  We study the ground state properties of an atom with nuclear charge $Z$ and
$N$ bosonic ``electrons'' in the presence of a homogeneous magnetic field $B$.
We investigate the mean field limit $N\to\infty$ with $N/Z$ fixed, and identify
three different asymptotic regions, according to $B\ll Z^2$, $B\sim Z^2$, and
$B\gg Z^2$. In Region 1 standard Hartree theory is applicable. Region 3 is
described by a one-dimensional functional, which is identical to the so-called
Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with
fermionic electrons in the region $B\gg Z^3$; i.e., for very strong magnetic
fields the ground state properties of atoms are independent of statistics. For
Region 2 we introduce a general {\it magnetic Hartree functional}, which is
studied in detail. It is shown that in the special case of an atom it can be
restricted to the subspace of zero angular momentum parallel to the magnetic
field, which simplifies the theory considerably. The functional reproduces the
energy and the one-particle reduced density matrix for the full $N$-particle
ground state to leading order in $N$, and it implies the description of the
other regions as limiting cases.
