Higher radial modes of azimuthal surface waves 
in magnetoactive cylindrical waveguides
V. Kondratenko (Prof. I. Girka)
ВИЩІ РАДІАЛЬНІ МОДИ АЗИМУТАЛЬНИХ ПОВЕРХНЕВИХ ХВИЛЬ

В МАГНІТОАКТИВНИХ ЦИЛІНДРИЧНИХ ХВИЛЕВОДАХ
Кондратенко В.М. (проф. Гірка І.О.)

	

	Fig. 1. Schematic of the problem

	

	Fig. 2. Dependence of ASW eigen frequency normalised by |ce| vs effective wave number kef=|m|c/(ea). d=4, (ba)/a=3, m=1, e /|ce|=10. Numerals nearby the lines denote the numbers of the radial modes
 


Both analytical and numerical studies of the dispersion properties of higher radial modes of electromagnetic surface type waves which propagate in cylindrical waveguides with axial external stationary magnetic field which are partially filled by plasma along the small azimuth are carried out. These branches complement the previous results of [1, 2] obtained for the zero-th radial mode and of [3] obtained for the waveguides without external stationary magnetic field. Better conditions for these higher radial modes propagation are observed for the waves with larger azimuthal wave numbers in the waveguides with wider dielectric layer, and larger dielectric constant. Approximate expression 

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ç

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æ

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b

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m

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b

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,       (1)
satisfactory describes the eigen frequency splitting by external magnetic field. In (1), ce is electron cyclotron frequency, =c/e is skin-depth, e is Langmuir frequency, l is radial wave number, d is dielectric constant of the layer, ba is the width of the layer, 1,2 are the components of the plasma dielectric permittivity tensor. Possibility of ASW higher radial modes propagation is proved for small values of effective wave number, i.e. in the waveguides with large radius of plasma column and plasma density. The demerit of the ASW higher radial modes dispersion properties is that a change in plasma waveguide parameters causes drastic change in ASW eigen frequency. This is in contrast to the possibility of getting advantage of smooth frequency tuning for the ASW zero-th radial mode.

The advantage of ASW higher radial modes is that their eigen frequencies are larger than those of the zero-th radial modes effectively studied earlier. In other words, ASW higher radial modes propagate with shorter vacuum wave length than the zero-th modes. These results promise to be of interest for the purposes of plasma electronics. 
1. V. Girka, I. Girka and M. Thumm. Surface Flute Waves in Plasmas: Theory and Applications, Heidelberg: Springer, 2014.

2. V. Girka, I. Girka, A. Kondratenko and V. Tkachenko. Azimuthal Surface Waves of Magnetoactive Plasma Wavequides// Soviet Journal of Communications Technology and Electronics. 1988. v. 33, No. 8, 37-41.
3. I. Girka, I. Omelchenko and R. Sydora. Higher Radial Modes of Azimuthal Surface Waves in Cylindrical Waveguides Without External Magnetic Field // Progress In Electromagnetics Research M. 2017, v. 54, 1-7.

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