The effects of ultrahigh-intensity laser radiation on dynamical processes such as electron scattering, bremsstrahlung emission, and pair production, have received growing theoretical interest as laser intensities in the laboratory continue to increase. Recently, for example, a calculation was published that predicted resonant increases of more than four orders of magnitude in bremsstrahlung emission in the presence of intense optical laser radiation [A. A. Lebed and S. P. Roshchupkin, Phys. Rev. A 81, 033413 (2010)]. The analysis in that paper was limited to laser intensities of $\ensuremath{\le}$${10}^{17}$ W/cm${}^{2}$, and it was applied only to bremsstrahlung emissions at the laser frequency. In the present paper, we extend this Lebed and Roshchupkin analysis in order to assess the possibility of achieving some enhancement in bremsstrahlung emissions at significantly higher harmonics of the optical laser photon energies ($\ensuremath{\sim}$6 keV) and thereby to appraise whether or not enhanced bremsstrahlung emissions may have played a hidden role in producing the population inversions and kilovolt x-ray amplifications that have been seen experimentally [A. B. Borisov et al., J. Phys. B 40, F307 (2007)]. In those experiments, light from a KrF laser was focused onto a gas of xenon clusters to intensities $\ensuremath{\gtrsim}$${10}^{19}$ W/cm${}^{2}$. A model of the expansion and ionization dynamics of a xenon cluster when heated by such laser intensities has been constructed [Tz. B. Petrova et al., High Energy Density Phys. 8, 209 (2012)]. It is capable of replicating the x-ray gains seen experimentally, but only under the assumption that sufficiently high inner-shell photoionization rates are generated in the experiments. We apply this model to show that such photoionization rates are achievable, but only if there are enhancements of the Bethe-Heitler bremsstrahlung emission rate of three to four orders of magnitude. Our extended analysis of the Lebed and Roshchupkin work shows that, for there to be emissions (whether or not enhanced by four orders of magnitude) at high-order KrF-laser harmonic energies, laser intensities $\ensuremath{\gtrsim}$${10}^{19}$ W/cm${}^{2}$ must be reached. Thus, further extensions of these calculations (or experimental measusurements) are needed to determine whether the enhancement factors that are predicted for small laser harmonics at laser intensities $\ensuremath{\lesssim}$${10}^{17}$ W/cm${}^{2}$ can be extrapolated to large laser harmonics at laser intensities $\ensuremath{\gtrsim}$${10}^{19}$, which are shown in our work to be needed in order to produce high laser harmonic kilovolt emissions.
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