We produce simultaneously dense and well-confined nonneutral plasmas b
y spherical focusing. A small (3 mm radius) Penning trap has low-energ
y electrons injected at a single pole of the sphere. Precisely when th
e trap parameters art adjusted to produce a spherical well, the system
self-organizes into a spherical state through a bootstrapping mechani
sm which produces 3 hysteresis. Additional confirmation of the dense s
pherical focus is provided by electrons scattered by the central core.
Core densities up to 35 times the Brillouin density have been inferre
d from the data.