Collective electromagnetic modes for beam-plasma interaction in the whole k space

The linear stability of the system in the equilibrium state formed by an electron beam and its return plasma current was studied. The system was relevant to the fast ignition scenario (FIS) as, when penetrating into the plasma, the electron beam generates the return current carried by the plasma electrons. The study was carried out by using a general electromagnetic formalism to derive the unstable proper modes such as propagating at any wave vector associated with the system formed by an electron beam. The result shows the limitations of the electrostatic approximation by displaying transverse modes for a wave vector around the beam axis or normal to it.