A stability property of a force-free surface bounding a vacuum gap

CEA/DSM/DAPNIA, Service d'Astrophysique (CNRS FRE 2591), CE Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: jjaly@discovery.saclay.cea.fr

Received: 9 July 2004
Accepted: 8 September 2004

Abstract

A force-free surface (FFS)  is a sharp boundary separating a void from a region occupied by a charge-separated force-free plasma. It is proven here under very general assumptions that there is on  a simple relation between the charge density μ on the plasma side and the derivative of  along  on the vacuum side (with  denoting the electric field and  the magnetic field). Combined with the condition  on , this relation implies that a FFS has a general stability property, already conjectured by Michel (1979, ApJ 227, 579):  turns out to attract charges placed on the vacuum side if they are of the same sign as μ. In the particular case of a FFS existing in the axisymmetric stationary magnetosphere of a “pulsar”, the relation is given a most convenient form by using magnetic coordinates, and is shown to imply an interesting property of a gap. Also, a simple proof is given of the impossibility of a vacuum gap forming in a field  which is either uniform or radial (monopolar).