Geometrical consideration of beam lingering correction for the 23 model of atmospheric turbulence in the problem of FEL power beaming to geostationary satellites

The influence of the angular aberration in laser power beaming to geostationary satellites is considered. The angular aberration, which is proportional to the difference of the satellite speed and the Earth surface speed, makes it impossible to direct the laser beam to a satellite if the conventional approach with the adaptive mirror and phase conjugation is used. Since the additional rotations of the beam to compensate beam lingering may cause bad phase restoration we face serious problems how to translate incoherent radiation to remote satellites. In the frame of the Kolmogorov turbulence model, simple conditions of energy transfer are derived and discussed.