The equilibrium states of plasma in a potential external field with equipotential magnetic surfaces

Abstract

Introduction. In this paper, the equilibrium states of plasma in a potential external magnetic field with equipotential magnetic surfaces are considered. A theory is given and an equation for a one-parameter family of magnetic surfaces is described. A general solution for the system of equations of magnetic hydrodynamics and an equation describing a family of one-parameter equations are given. The behavior of the plasma is largely determined by the spatial structure that limits the magnetic field, that is, the curved coordinates E₃. As a result of the proof of the lemma, expressions for pressure, density, and magnetic field potential are obtained. For arbitrary functions (b) in E₃. The theorem is proved that in the coordinate system (x'), it does not contain a derivative of the variable x', this variable is included as a parameter in the equations. Materials and methods. General solutions for the equilibrium states of plasma in an external potential field in curvilinear coordinates have been obtained analytically. Results and discussion. In this paper we consider the possibilities from the obtained theory for constructing solutions to the equations which allow us to choose arbitrary functions in qualitatively independent variables. Using the mathematical package Maple, examples of graphical representation of solutions for pressure, density, magnetic field force lines and magnetic field strength square for equilibrium states of plasma in an external potential magnetic field with equipotential magnetic surfaces are given. Conclusion. The results of the study can be used to study the equilibrium states of plasma in a potential external magnetic field.