The Xe(L) system is an amplifier with fundamentally different dynamic characteristics from all previously developed laser amplifiers; it represents the conceptual ideal through full utilization of the Kramers–Kronig relations that fundamentally couple the dispersive and absorptive components. The dispersive response of the system, through optimal governance of the power compression, rules the amplification and establishes a minimum gain for the amplifier. Accordingly, the amplification requires a minimum value of the dispersion to be surpassed; the corresponding gain follows automatically. As a leading consequence, since this minimum gain is sufficiently high, the key experimental observation is the uniform presence of saturated amplification signaled by strong spectral hole burning on all transitions exhibiting amplification, including double-vacancy lines. This cardinal signature demonstrates that the amplification is legislated by the saturated gain gs, not the corresponding small signal value g0. The chief outcome is that explosive dispersion yields perforce explosive amplification and the efficient generation of maximally bright coherent power.

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Cooling of the xenon nozzle flow to T = 230 K produces three leading effects. They are (1) a ∼2.5-fold enhancement of the Xe(L) hollow atom emission on the single-vacancy 3d → 2p charge state arrays, (2) the production of amplifying self-trapped plasma channels with significantly enhanced lengths and (3) very sharply augmented emission on (2s2p) Xe(L) double-vacancy transitions in the λ ∼ = 2.80 Å region.

The analysis of spatially resolved Xe(L) spectra obtained with Z−λ imaging reveals two prominent findings concerning the characteristics of the x-ray amplification occurring in self-trapped plasma channels formed by the focusing of multi-TW subpicosecond 248 nm laser pulses into a high-density gaseous Xe cluster target. They are (1) strongly saturated amplification across both lobes of the Xe(L) hollow atom 3d → 2p emission profile, a breadth that spans a spectral width of ∼600 eV, and (2) new evidence for the formation of x-ray spatial modes based on the signature of the transversely observed emission from the narrow trapped zone of the channel. The global characteristics of the spectral measurements, in concert with prior analyses of the strength of the amplification, indicate that the enhancement of the x-ray emission rate by intra-cluster superradiant dynamics plays a leading role in the amplification. This radiative interaction simultaneously promotes (a) a sharp boost in the effective gain, (b) the directly consequent efficient production of coherent Xe(L) x-rays from both single and double vacancy 3d → 2p transition arrays, estimated herein at ∼30%, and (c) the development of a very short x-ray pulse width τx. In the limit of sufficiently strong superradiant coupling in the cluster, the system assumes a dynamically collective character and acts as a single homogeneously broadened transition whose effective radiative width approaches the full Xe(L) bandwidth, a breadth that establishes a potential lower limit of τx ∼5–10 as, a value substantially less than the canonical atomic time ao/αc ≅ 24 as.

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Single-pulse and time-integrated spectral measurements of the characteristics of the Xe(L) amplifier at λ ∼ 2.8 Å indicate an efficiency of energy extraction of ∼30% over a bandwidth of ∼500 eV. These observations, together with data from prior studies, provide a basis for estimating a corresponding set of scaling limits for a laboratory sized ∼4.5 keV Xe(L) system. Specifically, they are a peak power Px ∼ 6.0 PW, an unfocused peak intensity Ix ∼ 3.4 × 1021 W cm−2, peak brightness figures corresponding to B ∼ 4.1 × 1034 photons s−1 mm−2 mrad−2 (0.1% bandwidth)−1 and Px/λ2 ∼ 7.6 × 1030 W cm−2 sr−1, and an x-ray pulse length τx ∼ 5–10 as.

The high repetition rate laser systems providing the ELI-ALPS facility with TW-to-PW peak intensity pulses are designed to generate secondary light sources with a duration of tens of attosecond for basic and applied researches.

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