Electrical Conductivity and Magnetic Permeability of Magnetohydrodynamic Turbulent Plasma of the Sun

Abstract

According to classical magnetohydrodynamics, the magnetic fields on the Sun are characterized by huge theoretically calculated time intervals of their ohmic dissipation due to the high inductance caused by the large size of the fields and the high gas kinetic electrical conductivity of the plasma. This is in striking contrast to the observed rapid changes in the structure of solar magnetism. To solve such a contradiction, it becomes relevant to search for new methods of studying magnetized plasma. Research efforts to consider turbulent motions in the plasma ended with the creation of macroscopic magnetohydrodynamics (MHD), within which substantial decreases in the electrical conductivity and magnetic permeability leading to a decrease in the calculated time of reconstruction of global magnetic fields are found. This study aims at calculating the coefficients of turbulent electrical conductivity and turbulent magnetic permeability of the solar plasma and analyzing changes in the spatiotemporal evolution of the global magnetism of the Sun considering these parameters. Macroscopic MHD methods are used for studying the behavior of global electromagnetic fields and hydrodynamic motions in turbulent plasma. For models of the photosphere and convection zone of the Sun, the distributions of the following parameters along the solar radius are calculated: coefficients of kinematic (ν), magnetic (ν_m), and turbulent (ν_T) viscosities; hydrodynamic (Re) and magnetic (Rm) Reynolds numbers; gas kinetic (σ) and turbulent (σ_T) electrical conductivities; and turbulent magnetic permeability μ_T. The theoretically calculated parameters have the following values: ν = 0.2–10 cm²/s; ν_m = 6 × 10⁸–8 × 10² cm²/s; ν_T = 10¹¹–10¹³ cm²/s; Re = 5 × 10¹¹–5 × 10¹³; Rm = 10⁴–10¹⁰; σ = 10¹¹–4 × 10¹⁶ CGS; σ_T = 10⁹–4 × 10¹¹ CGS; μ_T = 10^–2–4 × 10^–5. It is essential that σ_T \( \ll \) σ and μ_T \( \ll \) 1. Calculated turbulent magnetic diffusion D_T = c²/4πσ_Tμ_T turned out to be four to nine orders of magnitude higher than magnetic viscosity coefficient ν_m = 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. We have revealed the radial inhomogeneity of turbulent viscosity ν_T and condition μ_T \( \ll \) 1, which are indicative of the strong macroscopic diamagnetism of the solar plasma. In the lower part of the solar convection zone, the latter performs the role of negative magnetic buoyancy, thereby contributing to the formation of a magnetic layer of a steady state toroidal magnetic field of B_S ≈ 3000–4000 G near the bottom of the solar convection zone.