We have developed a fully coherent x-ray laser (XRL) at 13.9 nm by a double-target configuration. In the experiment, a seed XRL beam from the first target is injected into a plasma amplifier at the second target. The amplified XRL beam has full spatial coherence, 0.2 mrad of the nearly diffraction limited divergence, and 25 nJ of the output energy. For various application researches, we improve the output energy and the beam property of the x-ray laser. The gain-length product was gL ∼ 8.2, and the maximum output energy of about 1 μJ is achieved. The divergence of the XRL is affected by the refraction influence in the amplifier medium and/or the diffraction by the small size of the gain medium. We made the 2-D radiation hydrodynamics simulation code in order to investigate the generation of the gain medium plasma and the refraction influence.