Electromagnetic plasma modes at ωpe

The problem of the electromagnetic plasma radiation near the electron plasma frequency ω
_pe
is studied in the absence of an external magnetic field. Maxwell's equations together with the fluid equations, which include thermal effects, are solved for an infinite geometry as well as for a finite geometry, and the problem of the eigenmodes at a plasma frequency ≈ ω
_pe
is studied. The excitation of these modes by a small density relativistic beam is discussed. It is shown that the presence of a small density beam with finite u
_o
/c (where u
_o
/ is the beam velocity and c the velocity of light in a vacuum) in a plasma of finite thermal velocity, can couple linearly the plasma oscillations excited by the beam with the electromagnetic plasma mode at ω
_pe
. It is also shown that surface waves at a frequency ≈ ω
_pe
can be excited by the beam.