Ion acoustic envelope solitons in explosive ionospheric experiments
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SPHERIC PLASMA
Ion Acoustic Envelope Solitons in Explosive Ionospheric Experiments I. Kh. Kovaleva Institute of Geosphere Dynamics, Russian Academy of Sciences, Leninskiœ pr. 38-1, Moscow, 119334 Russia Received May 15, 2007
Abstract—The conditions are studied under which stable ion acoustic envelope solitons propagating perpendicular to the magnetic field lines can exist in the ionospheric plasma. The amplitudes, frequencies, and lengths of the waves are determined. The results obtained are compared with the experimental data. It is suggested that such solitons play an important role in both the formation of an ionization front and its motion across the magnetic field and also give rise to a fluctuation precursor in explosive ionospheric experiments. PACS numbers: 52.35.Sb, 94.20.Tt DOI: 10.1134/S1063780X0801008X
1. INTRODUCTION
ities, frequencies, and wavelengths. The theoretical results are compared with the experimental data, and the possible role of ion acoustic envelope solitons in the formation of the ionization front of an expanding plasma is discussed.
Interest in such nonlinear plasma phenomena as solitons, plasma vortices, etc. has stimulated the development of many new methods for describing them in both theoretical calculations and experimental data processing. One of the experimental methods for processing fluctuation signals is provided by wavelet analysis, which is best suited for revealing short signals and recording their frequencies. The wavelet method is widely used in a variety of investigations of laboratory plasmas [1–4]. In [5, 6], this method was applied to analyze electric field fluctuations at the boundary of a plasma produced in the course of an explosive experiment in the Earth’s ionosphere. In the experiment, short signals (having several periods) at ion acoustic frequencies were recorded in a direction perpendicular to the magnetic field and along the plasma density and temperature gradients. The signals were observed to be one-dimensional. An instrumental function was recognized in the fluctuation spectra [7–9]. It can thus be concluded that the signals recorded are short-wavelength ion acoustic envelope solitons propagating in the direction of the gradients across the magnetic field. The wavelength of these signals was much less than the ion gyroradius. This is why, in my earlier paper [5], they were described in the approximation in which the ions are unmagnetized and the plasma has steep density and temperature gradients, an approximation that was used in [10] and leads to a one-dimensional (1D) nonlinear Schrödinger equation (NSE) for the wave electric field. Envelope solitons are known to be one of the solutions to this equation. In the present paper, this approximation with the NSE supplemented by additional ion dissipative terms is used to obtain solutions in the form of stable envelope solitons. The plasma conditions under which the solitons can exist are investigated, as well as the main soliton parameters, such as amplitudes, veloc-
2. NONLINEAR SCHRÖDINGER EQUATION WIT
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