Results from three‐dimensional electromagnetic particle simulations of an electron–positron plasma with a relativistic electron beam (γ=2) are presented. As part of the initial conditions, a poloidal magnetic field is specified, consistent with the current carried by the beam electrons. The beam undergoes pinching oscillations due to the pressure imbalance. A transverse two‐stream instability is excited with large helical perturbations. In the process, background electrons and positrons are heated and accelerated up to relativistic energy levels. Only background electrons are accelerated farther along the z direction due the synergetic effects by both the damped transverse mode and the accompanying electrostatic waves caused by the breakdown of the helical perturbations. © 1994 American Institute of Physics.