Radial expansion of the magnetohydrodynamic equations for axially symmetric configurations

We introduce a general expansion approach to obtain a fully consistent closed set of magnetohydrodynamic equations in two independent variables, which is particularly useful to describe axially symmetric, time-dependent problems with weak variation of all quantities in the radial direction. This is done by considering the hierarchy of expanded magnetofluid equations in cylindrical coordinates and equating terms with equal powers in the radial coordinate r. From geometrical considerations it is shown that the radial expansions of the pertaining physical quantities are either even series or odd series in r; this introduces a significant reduction in the number of variables and equations. The closure of the system is provided by appropriate boundary conditions. Among other possible applications, the method is relevant for the analysis of structure and dynamics of magnetic field concentrations in stellar atmospheres.