Propagation of magnetoacoustic waves in the solar atmosphere with random inhomogeneities of density and magnetic fields

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Abstract
The propagation of acoustic waves in a plasma containing an ensemble of tightly settled bundles of magnetic flux tubes is studied for the case where all the parameters of the medium-magnetic field, plasma density, temperature, etc.-change by an order of unity over a length small compared to the acoustic wave-length. Such a model of random and strong inhomogeneities can correspond, for example, to sunspots in the solar atmosphere, to plage regions, and to other astrophysical objects, where domains of different size with different plasma parameters compose a dense conglomerate. The theoretical procedure is described that allows one to obtain the average equations containing the nonlinearity of a wave, dispersion properties of a system, and dissipative effects. It is shown that the statistical properties of the medium determine different scenarios of wave propagation: in the predominance of dissipative effects the primary wave is damped away, and the efficiency of heating due to inhomogeneities is much greater than that in homogeneous medium. This means that the regions containing closely packed inhomogeneities behave as a strong sink of incoming wave energy. It is important that the efficiency of the wave absorption crucially depends on the amplitude of the fluctuations of the background parameters rather than on their absolute values. Depending on the interplay of nonlinear and dispersion effects, the process of heating can be afforded through the formation of shocks or through the storing of energy in a system of solitons which are later damped away. Our computer simulation supports and extends the above theoretical investigations. In particular, the enhanced dissipation of waves due to the strong and random inhomogeneities is observed, and this is more pronounced for shorter waves.

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