from the analytical and numerical calculations are compared. 2. Propagation characteristics of the wave. General case In this work we consider the propagation of an electromagnetic wave along a uniform plasma cylinder surrounded by free space. Such a simplified model of a two-medium wave propagation is based on two main assumptions. One is that the actual, radially varying, plasma parameters can be replaced by properly chosen average values. The other is that the omission of the dielectric discharge tube in cases where it experimentally envelopes the plasma does not significantly 0022-3727/01/101474+05$30.00 © 2001 IOP Publishing Ltd Printed in the UK 1474