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

X-ray free-electron lasers delivering up to 1 × 10 13 coherent photons in femtosecond pulses are bringing about a revolution in X-ray science. However, some plasma-based soft X-ray lasers are attractive because they spontaneously emit an even higher number of photons (1 × 10 15), but these are emitted in incoherent and long (hundreds of picoseconds) pulses 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. 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 × 10 14 fully coherent soft X-ray photons in 200 fs pulses and with a peak power of 20 GW.