SOLUTIONS OF THE PLASMA EQUILIBRIUM WITHIN THE MAGNETIC-FIELD OF A POINT DIPOLE

For axial symmetry, in this study we report on analytical solutions of the magnetohydrodynamics (MHD) equilibrium of a plasma within the mag netic environment of a point dipole. Inside the plasma domain, the mag netic flux function is calculated for a given shape of the pressure pr ofile. Another magnetic flux function is derived outside the plasma do main, where the pressure vanishes. Both functions and their normal der ivatives are continuous through the boundary between the two domains; together they constitute the solution of our problem. A pressure profi le that is a quadratic function of the magnetic flux function is used. It leads to an exact solution which is a simple function of the spher ical coordinates. It is shown that, in this situation, the plasma ener gy is distributed over the entire plasma domain. This solution is well suited as a magnetospheric model. The magnetic flux function determin ed outside the plasma domain is expressed by a very general formula th at is valid for wide classes of both the pressure profiles and the sha pe of a plasma exterior boundary. Far away from this boundary, as near the coordinate center, the magnetic field tends to be dipolar. (C) 19 98 American Institute of Physics. [S1070-664X(98)02808-0].