High-gain plasma Cerenkov maser

The linearized fluid and Maxwell´s equations are used to calculate the dispersion relation for the transverse magnetic modes of a partially filled, plasma-lined, cylindrical waveguide interacting with a relativistic electron beam. Both the plasma liner and the electron beam are assumed to be cold, and the system is immersed in an infinite axial magnetic guide field. The dispersion relation is then used to calculate the growth rate for the instability between the slow-wave modes (Trivelpiece-Gould modes) of the plasma guide and the slow-space charge mode of the electron beam. The calculation is done in the high-gain, strong coupling limit