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Symmetric Surface Waves In Cylindrical Waveguide Structures With Radially Non-Uniform Plasma Filling

Yu. A. Akimov, V. P. Olefir and N. A. Azarenkov
Karazin Kharkiv National University, 31 Kurchatov av., 61108 Kharkiv, Ukraine
Abstract. This report is devoted to the dispersion properties of high-frequency axial symmetric potential surface waves propagating in a cylindrical waveguide structure. It is supposed to consist of the radially non-uniform plasma layer, partially filling the metal waveguide and immersed in an external axial magnetic field. The influence of the waveguide structure parameters, as well as the magnetic field value, on frequency, phase and group velocities, resonance damping of the surface waves is investigated both numerically and analytically.
Keywords: Surface waves, plasma waveguides, collisional and resonant damping
PACS: 52.35.Fp
INTRODUCTION
At the present time, intensive research on surface wave (SW) properties and their application to sustain gas discharge are carried out [1]. Increasing of plasma heating efficiency is one of the important problems in discharge maintenance by SWs under low gas pressure. At those conditions, the collision mechanism of SW power transfer to a plasma becomes ineffective. It stipulates the study of collisionless methods of plasma heating [2-4]. One of them is a resonant absorption of SWs that takes place in those plasma regions where the wave frequency is close to the upper hybrid one [5, 6].
In gas discharge and solid-state electronics multilayer structures are studied equally with ordinary planar and cylindrical waveguide structures. In gas discharge, a cylindrical coaxial plasma can be created by tubular beams propagating along an external axial magnetic field [7]. The aim of this paper is the theoretical study of plasma parameters and external magnetic field influence on propagation and resonant damping of symmetric SWs in coaxial vacuum-plasma-vacuum-metal structures.
TASK STATEMENT
Let us consider high-frequency axial symmetric potential SWs that propagate along a cylindrical waveguide structure, which consists of a radially non-uniform plasma layer partially filling a metal waveguide with a radius . The radial distribution of the plasma density is uniform, R0nn=, in the region dRrdR−<<+21 and varies from to zero in the transition regions 0ndRrR+<<11 and dRrR−<<22, where and are the internal and external radiuses of the plasma layer. Let us assume that the transition regions are small, . It allows to neglect the dependence of the SW dispersion on the plasma density non-uniformity [8], whereas its influence on the resonant wave damping at the upper hybrid resonance is essential. An external steady magnetic field, , is supposed to be directed along the waveguide structure axis. The plasma is described in the hydrodynamic approach, as a cold weakly collision medium with an effective electron collision frequency 1R2Rd<<1R0Hων<<, whereω is the wave frequency.
Equations describing the wave propagation consist of the particle motion and continuity equations, as well as Poisson’s equation. Solving them and applying then the boundary conditions consisting of the continuity of the potential and normal component of the electric induction vector at the interfaces vacuum – non-uniform plasma – uniform plasma – non-uniform plasma – vacuum gap – metal, the following dispersion relation can be obtained

Plasma Thickness Influence
Influence of the ratio of the external and internal radiuses of the plasma layer, , on properties of the SWs is investigated also. It is shown both numerically (fig. 3a) and analytically (2) that an increase of the parameter results in a decrease of the phase velocity of the waves propagating at the internal boundary of the layer. The phase velocity dependence for the waves at the external boundary of the layer on its width is more complicated. So, if the vacuum gap is wide enough, an increase of the layer thickness results in a growth of the SW phase velocity. However, at a fixed value of the metal radius, an increase of results in a decrease of the vacuum gap width. In this case, a decrease of the SW phase velocity by the metal coming to the plasma appears more essential, than its growth owing to the increase of the plasma layer width. Their relation for the case of a narrow waveguide is described by (3), and for the waveguide of a finite size is presented in fig. 3b (curve 4). 12/RR12/RR2R
024680.750.800.850.900.951.004321k3R1ω/Ωea024680.30.40.50.60.74321k3R1ω/Ωeb
FIGURE 3. Influence of the plasma layer thickness on the dispersion of SWs propagating at the internal (a) and external (b) boundaries of the cylindrical plasma layer, in the case of =2.1 and 1/RReeΩω/=0.3. The curves 1-4 correspond to =1.1; 1.3; 1.5; 2.0. 12/RR
CONCLUSIONS
In this paper, the dispersion properties and damping rates of the high-frequency axial symmetric potential surface waves propagating in the cylindrical metal waveguide partially filled with the radially non-uniform plasma immersed to the external steady axial magnetic field have been studied. The influence of the waveguide structure parameters and values of the external magnetic field on the frequency, phase, and group velocities, as well as on resonant attenuation, of the SWs has been investigated both numerically and analytically. It has been shown that the group velocity of the waves propagating at the internal and external interfaces of the cylindrical layer, have opposite signs. It has been obtained that the frequency of SWs, which can propagate at the internal plasma boundary, is greater than the frequency of SWs propagating at the external boundary. It has been shown that the metal has an essential influence on the waves propagating at the external boundary, decreasing their phase velocity, as it comes close to the plasma. An increase in the external magnetic field has been shown to cause a growth of the wave frequency, whereas the area of axial wavenumbers, at which the waves exist, decreases. The phase velocity of SWs propagating at the external and internal plasma boundaries has been shown to essentially depend on the layer width.
REFERENCES
1. M. Moisan, J. Hurbert, J. Margot and Z. Zakrzewski, “The Development and Use of Surface-Wave Sustained Discharges for Applications,” in Advanced Technologies Based on Wave and Beam Generated Plasmas, edited by H. Schlüter and A. Shivarova, Amsterdam: Kluwer Academic Publisher, 1999, pp. 1-42.
2. Yu. M. Aliev, A. V. Maximov, U. Kortshagen, H. Schluter and A. Shivarova, Phys. Rev. E 51, 6091 (1995).
3. A. Shivarova and Kh. Tarnev, Plasma Sources Sci. Technol. 10, 260 (2001).
4. H. Schlüter, A. Shivarova and Kh. Tarnev, Plasma Sources Sci. Technol. 10, 267 (2001).
5. K. N. Stepanov, Sov. Phys.-Tech. Phys. 10, 773 (1965).
6. Yu. A. Romanov, Sov. Phys.-Tech. Phys. 47, 2119 (1964).
7. N. I. Kabushev, Yu. A. Kolosov and A. I. Polovkov, Sov. J. Plasma Phys. 18, 27 (1992

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