Cholesteric pitch-transitions induced by a magnetic field in a sample containing incomplete number of pitches

We investigate the pitch transitions induced by an external bulk field in a Cholesteric Liquid Crystal slab of finite thickness ` that contains an incomplete number of -twists. The analysis is performed for a magnetic field that is (i) perpendicular to the helical axis, and (ii) tilted with respect to one of the easy directions imposed by planar and rigid boundary conditions. For finite ` we obtain a cascade of transitions, where the bulk expels a half-pitch at a time with increasing field to avoid divergences in the elastic energy. The dependence of the threshold magnetic field inducing the expulsion on the easy axes twist angle is investigated for all the cascade of pitch transitions and in particular for the final one, corresponding to the Cholesteric-Nematic transition. In the ` ! 1limit this dependence disappears and we reobtain the results of de Gennes for an infinite sample.