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 P_x 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 P_x/λ² 10³⁰ W cm⁻² sr⁻¹.