Effect of the geomagnetic field on the intensity of sodium laser guide stars

In calculating the return flux of sodium laser guide stars (LGS), often only the best return conditions are assumed, relying on strong optical pumping with a circularly polarized laser. However, one can obtain this optimal return only along one specific laser orientation on the sky, depending on the direction of the geomagnetic field. Sodium atoms precess around magnetic field lines which cycles the magnetic quantum number, reducing the effectiveness of optical pumping. The risk is hence for the system designer to overestimate the effective return flux for a given laser power. In this paper we present calculations for the effect of the geomagnetic field on the return flux. Optical pumping actually produces little improvement in most observing directions. In addition, we find that at many observatory locations, the direction of optimal return flux is very close to the horizon, often below the observing limit.