Fig. 5: Intensity Effects on 3D X-ray Spectra.

Panel a indicates the total ionization rate w (blue line). Panels b and c give partial rates into each ATI peak as a heat map, where b is on a log scale and c is on a linear scale. An additional dashed black line indicates w ∝ I scaling in a and ε_k ∝ U_p scaling in b. Vertical lines are included for intensity parameters at \({{{\mathcal{Z}}}}=0.1\) (light blue) and \({{{{\mathcal{Z}}}}}_{1}=0.1\) (green). The vertical pink line labeled T_1/2 = 50 as corresponds to a limit where 50% of the ground-state is depleted after 50 as. Panels d and e present the results of b and c alternatively. Panel e is a zoomed-in version of panel d. A black dashed line shows the ∝ I scaling of the first peak (1) with respect to intensity. Higher-order peaks are indicated by a line labeled (2) for the second-order peak, with subsequent higher-order peaks represented by thinner lines continuing sequentially to the right of (2) without labels. Panels d and e contains a vertical gray dot-dashed line at I ≈ 7 × 10¹⁸ W/cm² corresponding to the maxima for the n = 1 emission peak. ATI emission energy vs rate have been plotted in panel f for intensities at this maxima as blue bars and a location very close to the threshold as red bars (1.1 × 10¹⁹ W/cm²) to show suppression of n = 1 near threshold.