Not yet reviewed by Pith; the record is open.

Recent advances in strong x-ray laser techniques enable the study of nonlinear multiphoton ionization in extreme high-frequency fields. Although the stabilization regime in such fields is theoretically established, its modified properties in the nondipole regime for long laser pulses remains unknown. Here, we numerically investigate the strong-field ionization of an atom in a long XUV laser pulse in the nondipole regime. Our study of the time-dependent quantum dynamics reveals a quasiperiodic modulation of the ionization yield as a function of pulse duration. We demonstrate that the Coulomb-field-induced slow oscillation of the ionized electron wave packet during the interaction is responsible for the observed modulation of the ionization yield. Furthermore, we scrutinize the unusual photon momentum sharing between the photoelectron and the ion in this extreme regime. These effects are observable in upcoming x-ray free-electron laser facilities.