  We analyze the evolution of current driven kink instabilities of a highly
magnetized relativistic plasma column, focusing in particular on its
dissipation properties. The instability evolution leads to the formation of
thin current sheets where the magnetic energy is dissipated. We find that the
total amount of dissipated magnetic energy is independent of the dissipation
properties. Dissipation occurs in two stages: a peak when the instability
saturates, which is characterized by the formation of a helicoidal current
sheet at the boundary of the deformed plasma column, followed by a weaker
almost flat phase, in which turbulence develops. The detailed properties of
these two phases depend on the equilibrium configuration and other parameters,
in particular on the steepness of the pitch radial profile, on the presence of
an external axial magnetic field and on the amount of magnetization. These
results are relevant for high energy astrophysical sources, since current
sheets can be the sites of magnetic reconnection where particles can be
accelerated to relativistic energies and give rise to the observed radiation.
