The ionization of a highly excited Rydberg atom subjected to a periodic sequence of electric field impulses, or “kicks,” is chaotic. We focus on the dynamics of a single kicking period in order to isolate the ionization mechanism. Potassium Rydberg atoms, prepared in a quasi-one-dimensional state, are exposed to a sequence of ionization kicks, and the total fraction of ionized atoms is then measured. These experimental data are compared to a one-dimensional classical model. The classical analysis reveals that the ionization process is governed by a phase space turnstile—a geometric structure associated with chaotic transport in diverse systems. The turnstile geometry is reflected in the experimental data. Previous work explored the dependence of the turnstile geometry on the kicking period. The present work explores the dependence on the kicking strength. In particular, increasing the kicking strength allows us to observe the stretching of the turnstile lobe as it penetrates the region of phase space occupied by the electronic state, leading to a sharp rise in the total ionization fraction. This work thus highlights the importance of phase space geometry in organizing chaotic transport in atomic Systems.