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(ABBREVIATED) We consider the structure of neutron star magnetospheresthreaded by large-scale electrical currents, and the effect of resonant Comptonscattering by the charge carriers (both electrons and ions) on the emergentX-ray spectra and pulse profiles. In the magnetar model for the SGRs and AXPs,these currents are maintained by magnetic stresses acting deep inside the star.We construct self-similar, force-free equilibria of the current-carryingmagnetosphere with a power-law dependence of magnetic field on radius, B ~r^(-2-p), and show that a large-scale twist softens the radial dependence to p< 1. The spindown torque acting on the star is thereby increased in comparisonwith a vacuum dipole. We comment on the strength of the surface magnetic fieldin the SGR and AXP sources, and the implications of this model for the narrowmeasured distribution of spin periods. A magnetosphere with a strong twist,B_\phi/B_\theta = O(1) at the equator, has an optical depth ~ 1 to resonantcyclotron scattering, independent of frequency (radius), surface magnetic fieldstrength, or charge/mass ratio of the scattering charge. When electrons andions supply the current, the stellar surface is also heated by the impactingcharges at a rate comparable to the observed X-ray output of the SGR and AXPsources, if B_{dipole} ~ 10^{14} G. Redistribution of the emerging X-ray fluxat the ion and electron cyclotron resonances will significantly modify theemerging pulse profile and, through the Doppler effect, generate a non-thermaltail to the X-ray spectrum. The sudden change in the pulse profile of SGR1900+14 after the 27 August 1998 giant flare is related to an enhanced opticaldepth to electron cyclotron scattering, resulting from a sudden twist impartedto the external magnetic field.Comment: 31 January 2002, minor revisions, new section 5.4.

Electrodynamics of Magnetars: Implications for the Persistent X‐Ray Emission and Spin‐down of the Soft Gamma Repeaters and Anomalous X‐Ray Pulsars