Comparative single-pulse studies of self-trapped plasma channel formation in Xe and Kr cluster targets produced with 1–2 TW femtosecond 248 nm pulses reveal energy efficient channel formation (>90%) and highly robust stability for the channeled propagation in both materials. Images of the channel morphology produced by Thomson scattering from the electron density and direct visualization of the Xe(M) and Kr(L) x-ray emission from radiating ions illustrate the (1) channel formation, (2) the narrow region of confined trapped propagation, (3) the abrupt termination of the channel that occurs at the point the power falls below the critical power Pcr, and, in the case of Xe channels, (4) the presence of saturated absorption of Xe(M) radiation that generates an extended peripheral zone of ionization. The measured rates for energy deposition per unit length are ∼ 1.46 J cm−1 and ∼ 0.82 J cm−1 for Xe and Kr targets, respectively, and the single pulse Xe(M) energy yield is estimated to be > 50 mJ, a value indicating an efficiency >20% for ∼ 1 keV x-ray production from the incident 248 nm pulse.

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.

The Xe(L) system at λ ∼ 2.9 Å uniformly exhibits all of the canonical attributes of a strongly saturated amplifier on the full ensemble of single-vacancy Xeq+ transition arrays (q = 31, 32, 34, 35, 36) that exhibit gain. The key observables are (1) sharp spectral narrowing, (2) the detection of a narrow directed beam (δθx≅200 µrad), (3) an increase in the amplitude of the emission and the development of an intense output (⩾106 enhancement) and (4) the observation of deep spectral hole-burning on the inhomogeneously broadened spontaneous emission profile. Experimentally determined by two methods, (a) line narrowing and (b) signal enhancement, the observations for several single-vacancy 3d→2p transitions indicate a range of values for the effective small signal (linear) gain constant given by go≅25−100 cm−1. Quantitative analysis shows that this result stands in clear conflict with the corresponding upper bound go≅40−80 cm−1 that is based on available spectroscopic data and estimated with conventional theory. Overall, the observed values deviate substantially from expectations scaled to the spectral density of the measured Xe(L) spontaneous emission profile; they are systematically too high. The most extreme example is the heavily saturated Xe32+ transition at λ = 2.71 Å, a case that fails to reconcile the lower bound of the measured signal strength with the corresponding theoretically predicted maximal value; the former falls above the latter by a factor exceeding 400 giving an enormous gap. Moreover, although saturation is a prominent characteristic of the amplification at λ≅2.71 Å, as demonstrated by spectral hole-burning, the theoretical upper bound of go given for this transition is far too small for saturation to be reached. The Xe31+ transition at λ≅2.93 Å exhibits comparably pronounced anomalous behaviour. This double paradox is resolved with the Ansatz that the amplification is governed principally by the saturated gain gs, not the conventionally described small signal value go. This interpretation is further supported by the observation of deep spectral hole-burning, the signature of strong saturation, that occurs uniformly across the spectrum of the spontaneous emission profile. The effective amplification exhibits an anomalously weak dependence on the spectral density; saturation is the rule, not the exception. A lucid manifestation of the saturation is the recording of spectrally resolved x-ray yields on the Xe31+ array that are sufficiently high to produce gross structural damage to the material in the film plane of the spectrograph. The behaviour of the amplifier can be best described as an explosive supersaturated amplification. The source of this exceptionally strong amplification can be traced to the dynamically enhanced radiative response of the excited Xe hollow atom states located in the clusters that are mode coupled to the plasma waveguide forming the amplifying channel.

The spectral and spatial characteristics of the Xe(L) amplifier at λ ∼ 2.9 Å determine an optimum for the scaling of the peak power with channel length. The Xe31+ and Xe32+ (3d → 2p) transition arrays represent two identical spectral optima for amplification, a property stemming from the extremum of spectral components (3245) characteristic of their electron configurations. Adroit matching of the spatial distribution of the intensity characteristic of the propagating 248 nm pulse dynamically generating the self-trapped plasma channel with the intensity required to excite selectively and efficiently the Xe31+ and Xe32+ arrays can also simultaneously maximize the spatial volume of the excitation. The net outcome of this double maximization is an amplifying channel for the optimal transitions that possesses high gain (∼100 cm−1), low losses (<10−1cm−1) and a diameter of 15−20 µm, a size sufficient to produce an x-ray pulse energy of ∼50−100 mJ from a channel having an average xenon density of ∼1020 cm−3 and a length of 1 cm. Since previous studies have experimentally demonstrated the ability to produce a saturated bandwidth of ∼60 eV, a magnitude sufficient to support a pulse duration of ∼30 as, peak powers Px ≫ 1 PW are clearly within the scaling limits of the Xe(L) system. The corresponding peak brightness scaling limit is accordingly bounded from below by Px/λ2 ≅ 1030 W cm−2 sr−1.

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