  X-ray and gamma-ray emissions observed in lightning and long sparks are
usually connected with the bremsstrahlung of high-energy runaway electrons.
Here, an alternative physical mechanism for producing X-ray and gamma-ray
emissions caused by the polarization current and associated electromagnetic
field moving with relativistic velocity along a curved discharge channel has
been proposed. It is pointed out that lightning and spark discharges should
also produce a coherent radio-frequency radiation. The influence of the
conductivity and the radius of the lightning channel on the propagation
velocity of electromagnetic waves, taking into account the absorption, have
been investigated. The existence of fast electromagnetic surface waves
propagating along the lightning discharge channel at a speed close to the speed
of light in vacuum is shown. The possibility of the production of microwave,
X-ray and gamma-ray emissions by a polarization current pulse moving along a
curved path via synchrotron radiation mechanism during the lightning leader
steps formation and the very beginning of the return stroke stage is pointed
out. The existence of long tails in the power spectrum is shown, which explains
observations of photon energies in the range of 10-100 MeV in the TGF, as well
as measured power spectrum of laboratory spark discharge.
