  We study the damping process of electron cyclotron motion and the resulting
emission in a waveguide using the classical Friedrichs model without relying on
perturbation analysis such as Fermi's golden rule. A classical Van Hove
singularity appears at the lower bound (or cut-off frequency) of the dispersion
associated with each of the electromagnetic field modes in the waveguide. In
the vicinity of the Van Hove singularity, we found that not only is the decay
process associated with the resonance pole enhanced (amplification factor ~
$10^4$) but the branch-point effect is also comparably enhanced. As a result,
the timescale on which most of the decay occurs is dramatically shortened.
Further, this suggests that the non-Markovian branch point effect should be
experimentally observable in the vicinity of the Van Hove singularity. Our
treatment yields a physically-acceptable solution without the problematic
runaway solution that is well known to appear in the traditional treatment of
classical radiation damping based on the Abraham-Lorentz equation.
