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The two-color above-threshold ionization (ATI) of atoms and ions isinvestigated 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 theweak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angulardistribution of the photoelectrons and their sideband structure are affected bythe plane-wave NIR field. We here explore the energy spectra and angularemission of the photoelectrons in such two-color fields as a function of thesize and location of the target (atoms) with regard to the beam axis. Inaddition, analogue to the circular dichroism in typical two-color ATIexperiments with circularly polarized light, we define and discuss sevendifferent dichroism signals for such vortex Bessel beams that arise from thevarious combinations of the orbital and spin angular momenta of the two lightfields. For localized targets, it is found that these dichroism signalsstrongly depend on the size and position of the atoms relative to the beam. Formacroscopically extended targets, in contrast, three of these dichroism signalstend to zero, while the other four just coincide with the (standard) circulardichroism, similar as for Bessel beams with small opening angle. Detailedcomputations of the dichroism are performed and discussed for the $4s$valence-shell photoionization of Ca$^+$ ions.

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