PROBLEMS OF GEOCOSMOS

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
ANHARMONICITY OF THE ULF GEOELECTROMAGNETIC WAVES
A.V. Guglielmi 1 , B.I. Klain 2 , O.D. Zotov 2
1 Institute of Physics of the Earth, RAS, Moscow, Russia, e-mail: guglielmi@mail.ru;
2 Geophysical Observatory Borok, IPE, RAS, Borok, Russia, e-mail: ozotov@inbox.ru
Abstract. The theory of ponderomotive forces predicts the anharmonicity of standing Alfvén
waves. The goal of our work is to find an experimental evidence of the anharmonicity of Alfvén
oscillations of the Earth’s magnetosphere by using the ground based observation of the ULF waves
in the Pc3 frequency band. The method of remote diagnostics of the oscillating magnetic shells,
the spectral-polarization method and the method of synchronous detection are used. As the result
the true signs of anharmonicity of the ULF waves are found.
Keywords: Alfvén waves, ULF electromagnetic waves, ponderomotive forces.
1. INTRODUCTION
There are two reasons to believe that the ULF electromagnetic waves in the magnetosphere are the
nonlinear waves. The first reason is that the energy density of the magnetic field oscillations is of the order
of the background plasma pressure. The second one is that the ULF and other types of electromagnetic
waves in the magnetosphere arise mostly as a consequence of plasma instabilities. This results in the selfexcitation
of the diversity of nonlinear wave structures. A common property of the nonlinear waves is the
appearance of time-averaged ponderomotive forces providing the specific mechanisms of the wave-particle
interaction [Lundin and Guglielmi, 2006].
Ponderomotive forces of a standing Alfvén wave acts such that the plasma is pushed out of the nodes
and gathers at the antinodes of the electric field. This results in specific anharmonicity effects in the
oscillations. It would be very useful to analyze the observational manifestations of anharmonicity. With this
aim we have proposed new methods for analyzing ULF wave data. One method is based on the location of
the oscillating magnetic shells. One more method is based on the analyzing of the amplitude dependence of
the wave polarization by using the Stokes parameters. (More general approach is based on the extraction of
the nine Roman’s invariants from the wave data.) At last, the synchronous detection method may be used to
study the nonlinear generation of the 2 nd harmonics. In this paper we describe shortly some preliminary
results.
2. ULF RANGEFINDER
The ground based method of remote diagnostics of the oscillating magnetic shells by using the socalled
ULF rangefinder is described in the paper (Lundin and Guglielmi, 2006). This method provides a way
of estimating the distance x along the meridian from the observation point to the magnetic shell which
R
resonantly oscillates with the period T. It has been found that the distance and the period are both amplitude
dependent, suggesting that the standing Alfvén waves in the magnetosphere exhibit the nonlinear property of
anharmonicity. Here we would like to present some additional analysis of the experimental data presented in
the above-mentioned paper.
First of all let us note that by analogy with a mechanical oscillator we can really expect the
nonlinearity to cause effects of anharmonicity of the standing Alfvén oscillations. In particular, the quadric
dependence of the period on the oscillations amplitude is expected: T = T0+ χI
. Here T0
is the period of
2
infinitesimal oscillations ( I → 0 ), χ is the coefficient of nonlinearity, I ∝ H is the intensity, and H is the
amplitude. We would like to discuss the questions: How to detect the anharmonicity, and how to estimate the
coefficient χ by observation of the ULF oscillations?
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