Superradiant self-similar pulses in the evolution of the electron-beam-plasma instability

We derive a set of nonlinear partial differential equations describing the space-time evolution of Langmuir waves in a beam-plasma system, taking into account the propagation effects due to the difference between the beam and wave velocities. We demonstrate the existence of superradiant spikes behind the electron beam front that can be represented by a self-similar solution of the system of equations. These spikes are associated with self-bunching in the electron beam. The conditions in which the predicted spiking behavior could be experimentally observed are discussed.