A&A 429, 779-784 (2005)
A stability property of a force-free surface bounding a vacuum gapJ. J. Aly
CEA/DSM/DAPNIA, Service d'Astrophysique (CNRS FRE 2591), CE Saclay, 91191 Gif-sur-Yvette Cedex, France
(Received 9 July 2004 / Accepted 8 September 2004 )
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 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 . 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).
Key words: stars: pulsars: general -- magnetic fields -- plasmas
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