High-gain harmonic generation of soft X-rays with the `fresh bunch` technique

We report numerical simulations (using the TDA code) and analytic verification of the generation of 64 {Angstrom} high power soft X- rays from an exponential regime single pass seeded FEL. The seed is generated in the FEL using the High Gain Harmonic Generation (HGHG) technique combined with the `Fresh bunch` technique. A seed pulse at 2944 {Angstrom} is generated by conventional laser techniques. The seed pulse produces an intense energy modulation of the rear part of a I GeV, 1245 {Angstrom} electron beam in a `modulator` wiggler. In the `radiator` wiggler, (resonant to 64 {Angstrom}), the energy modulation creates beam density modulation followed by radiation of the 46{sup th} harmonic of the seed. We use a magnetic delay to position the 64 A{Angstrom} radiation at the undisturbed front of the bunch to serve as a seed for a single pass, exponential growth FEL. After a 9 m long exponential section followed by a 7 m long tapered section the radiation power reaches 3.3 GW.