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