We theoretically study the response of He atoms exposed simultaneously to an intense IR pulse and a weak extreme ultraviolet (XUV) pulse with photon energies far from the principal atomic He resonances. We find that XUV forward scattering from the nonstationary electronic wave packet promoted by the intense IR driving field is strongly enhanced as compared with the normal weak scattering from bound or free electrons. Based on this effect, we predict that large amplification of XUV radiation can be achieved in the cutoff spectral region of high-harmonic generation in He gas. DOI: 10.1103/PhysRevLett.111.133902 PACS numbers: 42.65.Ky, 32.80.Fb, 42.55.Vc The availability of tabletop coherent extreme ultraviolet (XUV) radiation sources with high photon energies has been largely pursued over the last two decades [1]. In this Letter we consider the amplification of the XUV yield generated in high-harmonic generation (HHG) processes by considering the simultaneous excitation of He atoms with an intense IR driving pulse and an XUV pulse. It is known that synchronization of one or several low-order harmonics of high peak intensities with the driving IR laser pulse can produce a large yield enhancement [2,3]. The target medium is in this case strongly ionized due to the XUV photon energies that are considered and due to their high intensity, so that the influence of the combined fields on the HHG spectrum is at spectral regions of higher photon energies than the added XUV pulse. The present research is crucially different from these previous approaches in that we consider weak intensity XUV pulses with photon energies that are far from the principal atomic resonances, with negligible XUV ionization [4]. In our approach, the only affect on the HHG spectrum is at about the same spectral region as the added XUV pulse. Specifically, we address the influence of the high-intensity IR driving pulse on the scattering of XUV radiation from He atoms in HHG processes. We find that forward scattering is largely enhanced when an XUV pulse is synchronized with the amplitude maxima of the IR laser pulse. It is shown numerically that this effect can be used for the amplification of coherent XUV radiation in the HHG cutoff spectral region to power levels that might be useful for most applications.We resolve the interaction of a He atom with the combined IR laser and XUV pulse by numerically solving the time-dependent Schrödinger equation in the singleatom strong-field approximation [5]. The strong-field approximation describes the interaction with laser light of arbitrary frequency content, accounts for most important quantum effects-such as quantum diffusion of wave packets and quantum interferences, and allows our study to be computationally efficient. The present results apply for low-pressure HHG processes, propagation effects in a higher-pressure gas will be discussed in a future paper. Resonant absorption from He atoms will be evaluated in the last part of the study.In the following we consider a 5 fs (FWHM) laser pulse with Gau...