We present, for the first time, the structure of the axisymmetric force-free magnetosphere of an aligned rotating magnetic dipole, in the case in which there exists a sufficiently large charge density (whose origin we do not question) to satisfy the ideal MHD condition, ${\bf E\cdot B}=0$, everywhere. The unique distribution of electric current along the open magnetic field lines which is required for the solution to be continuous and smooth is obtained numerically. With the geometry of the field lines thus determined we compute the dynamics of the associated MHD wind. The main result is that the relativistic outflow contained in the magnetosphere is not accelerated to the extremely relativistic energies required for the flow to generate gamma rays. We expect that our solution will be useful as the starting point for detailed studies of pulsar magnetospheres under more general conditions, namely when either the force-free and/or the ideal MHD condition ${\bf E\cdot B}=0$ are not valid in the entire magnetosphere. Based on our solution, we consider that the most likely positions of such an occurrence are the polar cap, the crossings of the zero space charge surface by open field lines, and the return current boundary, but not the light cylinder.

We examine the effects of a relativistic wind on the spin-down of a neutron star and apply our results to the study of soft gamma repeaters (SGRs), which are thought to be neutron stars with magnetic fields greater than 1014 G. We derive a spin-down formula that includes torques from both dipole radiation and episodic or continuous particle winds. We find that if SGR 1806-20 puts out a continuous particle wind of 1037 ergs s-1, then the pulsar age is consistent with that of the supernova remnant, but the derived surface dipole magnetic field is only 3x1013 G, in the range of normal radio pulsars. If instead the particle wind flows are episodic with small duty cycle, then the observed period derivatives imply magnetar-strength fields, while still allowing characteristic ages within a factor of 2 of the estimated supernova remnant age. Close monitoring of the periods of SGRs will allow us to establish or place limits on the wind duty cycle and thus the magnetic field and age of the neutron star.

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