  A magnetic bag is an abelian approximation to a large number of coincident
SU(2) BPS monopoles. In this paper we consider magnetic bags in hyperbolic
space and derive their Nahm transform from the large charge limit of the
discrete Nahm equation for hyperbolic monopoles. An advantage of studying
magnetic bags in hyperbolic space, rather than Euclidean space, is that a range
of exact charge N hyperbolic monopoles can be constructed, for arbitrarily
large values of N, and compared with the magnetic bag approximation. We show
that a particular magnetic bag (the magnetic disc) provides a good description
of the axially symmetric N-monopole. However, an abelian magnetic bag is not a
good approximation to a roughly spherical N-monopole that has more than N zeros
of the Higgs field. We introduce an extension of the magnetic bag that does
provide a good approximation to such monopoles and involves a spherical
non-abelian interior for the bag, in addition to the conventional abelian
exterior.
