Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 69, p. 38-44 (2024)
TURBULENT ELECTRICAL CONDUCTIVITY AND TURBULENT MAGNETIC PERMEABILITY OF SOLAR PLASMA
Valery KRIVODUBSKIJ, DSc (Phys. & Math.)
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Abstract
Background. The observed 22-year solar cycle is a clear manifestation of the rapid variability of global magnetism in astrophysical conditions. Explaining the mechanism of the Sun’s magnetic cycle provides a key to understanding the nature of cosmic magnetism. However, the rapid change of the observed magnetic fields on the solar surface cannot be explained only by their ohmic diffusion. The theoretically calculated characteristic time of such diffusion (which is proportional to the product of the electrical conductivity of the plasma by the square of the scale of the magnetic field) is very large even by astronomical standards. Therefore, the search for new methods of studying the solar magnetized plasma becomes relevant. We believe that reducing the calculated duration of the reconstruction of magnetic fields on the Sun (according to the data of observations) can be achieved if we take into account MHD turbulence, which significantly accelerates the processes of attenuation and excitation of fields. Involvement in the consideration of turbulent motions in the plasma ended with the creation of macroscopic MHD (Kopecký, & Kuklin, 1969; Weiss, 1966), in the framework of which there is a significant decrease in the electrical conductivity and magnetic permeability of the medium, which causes a decrease in the calculated time of reconstruction of global magnetic fields. The purpose of this study is to calculate the coefficients of turbulent electrical conductivity and turbulent magnetic permeability of the solar plasma and to analyze changes in the spatio-temporal evolution of the global magnetism of the Sun taking into account these turbulent parameters.
Method. Macroscopic magnetohydrodynamics, which studies the behavior of global electromagnetic and hydrodynamic fields in turbulent plasma.
The results. The distribution along the solar radius of the coefficients of kinematic n, magnetic nm and turbulent nT viscosities, hydrodynamic Re and magnetic Rm Reynolds numbers, gas-kinetic σ and turbulent sT electrical conductivities, and turbulent magnetic permeability mT were calculated for the photosphere and SCZ models. The theoretically calculated parameters have the following values: n ≈ 0.2-10 cm2/s, nm ≈ 8×108-8×102 cm2/s, nT ≈ 1011-1013 cm2/s, Re ≈ 5×1011-5×1013, Rm ≈ 104-1010, σ ≈ 1011‑4×1016 SGS, σT ≈ 109-4×1011 SGS, mT ≈ 10-2-4×10-5. It is relevant that σT << σ, and mT << 1.
Conclusions. Our calculated turbulent magnetic diffusion DT = c2/4πsTmT turned out to be 4 to 9 orders of magnitude higher than the magnetic viscosity coefficient nm = c2 /4πσ, which is responsible for the ohmic dissipation of magnetic fields. As a result, it becomes possible to theoretically explain the observed rapid reconstruction of magnetism on the Sun. The radial inhomogeneity of the turbulent viscosity nТ and the condition mT << 1, revealed by us, testify to the strong macroscopic diamagnetism of the solar plasma.
Key words
Magnetic fields, turbulence, macroscopic MHD, electrical conductivity, magnetic permeability, macroscopic turbulent diamagnetism, magnetic activity of the Sun.
References
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