Regular particle acceleration in relativistic jets

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.