  The radiative instability of the relativistic electron beam in a periodic
dielectric-filled cylindrical waveguide is considered. The dependence of the
beam instability increment on the radiated wave frequency near the region of
dispersion equation roots degeneracy is studied. It is shown that sharp change
in the instability of the beam under the conditions of two-wave diffraction in
Compton generation regime, making the increment proportional to the fourth root
from the beam density $\rho^{1/4}$ in contrast to conventional law
$\rho^{1/3}$, brings radiation generation (amplification) in the considered
system to be essentially improved in comparison with conventional devices (BWO,
TWT, FEL etc). Numerical calculations of the instability increment for various
parameters of the system are performed.
