Free electron lasers assisted by pseudo energy bands

We propose a new scheme for high gain harmonic generation free electron lasers (HGHG FELs), which is seeded by a pair of intersecting laser beams to interact with an electron beam in a modulator undulator located in a dispersive section. The interference of the laser beams gives rise to a two-dimensional modulation in the energy-time phase space because of a strong correlation between the electron energy and the position in the direction of dispersion. This eventually forms pseudo energy bands in the electron beam, which results in efficient harmonic generation in HGHG FELs in a similar manner to the well-known scheme using the echo effects, with the requirement on the energy modulation being much more relaxed.