Ions are released over time from an ion source into a beam area proximate a central axis. A radiofrequency (RF) system with a variable frequency and variable voltage accelerates the ions in orbiting trajectories expanding outward from the central axis. The ions are accelerated to different extraction energy levels within a given design range at a shared extraction radius from the central axis. An RF-frequency versus ion-time-of-flight scenario is set such that the frequency versus time scenario is the same for any ion extraction energy from the given design range, and a constant-or-variable-RF-voltage versus ion-time-of-flight scenario is adjusted to provide ion acceleration from injection to extraction for ions with different respective extraction energy levels within the given design range; and the ions are extracted at the different energy levels at the shared extraction radius.