Soft X-Ray free-electron laser with a laser undulator

We discuss the possibility of building a free-electron laser in the spectral region of tens of nanometers using a high-power laser pulse as the undulator. Requirements on the electron beam emittance, brightness, and energy spread are derived. The possibility of operation at the quantum limit is considered. The reduction of the gain due to diffraction of the undulator pulse (the variable mass-shift effect) is investigated, and several ways in which it could be overcome are suggested. Examples are presented showing that the device is feasible with moderate advances in current electron injector technology. Such a device would not require a large accelerator for high electron energies, nor a long wiggler made of permanent magnets.