EDP Sciences
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Volume 429, Number 3, January III 2005
Page(s) 779 - 784
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20041624

A&A 429, 779-784 (2005)
DOI: 10.1051/0004-6361:20041624

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

J. J. Aly

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 )

A force-free surface (FFS)  ${\cal S}$ 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  ${\cal S}$ a simple relation between the charge density  $\mu$ on the plasma side and the derivative of  $\delta={\vec E}\cdot{\vec B}$ along  ${\vec B}$ on the vacuum side (with  ${\vec E}$ denoting the electric field and  ${\vec B}$ the magnetic field). Combined with the condition  $\delta=0$ on  ${\cal S}$, this relation implies that a FFS has a general stability property, already conjectured by Michel (1979, ApJ 227, 579):  ${\cal S}$ turns out to attract charges placed on the vacuum side if they are of the same sign as  $\mu$. 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  ${\vec B}$ which is either uniform or radial (monopolar).

Key words: stars: pulsars: general -- magnetic fields -- plasmas

© ESO 2005