The Naval Research Laboratory three‐dimensional, first‐principles simulation code SAMI3 (Sami3 is Also a Model of the Ionosphere) is used to model plasmasphere refilling. A time‐dependent Volland‐Stern‐Maynard‐Chen potential is used to model an idealized magnetic storm that erodes the plasmasphere to L<3. The potential is then relaxed to the prestorm state, and refilling is simulated for a range of L shells 3≤L≤5 over a period of 7 days. Refilling rates compare well to observed refilling rates. The model plasmasphere during this quiet period displays a day‐to‐day repetition in its morphology that has not been previously observed.