A self-terminating X-ray amplifying medium: Kinetics of K-shell photoionization and stimulated emission

Abstract

A two-stage model for achieving X-ray amplifying action on photoionized K-transitions pumped by the soft X-ray broadband flux from laser-produced plasma is treated. A simple pumping criterion is considered by the analysis of the positive gain-length product for the two-stage model of innershell transitions (0) → (3) and (2) → (1). The incident photon flux integrated over the effective lifetime T₂₁ of an innershell transition (2) → (1) is related to the photoionization coefficient μ₀₃^(ph), stimulated emission cross section σ₂₁^(stim), and the effective gainlength L^(eff) ≃ 0.63/μ₀₃^(abs), where μ₀₃^(abs) is the absorption coefficient of a pump soft X-ray radiation. Numerical estimates for the feasibility of K-shell X-ray amplification are given for C, F, Na, Ti, and Sn. For the example of an exponential X-ray carrier pulse (XCP) propagating through a resonant medium, an amplifying effect depending on the ratio of the input pulse temporal bandwidth τ_band to the effective lifetime T₂₁ is investigated. It is shown that for an XCP with a finite bandwidth τ_band the logarithm of an energy gain, ln[U(z)], falls below a linear relation with z and thus, from the viewpoint of maximum amplifying effect bandwidths τ_band with τ_band/T₂₁ > 1 are preferable. The requirements for achieving X-ray K-shell photoionization amplification for C are discussed in more detail. PACS numbers: 32.80.Hd, 42.50.Md, 42.55.Vc, 42.65.Re, 52.25.Nr.