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In contrast to hydrodynamic vortices, vortices in plasma contain an electriccurrent circulating around the center of the vortex, which generates a magneticfield localized inside. Using computer simulations, we demonstrate that themagnetic field associated with the vortex gives rise to a mechanism ofdissipation of the vortex pair in a collisionless plasma, leading to fastannihilation of the magnetic field with its energy transforming into the energyof fast electrons, secondary vortices, and plasma waves. Two major contributorsto the energy damping of double vortex system, namely, magnetic fieldannihilation and secondary vortex formation, are regulated by the size of thevortex with respect to the electron skin depth, which scales with the electrongamma-factor, $\gamma_e$, as $R/d_e \propto \gamma_e^{1/2}$. Magnetic fieldannihilation appears to be dominant in mildly relativistic vortices, while forthe ultrarelativistic case, secondary vortex formation is the main channel fordamping of the initial double vortex system.

On annihilation of the relativistic electron vortex pair in collisionless plasmas