Ion density enhancements at the topside low-latitude ionosphere during a Bastille storm on 15-16 July 2000 and Halloween storms on 29-31 October 2003 were studied using data from ROCSAT-1/IPEI experiment. Prominent ion density enhancements demonstrate similar temporal dynamics both in the sunlit and in the nightside hemispheres. The ion density increases dramatically (up to two orders of magnitude) during the main phase of the geomagnetic storms and reaches peak values at the storm maximum. The density enhancements are mostly localized in the region of a South Atlantic Anomaly (SAA), which is characterized by very intense fluxes of energetic particles. The dynamics of near-Earth radiation was studied using SAMPEX/LEICA data on >0.6 MeV electrons and >0.8 MeV protons at around 600 km altitude. During the magnetic storms the energetic particle fluxes in the SAA region and in its vicinity increase more than three orders of magnitude. The location of increased fluxes overlaps well with the regions of ion density enhancements. Two mechanisms were considered to be responsible for the generation of storm-time ion density enhancements: prompt penetration of the interplanetary electric field and abundant ionization of the ionosphere by enhanced precipitation of energetic particles from the radiation belt.