A coherent x-ray generation scheme is proposed which involves characteristi
cs of free electron lasers and atomic high harmonic generation schemes. A t
hin solid layer or any other periodic atomic structure with limited dimensi
ons is exposed to a short, superintense laser pulse. The electrons are extr
acted from the layer due to the extreme force and penetrate periodically th
rough the ionic structure. Consequently, thousands of harmonics of the lase
r radiation field are shown to coherently amplify along the interaction len
gth. The small signal gain of the generated x-ray radiation exceeds that ar
ising from the multiphoton Compton process in plasmas and is competitive wi
th that in the leading x-ray free electron lasers.