Dispersion properties and field structures of eigenmodes of nonuniform plasma waveguides in a longitudinal magnetic field

Abstract

We study the field structure and dispersion properties of a hybrid eigenmode guided by a nonuniform magnetized plasma waveguide. It is shown that the rotational and quasi-potential waves contribute to the formation of such a mode in the whistler frequency range. Depending on the plasma density, the rotational component of the hybrid mode is determined by either waves with complex transverse wave numbers or whistler waves, or by true surface waves. In the presence of an axial nonuniformity of the plasma in a channel, the transverse field structure of the propagating mode changes, which is stipulated by changes in both the values of transverse wave numbers and their dependence on the radial coordinate. It is found that the spectrum of axial wave numbers of eigenmodes of a plasma waveguide undergoes a pronounced condensation when smoothing the waveguide walls. The damping of the hybrid mode of a nonuniform waveguide due to electron collisions is found and it is shown that collisional losses determine the damping of waves trapped in the waveguide in the experiments on ionization self-channeling of whistler waves. We have found the effect of "displacing" the strong field from the inner core to the background outer region of the waveguide with increasing plasma density on its axis and broadening background region.

Features of the dispersion characteristics of nonuniform plasma waveguides in a longitudinal magnetic field

“…From the boundary conditions on the interfaces of the multilayer waveguide, dispersion relations (7) and (8) for cylindrical waves in the uniform regions, and the requirement that the field decays for r > b, one can obtain a system of 28 equations. Its solution determines axial wave numbers and relationships between the coefficients A m , B m , C m , and D m for given parameters of the plasma in the waveguide.…”

“…The presentation of a waveguide as a uniform circular cylinder [5,6] or a uniform cylindrical tube [7] is conventional and significantly simplifies the determination of the dispersion characteristics of such waveguides and the field structures of their eigenmodes. However, the side walls of actual plasma waveguides (density ducts and discharge channels) are always smooth, and the background sheathes are often present [8]. In the nonuniform near-wall region of the waveguide, resonance surfaces, in the vicinity of which the diagonal elements of the dielectric permittivity tensor are close to zero, can appear maxima in the distribution of the wave-field amplitude are observed [9], and the damping is relatively high.…”

“…Representing the electron number (plasma) density in the cross section of the waveguide by a stepwise function [8], one can easily see that the field of a nonuniform waveguide is formed by fields of cylindrical waves of various types (plasma, or quasi-potential waves [9], electromagnetic whistler waves [6,9], and waves with complex-conjugate transverse wave numbers [6,10]), which can be of volume, surface, or leaky character. Depending on the plasma density at the step and the magnitude of the magnetic field, contributions of these waves to the total field and their transverse wave numbers can differ significantly when passing from one step to another (the real wave numbers can transform to complex or imaginary ones, and vice versa).…”

“…This work is the continuation of [8] and comprises new data on the features of the dispersion characteristics and field structures of eigenmodes of nonuniform plasma waveguides in a longitudinal magnetic field for significantly different values of the external magnetic field, the plasma density, and the scales of its transverse nonuniformity. The distribution of plasma density in the cross section of the waveguide was chosen in the form of seven (and more) steps in the power-law distribution N = N 0 /[1 + (r/R ⊥ ) 3 ], where N 0 is the plasma density on the waveguide axis and R ⊥ is the scale of a twofold decrease in plasma density.…”

10.1007/s11452-008-3009-x

“…Based on the results obtained in the model of a uniform plasma column, RF discharges excited by waves in this frequency range are often referred to as helicon discharges [3][4][5]. However, it can easily be shown [6] that, if the plasma density on the axis of a narrow ( a Ӷ λ vac , where a is the waveguide radius and λ vac is the radiation wavelength in vacuum) nonuniform plasma waveguide is much higher than the critical density ( ω pe (0) ӷ ω ), then the contribution from helicons to the field of the eigenmodes of such a waveguide is negligibly small.…”