Title: Multi-photon stimulated grasers assisted by laser-plasma interactions

Abstract: We investigate theoretically the possibility of achieving the stimulated amplification of $\gamma$-rays. Herein, our approach circumvents the so-called ``graser dilemma" through a non-linear, multi-photon mechanism. Our work foresees the combination of a high-intensity $\gamma-$flash generated by the interaction of a high-intensity laser pulse with plasma and intensive photons supplied by an additional laser. We show that multi-photon stimulated emission processes can have a larger effective cross-section compared to a one-photon process. The bandwidth of the supplied photons can also be tuned to curtail linewidth broadening. Naturally, Mossbauer transitions can be chosen to apply the scheme in the first instance. Furthermore, we derive that even multi-photon stimulated emission in the form of an anti-Stokes type could allow our scheme to be applied to non-Mossbauer nuclei, provided that the supplied photon energy can be tuned to compensate for the recoil and other broadening induced losses. The graser development can be spearheaded using multi-PW class high-power laser systems such as the 10 PW installation at Extreme Light Infrastructure - Nuclear Physics (ELI-NP) in Romania.