  Electron-beams with a sinusoidal energy modulation have the potential to emit
sub-femtosecond x-ray pulses in a free-electron laser. The energy modulation
can be generated by overlapping a powerful infrared laser with an electron-beam
in a magnetic wiggler. Here we report on a new infrared source for this
modulation, coherent radiation from the electron-beam itself. In this
self-modulation process, the current spike on the tail of the electron-beam
radiates coherently at the resonant wavelength of the wiggler, producing a
six-period carrier-envelope-phase (CEP) stable infrared field with gigawatt
power. This field creates a few MeV, phase-stable modulation in the
electron-beam core. The modulated electron-beam is immediately useful for
generating sub-femtosecond x-ray pulses at any machine repetition rate, and the
CEP-stable infrared field may find application as an experimental pump or
timing diagnostic.
