Abstract
We determine the phase diagram of a quasi-one-dimensional conductor (weakly coupled chains system with an open Fermi surface) in a magnetic field. The superconducting state evolves from an Abrikosov vortex lattice in weak field to a Josephson vortex lattice in very strong field, with a reentrance of the superconducting phase. Between these two limits, there is a cascade of first order transitions between different superconducting phases due to commensurability effects between the crystalline lattice and different superconducting phases due to commensurability effects between the crystalline lattice and the order parameter. In these phases, the order parameter has a laminar structure.
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