Freedericksz transitions in circular toroidal layers of smectic C liquid crystals

The aim of this paper is to consider theoretically a Freedericksz transitio n for concentric toroidal layers of smectic C liquid crystal arising from a simple geometric setup, thereby extending the results of Atkin & Stewart [ Q. Jl Mech. Appl. Math., 47, 1994] who considered spherical layers of smect ic C in the usual cone and plate geometry. Application of smectic continuum theory leads, after suitable approximations are made, to a linear governin g equilibrium equation which is satisfied by both the trivial solution and a variable solution involving Bessel functions, We are able to determine th e critical magnitude H-C of the magnetic field H at which this variable sol ution exists, and a standard energy comparison reveals that the variable so lution is expected to be more energetically favourable than the zero soluti on provided H > H-C. Numerical examples of critical thresholds are given, w hich are comparable to those in the literature for nematics. The paper ends with a discussion section and some indication of possible future work.