  The effect of a magnetic field on the charged vacuum is investigated. The
field dependence of the energy levels causes jumps in the total vacuum charge
that occur whenever an energy level crosses the Fermi level and this leads to
re-entrant cycles of vacuum charging and discharging. In atomic systems these
effects require astrophysical magnetic fields of around 10^8 T but in graphene
with a mass gap they occur in laboratory fields of about 1 T or lower. It is
suggested that an electrostatic graphene quantum dot defined by a gate
electrode provides a solid state model of the as yet unobserved charged vacuum
as well as a model of an atomic system in an extreme astrophysical environment.
Phase diagrams are computed to show how the total vacuum charge depends on the
confining potential strength and applied magnetic field. In addition the field
dependence of the vacuum charge density is investigated and experimental
consequences are discussed.
