Brillouin‐density pure ion plasmas have been generated in a quadrupole Penning tray by electron‐beam ionization of a low‐pressure gas. Large, spheroidal, steady‐state plasmas are produced that extend to one of the trap electrodes. With the density fixed at the Brillouin limit by the high ion production rate, the electrode potentials determine the plasma shape. The frequencies of azimuthally propagating cyclotron and diocotron modes are found to vary significantly with the plasma aspect ratio. For oblate plasmas, we are able to test theoretical predictions of a simple fluid model, and the frequencies are in good agreement. © 1995American Institute of Physics