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Two-color above threshold ionization of atoms and ions in XUV Bessel beams and combined with intense laser light

The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam axis. In addition, analogue to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the (standard) circular dichroism, similar as for Bessel beams with small opening angle. Detailed computations of the dichroism are performed and discussed for the $4s$ valence-shell photoionization of Ca$^+$ ions.