Dependence of sodium laser guide star photon return on the geomagnetic field

Aims. The efficiency of optical pumping that increases the backscatter emission of mesospheric sodium atoms in continuous wave (cw) laser guide stars (LGSs) can be significantly reduced and, in the worst case, eliminated by the action of the geomagnetic field. Our goal is to present an estimation of this effect for several telescope sites. Methods. Sodium atoms precess around magnetic field lines that cycle the magnetic quantum number, reducing the effectiveness of optical pumping. Our method is based on calculating the sodium magnetic sublevel populations in the presence of the geomagnetic field and on experimental measurements of radiance return from sodium LGS conducted at the Starfire optical range (SOR). Results. We propose a relatively simple semi-empirical formula for estimating the effect of the geomagnetic field on enhancing the LGSs photon return due to optical pumping with a circularly polarized cw single-frequency laser beam. Starting from the good agreement between our calculations and the experimental measurements for the geomagnetic field effect, and in order to more realistically estimate the sodium LGSs photon return, we introduce the effect of the distance to the mesospheric sodium layer and the atmospheric attenuation. The combined effect of these three factors is calculated for several telescope sites. Conclusions. In calculating the return flux of LGSs, only the best return conditions are often assumed, relying on strong optical pumping with circularly polarized lasers. However, one can only obtain this optimal return along one specific laser orientation on the sky, where the geomagnetic field lines are parallel to the laser beam. For most of the telescopes, the optimum can be obtained at telescope orientations beyond the observation limit. For the telescopes located close to the geomagnetic pole, the benefit of the optical pumping is much more important than for telescopes located close to the geomagnetic equator