  Generation of electromagnetic radiation near the second harmonic of the
plasma frequency during the injection of an electron beam into a
rippled-density plasma channel is investigated using both analytical theory and
particle-in-cell simulations. The generating scheme is based on nonlinear
interaction of the most unstable beam-driven potential plasma wave with its
satellite arising due to scattering on the longitudinal modulation of plasma
density. Resulting superluminal oscillations of electric current in a
finite-size plasma channel radiate electromagnetic waves via the same mechanism
which has been recently studied for the fundamental harmonic emission and
reffered as a beam-driven plasma antenna. It is shown that theoretical
predictions for the optimal plasma width and modulation period are confirmed by
simulation results and the power conversion efficiency of the second harmonic
emission reaches several percent. Such an efficient mechanism opens the path to
explanation of laboratory experiments with a thin electron beam at the GOL-3
mirror trap as well as to developing the scheme of terahertz generation at the
gigawatt power level.
