Per Mill Level Control of the Circular Polarisation of the Laser Beam for a Fabry-Perot Cavity Polarimeter at HERA

A precise and fast Fabry-Perot cavity polarimeter, installed in the HERA tunnel in the summer of 2003, was used to measure the longitudinal polarisation of the lepton beam. A complete theoretical model has been developed in order to control at the per mill level the degree of circular polarisation of the laser beam. The transport of this quantity within the whole optical setup has also been performed and controlled at the same level of precision. This is the first time that such a precision is achieved in the difficult, hostile and noisy environment of a particle collider.