The nonequilibrium nanoplasma created by irradiation of a cluster, or other nanosystems such as large molecules, with an intense infrared-laser field may be used as an amplifying medium for a high-frequency probe field. We employ a simple description where the nanosystem is modeled by particles bound by a self-consitent potential. An incident probe field suffers gain or loss depending on the respective parameters by a mechanism that is usually referred to as collisionless damping. The model is simple enough to allow for an essentially analytical solution. Absorption rate of the nonequilibrium cluster. Negative absorption corresponds to amplification. See text below for further explanations