  A physical model of the formation of a vortex current in a plasma channel of
lightning discharges due to the anomalous Hall effect caused by relativistic
spin-orbit interaction phenomenon is proposed. The existence of fast
electromagnetic surface plasmon waves propagating along the lightning discharge
channel at a speed close to the speed of light in vacuum is shown. The spin
properties of electrons become important at relativistic velocities, so the
spin-orbit coupling arises as an effective magnetic force acting on the spin of
an electron, leading to the formation of a spin-induced vortex current in the
absence of an external magnetic field. This makes it possible to consider the
lightning discharge channel as a charged particle accelerator that generates
microwave, X-ray, gamma-ray and RF emissions by a current pulse moving along a
helical trajectory via synchrotron and cyclotron radiation mechanisms. The
proposed theoretical model of the formation of a spin-induced vortex current in
the lightning plasma channel is consistent with observations of lightning and
spark discharges.
