Inner-shell x-ray lasing in x-ray free-electron laser-driven highly ionized plasmas

We present an efficient time-dependent Maxwell-Bloch transport model for simulating inner-shell x-ray lasing (XRL) in x-ray free-electron laser-driven highly ionized and excited nonlocal thermodynamic equilibrium plasmas. The model selectively retains all coherences between lasing levels together with nonradiative coherences linking adjacent lasing transitions. This model fully accounts for all processes governing population evolution, enabling accurate and efficient simulation of complex atomic systems. Applications to neon and argon gases reveal distinct amplification behaviors across charge states. In neon, multiple lasing lines spanning low to high ionization stages are identified, where low-charge-state transitions are strongly shaped by autoionization and saturation, while high-charge-state transitions exhibit pronounced coherence signatures such as Rabi oscillations and Rabi splitting. In argon, amplification is dominated by a few strong channels, while weaker ones are suppressed by nonradiative coherence effects in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi mathvariant="normal">Λ</a:mi> </a:math> -type subsystems. Overall, our results demonstrate that laser field-induced multilevel coherent coupling plays a crucial role in shaping XRL gain and spectra. This framework provides a versatile and predictive tool for designing XRLs with tailored temporal and spectral properties, with potential applications in ultrafast science, nonlinear x-ray optics, and precision spectroscopy.