Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind

Abstract

The magnetic field in the interplanetary medium is formed by the action of magnetic field sources on the photosphere of the Sun and currents in the expanding atmosphere of the Sun and the solar wind. In turn, the high-speed plasma flow changes the configuration of the magnetic field lines. The problem of determining the parameters of the magnetic field near the Sun is thus a three-dimensional problem of the interaction of the magnetic field and the plasma of the solar wind. We present analytical expressions for calculating the total magnetic field vector B→(r, θ, ϕ) (in spherical coordinates) for a radially expanding solar wind flow of finite conductivity. The parameters of the solar wind are given in the form of a dimensionless magnetic Reynolds number given as an arbitrary function of the radius, r: Rm = rσμv=ξ(r), where σ, μ, and v denote, respectively, the conductivity, magnetic permeability, and velocity of the solar wind. The solution for the magnetic field components is obtained in the form of a decomposition in spherical functions and a radial part depending on the distance from the Sun. Examples of calculations of the configuration of magnetic fields and structures of the solar corona for the solar eclipse of 21 August 2017 are given.