Dislocation Geometry in the TGB-A Phase: Linear Theory

We demonstrate that an arbitrary system of screw dislocations in a smectic-A liquid crystal may be consistently treated within harmonic elasticity theory, provided that the angles between dislocations are sufficiently small. Using this theory, we calculate the ground state configuration of the TGB-A phase. We obtain an estimate of the twist-grain-boundary spacing and screw dislocation spacing in a boundary in terms of the macroscopic parameters, in reasonable agreement with experimental results.