Physical principles of recuperation (return) of charged particle energy in traps with rotating plasma are discussed. A specificity of these systems is that normally ion injection occurs due to ionization of neutral atoms in a volume with crossed fields. As this takes place, ions are accelerated in these fields in such way that the speed of cyclotron rotation equals the speed of azimuth drift of the plasma as a whole. A particle moves in the laboratory reference system along a cycloid, the ion energy being zero at the top point of the cycloid. This specificity of ion movement is used for recuperation of its energy when it leaves the trap. A two-stage recuperation scheme is considered. These stages are the ion's transition of the centrifugal barrier and collection of ions on the electrodes that form the radial electric field. The conditions for rather efficient realization of such recuperation are discussed.