A subset of the electrostatic modes of a cold cloud of electrons, a no
n-neutral electron plasma, trapped in a Penning trap has been observed
and identified using a recent theoretical model. The detection of the
se modes is accomplished using electronic techniques which could apply
to any ion species. The modes are observed in the low-density, low-ro
tation limit of the cloud where the cloud approaches a two-dimensional
charged disk. We observe both axially symmetric and asymmetric drumhe
ad modes. The shape, rotation frequency, and density of the cloud are
found in a real-time nondestructive manner by measuring the frequency
of these modes. In addition, it is found that radio-frequency sideband
cooling compresses the cloud, increasing its density. The ability to
measure and control the density of a trapped ion cloud might be useful
for experiments on low-temperature ion-neutral-atom collisions, recom
bination rates, and studies of the confinement properties of non-neutr
al plasmas.