On a sidereal time variation of the Lorentz force

We consider a search for a sidereal time variation of the beam trajectory in the cyclotron motion in a static magnetic field. The combination of two beams moving in opposite directions could allow a test of the radius stability with sensitivity approaching $10^{-10}$. Such a level of variation of the Lorentz force, if it exists, would require a speed of light anisotropy on the level of $10^{-18}$.