A proposal for multi-tens of GW fully coherent femtosecond soft X-ray lasers

X-ray free-electron lasers(1,2) delivering up to 1 x 10(13) coherent photons in femtosecond pulses are bringing about a revolution in X-ray science(3-5). However, some plasma-based soft X-ray lasers(6) are attractive because they spontaneously emit an even higher number of photons (1 x 10(15)), but these are emitted in incoherent and long (hundreds of picoseconds) pulses(7) as a consequence of the amplification of stochastic incoherent self-emission. Previous experimental attempts to seed such amplifiers with coherent femtosecond soft X-rays resulted in as yet unexplained weak amplification of the seed and strong amplification of incoherent spontaneous emission(8). Using a time-dependent Maxwell-Bloch model describing the amplification of both coherent and incoherent soft X-rays in plasma, we explain the observed inefficiency and propose a new amplification scheme based on the seeding of stretched high harmonics using a transposition of chirped pulse amplification to soft X-rays. This scheme is able to deliver 5 x 10(14) fully coherent soft X-ray photons in 200 fs pulses and with a peak power of 20 GW.