  We investigate the collective electron dynamics in a recently proposed
graphene-based terahertz emitter under the influence of the radiative damping
effect, which is included self-consistently in a molecular dynamics approach.
We show that under appropriate conditions synchronization of the dynamics of
single electrons takes place, leading to a rise of the oscillating component of
the charge current. The synchronization time depends dramatically on the
applied dc electric field and electron scattering rate, and is roughly
inversely proportional to the radiative damping rate that is determined by the
carrier concentration and the geometrical parameters of the device. The
emission spectra in the synchronized state, determined by the oscillating
current component, are analyzed. The effective generation of higher harmonics
for large values of the radiative damping strength is demonstrated.
