Astronomy and Astrophysics – Astrophysics – Solar and Stellar Astrophysics
Scientific paper
2010-05-25
Astron. Astrophys. 429, 779-784 (2005)
Astronomy and Astrophysics
Astrophysics
Solar and Stellar Astrophysics
Scientific paper
10.1051/0004-6361:20041624
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 $\delta=\E\cdot\B$ along $\B$ on the vacuum side (with $\E$ denoting the electric field and $\B$ 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 $\B$ which is either uniform or radial (monopolar).
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