  Like the solar corona, the external magnetic field of magnetars is twisted by
surface motions of the star. The twist energy is dissipated over time. We
discuss the theory of this activity and its observational status. (1) Theory
predicts that the magnetosphere tends to untwist in a peculiar way: a bundle of
electric currents (the "j-bundle") is formed with a sharp boundary, which
shrinks toward the magnetic dipole axis. Recent observations of shrinking hot
spots on magnetars are consistent with this behavior. (2) Continual discharge
fills the j-bundle with electron-positron plasma, maintaining a nonthermal
corona around the neutron star. The corona outside a few stellar radii strongly
interacts with the stellar radiation and forms a "radiatively locked" outflow
with a high e+- multiplicity. The locked plasma annihilates near the apexes of
the closed magnetic field lines. (3) New radiative-transfer simulations suggest
a simple mechanism that shapes the observed X-ray spectrum from 0.1 keV to 1
MeV: part of the thermal X-rays emitted by the neutron star are reflected from
the outer corona and then upscattered by the inner relativistic outflow in the
j-bundle, producing a beam of hard X-rays.
