Theory of azimuthal surface waves propagating in non-uniform waveguides

Abstract

This paper is devoted to the theory of surface waves propagating across axis of symmetry in non-uniform cylindrical metal waveguides with plasma filling. The presented results are devoted to: first, studying an influence of plasma density non-uniformity on the features of these waves; second, studying an influence of an external magnetic fields' non-uniformity on their dispersion properties; third, studying possibility to sustain gas discharge by propagation of these waves under different operating regimes. The problems have been solved both analytically and numerically. Plasma particles are described in the framework of hydrodynamics; fields of the studied waves are determined by a set of Maxwell equations. Analytical research of the obtained equations is carried out by the method of successive approximation; adequacy of such approach is proved here as well. Numerical evaluations of the possibilities to observe experimentally the phenomena, which accompany propagation of these waves, are carried out.

Excitation of Azimuthal Eigen Modes by Modulated Annular Electron Beam

“…In the case, when flows of charged particles are absent in the region R 2 > r > R 1 (it means j r = j ϕ = 0 and hence F b = 0) expressions for the AMs coincide with that are obtained in [6] for studying dispersion properties of these modes in the case of a dense plasma (Langmuir frequency is larger than electron cyclotron frequency). Thus for tangential components of the AMs fields one can derive the following expressions in the region occupied by the electron beam:…”

“…the AMs propagating in the considered waveguide (see [6]) under the condition of α b = 0 (that means absence of the beam), R j = r j Ω e c −1 is dimensionless radial co-ordinate of the j-th particle of the beam. It is suitable for formulate momentum equation, which describes the beams' electrons motion, using terms of their impulses p = γm e V (γ is relativistic factor), because it allows one to take into the account a weak relativism of the beam:…”

“…According to results of [6], AM can propagate in the range of electron cyclotron frequency in such waveguides if inequality z < 1 is satisfied, so we apply here this condition.…”

“…Solution of the set of equations for amplitude (6) and phase (7) of the AMs envelope, motion equations for the beams' electrons (10)- (12) has been found by the Runge-Kutta method of the fourth order, which is widely used for the research of such problems [1,2,14,15]. Quantity of the beams' macro -particles was assumed to be here N = 2000.…”

“…This allows one to develop radio-electronic devices, which operate at modes with interesting features like non-reciprocal waves or unidirectional waves. Among them, it should be indicated azimuthal eigen modes, which propagate in cylindrical plasma filled waveguide structures across an external steady axial magnetic field [6]. As it is shown in [7] azimuthal modes (AMs) can be excited by charged particle beams rotating above plasma interface across a strong external steady axial magnetic field.…”