Chelyabinsk region, p.o. box 245, Russia 1. Optimization of the X-ray laser on the 3p-3s transition of Ne-like titanium ion. The previous experiments performed on the facility SOKOL-P have demonstrated generation of the laser X-radiation (LXR) with the wavelength λ=326 Å on Ne-like Ti ions at sequential irradiation of the targets by two laser pulses, focused into a narrow line, having the nanosecond and picosecond duration [1]. In these experiments, the effective small signal gain equaled ≈30 cm -1 . This paper presents results of experiments, which studied the effect of focusing conditions and pumping laser energy on the laser X-radiation yield.The dependence of the LXR yield on the target position relative to the focusing plane of the pumping laser beam was studied. This dependence has a well-defined maximum when the target is positioned at a distance of about 300 µm behind the focusing plane. In this position, the width of the focal line is about 120 µm, and the energy flux density of the pumping laser is 0.5⋅10 12 W/cm 2 in the prepulse of ≈ 400 ps duration and about (1÷2)⋅10 14 W/cm 2 in the master pulse of 4 ps duration. The master pulse delay is ≈ 1.5 ns.The traveling pumping wave mode was realized using the step mirror. At the maximum target length (8 mm) the LXR yield is as great as 5-fold, if compared to target irradiation without the step mirror. The value of the total laser radiation energy changed from 5.9 to 11.5 J. The energy ratio in the prepulse and the master pulse was kept constant and came to 1:2.4. In this mode, the dependence of LXR yield on the total laser energy was measured. This dependence is demonstrated to have an exponential form.2. LXR generation on 4d-4p transitions of Ni-like molybdenum. At present, a basic tendency in the development of laboratory X-ray lasers (XL) is going to the short-wave range, including the so-called "water window" (22÷44 Å) being biologically important. The use of Ni-like ions offers an advantage over the Ne-like ions as the pumping energy required for generation on the same wavelength is considerably lower for them. The latest experiments performed on the facility SOKOL-P have demonstrated the amplification on the wavelength λ=189 Å (Ni-like molybdenum, Z=42). Using the traveling pumping wave, the saturated operating mode for XL was obtained when the exponential growth of the output energy with target length becomes smoother and close to the linear one.3. The development of LXR generation model, and numerical codes which allow for the quanta delay effects, quanta refraction in plasma with heavy density gradient, and also the saturation effect have made it possible to understand and describe the experimental dependence of the output LXR intensity on the active medium length. Good quantitative agreement is also evident when estimating the total output energy of XL on Ne-like Ti ions. References 1. A.V. Andriyash, D.A. Vikhlyaev, D.S. Gavrilov, et al. "X-ray lasing upon two-pulse irradiation of targets on the picosecond SOKOL-P facility", Quantum Electroni...