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.
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