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 Soft Gamma Repeaters and Anomalous X-ray Pulsars , these currents are maintained by magnetic stresses acting deep inside the star , which generate both sudden disruptions ( SGR outbursts ) and more gradual plastic deformations of the rigid crust .
We construct self-similar force-free equilibria of the current-carrying magnetosphere with a power law dependence of magnetic field on radius , { \bf B } \propto r ^ { - ( 2 + p ) } , and show that a large-scale twist of field lines softens the radial dependence of the magnetic field to p < 1 .
The spindown torque acting on the star is thereby increased in comparison with an orthogonal vacuum dipole .
We comment on the strength of the surface magnetic field in the SGR and AXP sources , as inferred from their measured spindown rates , 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 \sim 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 } \sim 10 ^ { 14 } G. Redistribution of the emerging X-ray flux at the cyclotron resonance will strongly modify the emerging pulse profile and , through the Doppler effect , generate a non-thermal tail to the X-ray spectrum .
We relate the sudden change in the pulse profile of SGR 1900 + 14 following the 27 August 1998 giant flare , to an enhanced optical depth at the electron cyclotron resonance resulting from a sudden twist imparted to the external magnetic field during the flare .
The self-similar structure of the magnetosphere should generate frequency-independent profiles ; more complicated pulse profiles may reflect the presence of higher multipoles , ion cyclotron scattering , or possibly non-resonant Compton scattering of O-mode photons by pair-loaded currents .