High gain x-ray lasers at the water window.

We propose a scheme for producing a spatial and temporal averaged gain of 45 cm[sup [minus]1] in nickel-like Ta, including refraction. This result is achieved by irradiating a 40 [mu]g/cm[sup 2] target with a low intensity pulse [2[omega]([lambda]=0.53 [mu]m), 5[times]10[sup 13] W/cm[sup 2], 80 ps] to make the plasma subcritical. This is followed by a high intensity pulse (2[omega], 2[times]10[sup 15], 20 ps) to give the proper ionization. Therefore the principle of pulse shaping to achieve high gain using high intensity pump radiation is demonstrated.