Adiabatic cooling is shown to be a simple and effective method to cool many charged particles in a trap to very low temperatures. Up to 3×10(6) p are cooled to 3.5 K-10(3) times more cold p and a 3 times lower p temperature than previously reported. A second cooling method cools p plasmas via the synchrotron radiation of embedded e(-) (with many fewer e(-) than p in preparation for adiabatic cooling. No p are lost during either process-a significant advantage for rare particles.