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A new pumping scheme named exploding pumping is proposed for realizing recombination x-ray lasers with high excitation efficiency. In the new scheme, a very thin membrane is employed as a target and it is heated instantaneously before the plasma starts to move by a high peak power sub- picosecond pumping laser. In the scheme, the plasma heating efficiency is improved by being free from heat conduction loss to bulk, and by suppressing the energy loss to hydrodynamic motion. Inertia of the mass delays the start of the plasma motion and gives sufficient time for full ionization. Owing to the extreme thinness of the initial high density plasma, only a few micrometers expansion leads to great reduction of the density and cools down rapidly to produce large gain. Efficient heating of a membrane plasma is confirmed in experimentally observed x-ray spectra and charge collector signals. It is discussed that the most serious problem for realizing water window x-ray lasers is conventional ablation pumping is density gradient which causes refraction of x-rays and limits gain length. The new pumping scheme can solve this refraction problem. The density profile of the expanding plasma in this scheme is fairly uniform because all material expand explosively and because no mass is supplied during the expansion. According to a numerical simulation, 3.34-nm water window of gain length product of 10 will be realized with the 6 J/ 0.3 ps laser irradiation. Longer wavelength x-ray lasers around 13- nm will be realized with a few J/ a few ps pulse pumping. The key technology in the new pumping scheme is suppression of pre-pulse. The effect of pre-pulse is experimentally observed, and means for pre-pulse suppression is discussed.
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