We study ring current dynamics on a day of exceptionally low solar wind density (of ∼0.1 cm−3). Inner magnetospheric measurements of geomagnetic activity show geomagnetic quiet par excellence. On May 11, 1999, the values were |Dst| < 10 nT and Kp = 0+. The field at geostationary orbit was very close to dipolar. We simulate the global evolution of the ring current ion population during this period and compare the effect of the magnetopause, ring, magnetotail, and field‐aligned currents on the Dst index. Measured H+, He+, and O+ energy and pitch angle distributions by the Magnetospheric Ion Composition Spectrometer (MICS) and HYDRA instruments on Polar on May 9 are used as initial conditions for our kinetic model. Comparing model results with Polar data on May 11, we find remarkable agreement, proving the applicability of our model for these magnetospheric conditions. We compare modeled H+ and He+ ion distributions with quiet time ring current distributions inferred from statistical studies, and we find that as a general trend, the simulation results have lower values than the statistical patterns. The ground magnetic field disturbances due to the ring and the magnetopause currents decrease quasi‐monotonically on May 11, reaching limiting magnitudes of ∼5 and ∼3 nT, respectively. These values are substantially smaller than the ∼20 nT quiet time values obtained from statistical studies.