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

X-ray free-electron lasers1,2 delivering up to 131013 coherent photons in femtosecond pulses are bringing about a revolution in X-ray science3?5. However, some plasma-based soft X-ray lasers6 are attractive because they spontaneously emit an even higher number of photons (131015), but these are emitted in incoherent and long (hundreds of picoseconds) pulses7 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 emission8. 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 531014 fully coherent soft X-ray photons in 200 fs pulses and with a peak power of 20 GW.