  The twisted magnetospheres of magnetars must sustain a persistent flow of
electron-positron plasma. The flow dynamics is controlled by the radiation
field around the hot neutron star. The problem of plasma motion in the
self-consistent radiation field is solved using the method of virtual beams.
The plasma and radiation exchange momentum via resonant scattering and
self-organize into the "radiatively locked" outflow with a well-defined,
decreasing Lorentz factor. There is an extended zone around the magnetar where
the plasma flow is ultra-relativistic; its Lorentz factor is self-regulated so
that it can marginally scatter thermal photons. The flow becomes slow and
opaque in an outer equatorial zone, where the decelerated plasma accumulates
and annihilates; this region serves as a reflector for the thermal photons
emitted by the neutron star. The e+- flow carries electric current, which is
sustained by a moderate induced electric field. The electric field maintains a
separation between the electron and positron velocities, against the will of
the radiation field. The two-stream instability is then inevitable, and the
induced turbulence can generate low-frequency emission. In particular, radio
emission may escape around the magnetic dipole axis of the star. Most of the
flow energy is converted to hard X-ray emission, which is examined in the
accompanying paper.
