  We investigate the effect of a magnetic field on a bosonic ladder. We show
that such a system leads to the one dimensional equivalent of a vortex lattice
in a superconductor. We investigate the physical properties of the vortex
phase, such as vortex density and vortex correlation functions and show that
magnetization has plateaus for some commensurate values of the mag netic field.
The lowest plateau corresponds to a true Meissner to vortex transition at a
critical field $H_{c1}$ that exists although the system has no long range
superconducting order. Implications for experimental realizations such as
Josephson junction arrays are discussed.
