From amplification of spontaneous emission to saturation in x-ray lasers: A Maxwell-Bloch treatment.

The interaction between radiation and matter in an x-ray laser occurring in a cylindrical laser-produced plasma is investigated by means of the Maxwell-Bloch equations with level degeneracies explicitly taken into account. Radiation is initiated by spontaneous emission and amplified while propagating along the cylinder axis. This theory generalizes the current simple theory of the small-signal gain coefficient and is suited to correctly describe the gradual transition to the saturation regime. A detailed numerical study of the germanium x-ray laser is performed to illustrate the theory for the case of the Ne-like ion collisional laser. The effect of electron-ion collisions leading to transitions between degenerate states on linewidths, as well as on saturation behavior is outlined.