We describe some recent experiments that use a new Penning trap to trap and laser‐cool more than 105Be+ions. In this wrok the Coulomb coupling parameter was estimated to by typically greter than 100 and in some cases greater than 300. Shell structure was difficult to observe in the ion fluorescence from these large clouds. An initial Bragg scattering experiment to obtain information on the ion correlations is described. We also briefly review our work on the electrostatic modes of a Penning trap plasma including the use fo the modes to diagnose the shape and density of a cryogenic electron plasma. Some applications of laser‐cooled plasmas in Penning traps, such as atomic clocks, are discussed. © 1995American Institute of Physics