  We are developing a positron-electron plasma trap based on a dipole magnetic
field generated by a levitated superconducting magnet to investigate the
physics of magnetized plasmas with mass symmetry as well as antimatter
components. Such laboratory magnetosphere is deemed essential for the
understanding of pair plasmas in astrophysical environments, such as magnetars
and blackholes, and represents a novel technology with potential applications
in antimatter confinement and development of coherent gamma-ray lasers. The
design of the device requires a preemptive analysis of the achievable
self-organized steady states. In this study, we construct a theoretical model
describing maximum entropy states of a collisionless positron-electron plasma
confined by a dipole magnetic field, and demonstrate efficient confinement of
both species under a wide range of physical parameters by analysing the effect
of the three adiabatic invariants on the phase space distribution function. The
theory is verified by numerical evaluation of spatial density, electrostatic
potential, and toroidal rotation velocity for each species in correspondence of
the maximum entropy state.
