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Concepts of high precision studies of the one-way speed of light anisotropy are discussed. The high energy particle beam allows measurement of a one-way speed of light anisotropy (SOLA) via analysis of the beam momentum variation with sidereal phase without the use of synchronized clocks. High precision beam position monitors could provide accurate monitoring of the beam orbit and determination of the particle beam momentum with relative accuracy on the level of 10−10, which corresponds to a limit on SOLA of 10−18 with existing storage rings. A few additional versions of the experiment are also presented.