Approximate theory of multipass amplification and its application to energy characteristics of an amplifier

A simplified model of the interaction between a short laser radiation pulse and an active medium is used as the basis of an approximate theory of a multipass amplifier with an arbitrary degree of overlap of the amplified beams. It is shown that, depending on the degree of saturation of the gain, such an amplifier can operate in a number of very different regimes. Analytic expressions relating the input and output energy parameters of an amplifier are obtained for each regime. It is shown that the expressions obtained in this way represent asymptotic forms of the exact solution applicable to high values of the gain. Some practical recommendations on the selection of the parameters of multipass amplifiers are put forward.