Electron beam of finite duration in a plasma

The fundamental solutions of Maxwell's equations are constructed for the injection of an electron beam of finite duration into a plasma. These solutions permit calculation of the self-consistent electromagnetic fields of the plasma-beam system for an arbitrary relationship between the Langmuir frequency and the collision frequency of plasma electrons and yield a closed system of equations describing the evolution of the beam on the level of equations for the beam alone, under conditions such that nonlinear effects appear first in the beam and the medium can still be treated linearly