ELTE Űrkutató Csoport

Propagation of electromagnetic signals in anisotropic plasma - wave propagation models

Waveforms recorded in space physics applications, wave experiments are electromagnetic waves that propagated in the magnetized (anisotropic) plasma medium. Another type is of waves is the oscillation of the medium itself (plasma waves). Emissions of natural origins are mostly short duration events with either coherent signals or unstructured, noise-like waves, due to their unknown phase. Waves describing the temporal changes of the magnetic and electric fields are generally wide-band or ultra-wide band (UWB) wave packets, or pulses.
Fourier-analysis, widely used for the description of electromagnetic waves propagating in the plasma, treats the signals as a composite of independent frequency components (monochromatic description). In this picture, the wave components, according to the refractive index that depends on the location in the medium and the frequency, propagate independently of each other, on different paths, from the source to the sensors of the recording equipment. In addition, the monochromatic model relies infinitely long harmonic components, which is an unreal assumption.

Thus, the monochromatic picture has a number of theoretical limitations that can also be shown experimentally. The ELTE Space Research Group started a development of wave propagation models in the 1990's, based on field theory and attempting to give an exact solution of the waveform, to be used in the interpretation of experimental measurements. This new model makes no assumption on the original, generating signal (arbitrary signals) before solving Maxwell's equations. The first results of this development are the closed-form solutions of the full-wave (arbitrary, e.g. Dirac) generating pulses propagating parallel to the magnetic field lines (i.e. longitudinally) in anisotropic, homogeneous or weakly inhomogeneous electron plasma [Ferencz 1978]. This was the first result in the history of wave propagation research that provided the waveform (in the time domain) of the electron-whistler as a coherent pulse. (It should be noted that the term full-wave (arbitrary shape) solution is also used on models where the wave pulse is a result of monochromatic wave packets, and therefore in these models the signal is in principle not a pulse, but clearly monochromatic, with all its disadvantages.)

Waveform (bottom) and frequency-time shape (top) of whistlers that propagated longitudinally in homogeneous plasma, calculated using different parameters for the medium. Here the nose-frequency of the whistlers, in agreement with theoretical considerations, is one quarter of the electron gyrofrequency [Fig 1.9 in Ferencz et al., 2001.].

O. Ferencz continued the development of the full-wave propagation model of solving Maxwell's equations. She gave exact solution to signals propagating obliquely (at an angle to the magnetic field), in plasmas of arbitrary ion components (ion-whistlers), lossy plasmas and in linear conducting structures [Ferencz et al., 2001.]. Subsequently, she gave a description of propagation in inhomogeneous plasmas, for arbitrarily large inhomogeneities, which are ubiquitous in space physics, and therefore important in the interpretatoin of actual measurements [Ferencz O. 2005]. The validity of this solution is not limited by the widely used WKB approximation, which is applicable only in case of weak inhomogeneities.

Picture of electron and proton whistler modes generated by the same source and propagating together, a result from the UWB solution. [Fig 2.30 in Ferencz et al., 2001.]

The general UWB solution is valid also in the frequency region above the electron gyrofrequency (the upper limit of whistler mode propagation). The lower part of the VHF signal generated by lightning strokes have been recorded as 'mega-whistlers' (so-called transionospheric pulse pairs, TiPP, [Holden et al., 1995]) on satellites in low Earth orbit. The measured waveform and dynamic spectrum can be reconstructed exactly using the above-mentioned model. When calulculating the full waveform, the effect of the magnetic field while propagating in the anisitropic plasma can be seen in the signal as a Faraday-rotation (in agreement with the measured signal).

The short pulse of the lightning stroke can propagate several thousand kilometers in the Earth-ionosphere waveguide before exiting to the plasma. They can be observed at low satellite altitudes as fractional-hop whistlers, traveling obliquely in the ionosphere. Such signals carry the signature of the propagation modes (tweek) along the surface. They appear in low-altitude measurements as so-called spiky whistlers (SpW) O. Ferencz et al., 2007]. Using a modular code based on the UWB solutions, propagation below the ionosphere, in the waveguide, and in the plasma can be modeled together. Tweeks measured at the Marion Island station of the AWDANET network (left) and modelled tweeks and SpWs measurable on LEO satellites (right).

References:
Ferencz Cs. (1978): Electromagnetic wave propagation in inhomogeneous media: Method of inhomogeneous basic modes; Acta Technica Ac. Sci. H., 86(1 2), 79.

Ferencz Cs., Ferencz O.E., Hamar D. and Lichtenberger J. (2001): Whistler Phenomena, Short Impulse Propagation. Kluwer Academic Publisher, Netherlands, 1-260. ISBN 0-7923-6995-5

Ferencz O. E. (2005): Full-wave solution of short impulses in inhomogeneous plasma. Pramana Journal of Physics, 64(2), 1-20. ISSN 0304-4289

Holden D.N., Munson C.P. and Devenport J.C. (1995): Satellite observations of transionospheric pulse pairs; Geophys. Res. Lett., 22, 889.

O.E. Ferencz et al., Ann.Geophys,25,1103,2007