Vortices in relativistic electron beams

We demonstrate that a relativistic electron beam is properly described in t he moving frame by the electron-magnetohydrodynamic equations of plasma phy sics. For large beam currents, the accelerator magnetic held is expected to be unstable to the fast magnetic reconnection. We present a plausible satu rated state of the fast reconnection, in the form of a complex vortex patte rn. The nonlinear dispersion equations of the vortex are derived and the re lationship between the vortex structure and the background magnetic field i s discussed.