Radiation pressure acceleration (RPA) theoretically may have great potential to revolutionize the study of laserdriven ion accelerators due to its high conversion efficiency and ability to produce high-quality monoenergetic ion beams. However, the instability issue of ion acceleration has been appeared to be a fundamental limitation of the RPA scheme. To solve this issue is very important to the experimental realization and exploitation of this new scheme. In our recent work, we have identified the key condition for efficient and stable ion RPA from thin foils by CP laser pulses, in particular, at currently available moderate laser intensities. That is, the ion beam should remain accompanied with enough co-moving electrons to preserve a local "bunching" electrostatic field during the acceleration. In the realistic LS RPA, the decompression of the co-moving electron layer leads to a change of local electrostatic field from a "bunching" to a "debunching" profile, resulting in premature termination of acceleration. One possible scheme to achieve stable RPA is using a multi-species foil. Two-dimensional PIC simulations show that 100 MeV/u monoenergetic C6+ and/or proton beams are produced by irradiation of a contaminated copper foil with CP lasers at intensities 5 × 1020W/cm2, achievable by current day lasers.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.