Recent experiments undertaken at the Rutherford Appleton Laboratory to produce X-ray lasing over the 5-30 nm wavelength range are reviewed. The efficiency of lasing is optimized when the main pumping pulse interacts with a preformed plasma. Experiments using double 75-ps pulses and picosecond pulses superimposed on 300-ps background pulses are described. The use of travelling wave pumping with the approximately picosecond pulse experiments is necessary as the gain duration becomes comparable to the time for the X-ray laser pulse to propagate along the target length. Results from a model taking account of laser saturation and deviations from the speed of light c of the travelling wave and X-ray laser group velocity are presented. We show that X-ray laser pulses as short as 2-3 ps can be produced with optical pumping pulses of approximate to1-ps
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