  We develop a theory of particle acceleration inside relativistic rotating
electron-positron force-free jets with spiral magnetic fields. We considered
perturbation of the stationary magnetic field structure and found that
acceleration takes place in the regions where the Alfven resonant condition
with the eigenmodes in the jet is fulfilled, i.e. where the local Alfven speed
is equal to the phase speed of an eigenmode. The acceleration mechanism is
regular acceleration by the electric field of the electromagnetic wave, which
is the eigenmode of the force-free cylindrical jet: particles drift out of the
region of the large wave amplitude near the Alfven resonant surface and gain
energy. Acceleration in the strong electric field near the Alfven resonance and
synchrotron losses combine to form a power-law energy spectrum of
ultra-relativistic electrons and positrons with index between 2 and 3 depending
upon the initial energy of the injected particles. The power law distribution
ranges from 10 MeV to 1000 MeV.
