Rotating Magnetosphere: Far-Field Solutions

Abstract

General principles are established for the solution of the distant magnetic field structure about a rotating axisymmetrically magnetized object surrounded by plasma of negligible inertia. These principles are applied to the interesting case of a dipole magnetic field (as well as the monopole case) and can readily be extended to any other axisymmetric multipole. Analytic solutions are shown, and we thereby compute relevant physical quantities (charge density, magnetic field intensity, torque, etc.). The result, that the magnetic field lines form a perfect universal Archimedean spiral according to the relationship tan = wp/c, is found to be general and applies to all axisymmetric multipoles in the zero inertia limit. In the above equation, is the angular deviation of the field line from radial, w is the rotation rate, p is the distance from the rotation axis, and c is the velocity of light. Also general, the flow velocity is everywhere purely radial and equal to c. Subject headings: hydromagnetics - magnetic stars - rotation