High gain x-ray lasers at the water window

We propose a scheme for producing a spatial and temporal averaged gain of 45 ${\mathrm{cm}}^{\mathrm{-}1}$ in nickel-like Ta, including refraction. This result is achieved by irradiating a 40 μg/${\mathrm{cm}}^2$ target with a low intensity pulse [2ω(λ=0.53 μm), 5×${10}^{13}$ W/${\mathrm{cm}}^2$, 80 ps] to make the plasma subcritical. This is followed by a high intensity pulse (2ω, 2×${10}^{15}$, 20 ps) to give the proper ionization. Therefore the principle of pulse shaping to achieve high gain using high intensity pump radiation is demonstrated.