  (ABBREVIATED) We consider the structure of neutron star magnetospheres
threaded by large-scale electrical currents, and the effect of resonant Compton
scattering by the charge carriers (both electrons and ions) on the emergent
X-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-carrying
magnetosphere 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 comparison
with a vacuum dipole. We comment on the strength of the surface magnetic field
in the SGR and AXP sources, and the implications of this model for the narrow
measured 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 resonant
cyclotron scattering, independent of frequency (radius), surface magnetic field
strength, or charge/mass ratio of the scattering charge. When electrons and
ions supply the current, the stellar surface is also heated by the impacting
charges at a rate comparable to the observed X-ray output of the SGR and AXP
sources, if B_{dipole} ~ 10^{14} G. Redistribution of the emerging X-ray flux
at the ion and electron cyclotron resonances will significantly modify the
emerging pulse profile and, through the Doppler effect, generate a non-thermal
tail to the X-ray spectrum. The sudden change in the pulse profile of SGR
1900+14 after the 27 August 1998 giant flare is related to an enhanced optical
depth to electron cyclotron scattering, resulting from a sudden twist imparted
to the external magnetic field.
