[en] Our interest in efficient storage of cold, nonneutral plasma has been motivated by the elegant studies on cryogenic nonneutral electron plasmas at UCSD and by the remarkable results obtained from the laser-cooled ion plasmas at the NIST, Boulder, Colorado. Also motivating our study is the perceived need to develop the most expedient means of storing antimatter, whether it be antiprotons for gravitational studies or positrons for a variety of physics experiments and diagnostic purposes. One of the most explored technologies of confining nonneutral plasmas is the Penning trap. The maximum number density of cold nonneutral plasma that can be stored in such a trap is B²/2μ₀mc², in which B²/2μ₀ is the (homogeneous) magnetic energy density and mc² is the rest energy of the stored charges. In this paper, we shall present a synopsis of the results of our theoretical exploration of the effect on this hydrostatic limit, the so-called ''Brillouin'' limit, of altering the geometry of the confining vacuum magnetic field while maintaining the field's azimuthal symmetry. In particular, we shall analyze equilibrium confinement by, first, a poloidal magnetic field, B₄(r,z)r + B_z(r,z)z, and second, a toroidal magnetic field, along with the concomitant electrostatic fields