Figure plots the ionization rates for the simulations in Fig. . For the three sets of CAP parameters (r 0 , η) leading to clear HHG peaks (Figs. and), the ionization rates are plotted together in Fig. and are rather slow, such that only ≈ 0.02 electrons are lost over the course of 5,000 a.u. of time propagation. The ionization rate is much larger when r 0 = 4.0 bohr (Fig. ), such that the entire electron density is annihilated by the CAP over the course of 5,000 a.u. of time propagation. The corresponding HHG spectrum is shown in Fig. and fails to evince any clear harmonics beyond the first three, and two of those are severely attenuated. The conclusion is that the CAP plays a critical role in obtaining characteristic HHG spectra, as without it the spectra are overwhelmed by noise and higher harmonics are miss-ing. The 1% of the electron density that is annihilated in Fig. is critical to obtaining a clean HHG spectrum, for otherwise this part of the density becomes a reflected wave whose interference with the outgoing wave leads to noise in the spectrum. On the other hand, if the turn-on radius of the CAP is set too close to the nuclei (small r 0 ), then the electron density is absorbed too quickly and the system does not experience enough pulse cycles to generate well-resolved harmonics.