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Calculations on the dynamics of ions and electrons in near-infrared laserfields at intensities up to $3 \times 10^{23}$ W/cm$^2$ are presented. Weexplore the acceleration of ions in a laser focus by conservation of canonicalmomentum during ionization events and by the ponderomotive force in the f/1focal geometry required to reach such intensity. At intensity exceeding10$^{23}$ W/cm$^2$, highly charged ions are expelled from the laser focusbefore they can interact with the laser pulse at peak intensity, decreasing thepredicted ionization yields of deeply-bound states. We consider the interactionof a tightly-focused, f/1 laser pulse with krypton at an intensity of $3 \times10^{23}$ W/cm$^{2}$ and a pulse duration of 140 fs. We find that the ions andelectrons are accelerated to energies in excess of 2 MeV/nucleon and 1.4 GeV,respectively. Ponderomotive expulsion of the parent ions decreases the totalnumber of ultra-relativistic ATI electrons produced by tunneling ionizationfrom the K-shell states of krypton but does not change their energy spectrum.

Direct Laser Ion Acceleration and Above-Threshold Ionization at Intensities from $10^{21}$ W/cm$^{2}$ to $3 \times 10^{23}$ W/cm$^{2}$