  Cholesteric Liquid Crystals (CLCs), subject to externally applied magnetic
fields and confined between two parallel planar surfaces with strong
homeotropic anchoring conditions, are found to undergo transitions to different
types of helicoidal configurations with disclinations. Analytical and numerical
studies are performed in order to characterise their properties. In particular,
we produce a phase diagram for the transitions from the nematic state to the
helicoidal phases in terms of the molecular chirality and the strength of the
applied magnetic field.
