Computed dynamics of stable plasma channel formation in Xe corresponding to the recorded data shown in figure 2 are represented by the green trajectory A<sub>gradient</sub> → B<sub>gradient</sub> in the (η, ρ<sub>0</sub>) plane, where η and ρ<sub>0</sub> correspond to the normalized power and the normalized radius of the laser beam

<p><strong>Figure 3.</strong> Computed dynamics of stable plasma channel formation in Xe corresponding to the recorded data shown in figure <a href="http://iopscience.iop.org/0953-4075/46/18/185601/article#jpb469036f2" target="_blank">2</a> are represented by the green trajectory A<sub>gradient</sub> → B<sub>gradient</sub> in the (η, ρ<sub>0</sub>) plane, where η and ρ<sub>0</sub> correspond to the normalized power and the normalized radius of the laser beam. The trajectory illustrates the efficient multi-stage self-channeling with the electron density gradient in the initial phase of channel formation. The dynamics of channel formation corresponding to an initially uniform plasma that suffers a substantial channeling power loss are represented by the red trajectory A<sub>uniform</sub> → B<sub>uniform</sub> (see text for details). The channel eigenmode curve is designated by ρ<sub>e,0</sub>(η) [<a href="http://iopscience.iop.org/0953-4075/46/18/185601/article#jpb469036bib4" target="_blank">4</a>]. The normalized incident peak power of the pulse is given by the value of η for point A<sub>uniform</sub>. The normalized peak power trapped in the channel corresponds to the value of η for point B<sub>gradient</sub> in the case of multi-stage self-channeling, while point B<sub>uniform</sub> represents the situation for the self-channeling in an initially uniform plasma. The evolution of a stable channel launched in a density gradient is illustrated by the trajectory A<sub>gradient</sub> → B<sub>gradient</sub>; the efficiency of energy transport into the channel is ~ 95%. The contrasting trajectory from point A<sub>uniform</sub>, that is, associated with no spatial density gradient, corresponds to the formation of the channel denoted by the point B<sub>uniform</sub> on the eigenmode; the outcome is a considerably reduced efficiency (~ 60%) for transport of the energy into the channel. The zone of the η, ρ<sub>0</sub> parameters that corresponds to the highly unstable mode of the relativistic self-channeling, that leads to strong filamentation of the laser beam [<a href="http://iopscience.iop.org/0953-4075/46/18/185601/article#jpb469036bib6" target="_blank">6</a>, <a href="http://iopscience.iop.org/0953-4075/46/18/185601/article#jpb469036bib11" target="_blank">11</a>], is shown in the upper right.</p> <p><strong>Abstract</strong></p> <p>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 <em>P</em><sub>cr</sub>, 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<sup>−1</sup> and ~ 0.82 J cm<sup>−1</sup> 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.</p>