The high brilliance expected from the X-ray Free-Electron Lasers (XFEL’s) now under construction suggest re-investigating the feasibility of a photopumped soft X-ray laser. We present simulations of a Lyman-α X-ray laser in hydrogenic He (λ = 30.4 nm) pumped by XFEL radiation with parameters of the TESLA Test Facility, phase II, at DESY/Hamburg. The simulations show that high gain can be achieved at a pump intensity of 1015 W/cm2. The realization of such a laser could provide a better understanding of the physics of photopumped lasers and thus help to develop table-top X-ray lasers.
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