On the "force-free surface " of the magnetized celestial bodies

TL;DR

This paper analyzes the force-free surface of a magnetized rotating sphere, deriving its equation at any distance, and discusses particle trapping and the influence of centrifugal force near the light cylinder.

Contribution

It provides a general equation for the force-free surface of a rotating magnetized sphere and examines particle dynamics and the effects of centrifugal force near the light cylinder.

Findings

The force-free surface can trap particles with strong radiation damping.

Outside the light cylinder, the surface moves superluminally.

Centrifugal force is negligible except near the light cylinder.

Abstract

The field of a uniformly magnetized rotating sphere is studied with special attention to the surface where the electric and magnetic fields are orthogonal to each other. The equation of this surface, valid at arbitrary distances from the rotating magnetized sphere, is obtained. Inside the light cylinder this surface can be considered as a force-free surface, i.e. as a place where the particles with strong radiation damping can be trapped due to their energy loss. Outside the light cylinder this surface makes just a geometric locus which moves with a superlight velocity around the axis of rotation. The 2- and 3-dimensional plots of the force-free surface are constructed. Estimation of influence of the centrifugal force on the particle dynamics is made. It is shown, that in case of strong magnetic field the centrifugal force is negligible small everywhere except a narrow neighbourhood of the light cylinder.