  The condensation of the spinless ideal charged Bose gas in the presence of a
magnetic field is revisited. The conventional approach is extended to include
the macroscopic occupation of excited kinetic states lying in the lowest Landau
level, which plays an essential role in the case of large magnetic fields. In
that limit, signatures of two diffuse phase transitions (crossovers) appear in
the specific heat. In particular, at temperatures lower than the cyclotron
frequency, the system behaves as an effectively one-dimensional free boson
system, with the specific heat equal to $(1/2)N k_B T$ and a gradual
condensation at lower temperatures.
