  Exact solution is obtained for electromagnetic field around a conducting
cylinder of infinite length and finite radius, with a periodical axial current,
when the wave length is much larger than the radius of the cylinder. The
solution describes simultaneously the fields in the near zone close to the
cylinder, and transition to the wave zone. Proper long-wave oscillations of
such cylinder are studied. The electromagnetic energy flux from the cylinder is
calculated. These solutions could be applied for description of the
electromagnetic field around relativistic jets from active galactic nuclei and
quasars and particle acceleration inside jets.
