Whistler Wave Propagation in a Magnetic-Field Duct

P.V. Bakharev and A.V.Kudrin
Department of Radiophysics, University of Nizhny Novgorod
23 Gagarin Ave., Nizhny Novgorod 603950, Russia
Abstract. We study the guided propagation of whistler-mode waves in a constant-density magnetoplasma in the presence of
cylindrically symmetric enhancements of external axial dc magnetic field. It is shown that such nonuniformities, which may
be called magnetic-field ducts, are capable of guiding whistler eigenmodes whose properties are similar to those of density
depletions in a uniform magnetic field. The results of calculation of the dispersion characteristics and field structures of modes
guided by magnetic-field ducts are presented.
Keywords: magnetoplasma, whistler wave guidance, magnetic-field ducts
PACS: 52.35.Hr, 52.40.Fd
It has long been known that whistler-mode waves can be guided by ducts consisting of enhancements or depletions
of plasma density, or combinations thereof (see, e.g., [1, 2] and references therein). In contrast to much previous
work which applies to density ducts, there exists very little theory of phenomena caused by the guiding or trapping of
whistler-mode waves in structures that are formed by variation in other parameters of a magnetoplasma. In this paper
we study the guided propagation of whistler-mode waves in a constant-density magnetoplasma in the presence of a
cylindrically symmetric nonuniformity of an external axial dc magnetic field. Although the whistler wave guidance by
such plasma structures, also called magnetic tubes or magnetic-field ducts, was considered for the first time long ago
(see, e.g., [3]), earlier studies employed various approximate approaches such as the geometrical optics or the WKB
approximation. In the present work, the full-wave approach is used to analyze the features of whistler wave guidance
by a cylindrically symmetric enhancement of magnetic field.
Consider a cold unbounded collisionless magnetoplasma in which the magnitude of an external magnetic field
B0 = B0 ˆz0 is a function, B0(r), only of distance r from the axis of a cylindrical coordinate system (r,f, z). It is
a constant, ˜B0, in an inner core r < a0, a constant, Ba, in an outer region r > a1, and varies smoothly from ˜B0 to Ba
within the duct wall a0 <r <a1. For analysis, we chose a sinusoidal variation in the dc magnetic field between r =a0
and r = a1 with half-period a1−a0, giving a maximum magnetic-field gradient half way through the duct wall. Thus,
the magnetic-field profile for a0 < r < a1 is represented as
B0(r) = {˜B0+Ba+(˜B0−Ba) sin[p(a−r)/(a1−a0)]}/2, (1)
where a = (a0+a1)/2. It is assumed that ˜B0 > Ba and the wave frequency w belongs to the whistler range
wLH w wH wp, (2)
where wLH is lower hybrid frequency and wH and wp are the electron gyrofrequency and plasma frequency, respectively.
Recall that the dielectric tensor of a cold magnetoplasma is written as ˆe = e0(e ˆ r0 ˆ r0 −ig ˆ r0
ˆ f0 +ig ˆ f0 ˆ r0 +e ˆ f0
ˆ f0
+ hˆz0ˆz0), where e0 is the permittivity of free space. The quantities e, g, and h are determined by the medium
parameters and are given elsewhere (see, e.g., [4]). In what follows we denote the tensor elements for the regions
r < a0 and r > a1 by e˜ , g˜, and h˜ and ea, ga, and ha, respectively.
The fields of modes guided by the duct are represented.

We calculated the dispersion characteristics and field structures of whistler modes guided by the magnetic-field duct
in a constant-density magnetoplasma. It is shown that cylindrical enhancements of dc magnetic field are capable
of guiding whistler eigenmodes whose properties turn out to be similar to those of density depletions in a uniform
magnetic field (see [2]). It is evident from the presented results that for the used calculation parameters, the studied
modes of magnetic-field ducts can be observed in a laboratory magnetoplasma with radially nonuniform dc magnetic
This work was supported by the Russian Foundation for Basic Research (project No. 04–02–16506-a) and the Council
of the President of the Russian Federation for the State Support of the Leading Scientific Schools of the Russian
Federation (project No. NSh–1087.2006.2).
1. R. A. Helliwell, “40 years of whistlers,” in Modern Radio Science 1993, edited by H. Matsumoto, Oxford University Press,
New York, 1993, pp. 189–212.
2. I. G. Kondrat’ev, A. V. Kudrin, and T. M. Zaboronkova, Electrodynamics of Density Ducts in Magnetized Plasmas, Gordon
and Breach, Amsterdam, 1999.
3. R. N. Kaufman, Radiophys. Quantum Electron., 29, 579–585 (1986).
4. V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas, Pergamon Press, Oxford, 1970.

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