We summarize over 6 years of observations of ~1--4 MeV/nucleon heavy ions trapped in the Earth's magnetosphere on L shells of 1.7--3. We obtained these new results in low Earth orbit with the SAMPEX spacecraft; they extend the observations of trapped heavy ions in this L range to much lower energies than had previously been examined in detail. At 1--4 MeV/nucleon we observed a trapped population with a peak intensity near L~2.3 that includes the anomalous cosmic ray species O, Ne, and Ar also observed in interplanetary space at 1 AU. We also found elements with low first ionization potential (C, Mg-S, and Fe) trapped with the same spatial distribution. The low-energy trapped population increased in intensity between 1996 and 1997, roughly during solar minimum and minimum geomagnetic activity. It is possible that the 1--4 MeV/nucleon trapped population originates from a number of sources, including high-energy trapped anomalous cosmic rays that have lost energy in the residual atmosphere in the case of O and Ne, and directly incident, singly charged anomalous cosmic rays that have become stripped and subsequently trapped in the case of Ar. The group of trapped elements with low first ionization potential (C, Mg-S, and Fe) have roughly solar wind abundances relative to one another, suggesting a possible link between this trapped component and recently discovered solar wind pickup ions released from dust grains within the inner heliosphere. ¿ 2000 American Geophysical Union