Realization of the optimal beam dilution pattern of the FCC-hh ring using beating frequencies

In order to avoid the damage of dump target Future Circular Collider’s proton ring, beam will be swept over its surface using dilution kickers oscillating in x/y planes with 90∘ phase difference, and an amplitude changing time, thereby creating a spiral-like pattern. The natural time-dependence is exponential decay damped circuit, which results decreasing pitch, increasing energy deposition density towards small radii. Compared optimal pattern flat density, this requires larger size, total kicker strength or higher allowed material. We propose realization two beating frequencies. This method has advantage same, very simple circuitry as baseline proposal: independent oscillator circuits (including magnets), interfere only their effect on beam. concept 18% decrease maximum excursion (i.e. size), 13% power respect solution, at no extra cost. Besides demonstration concept, sensitivity analysis circuit parameters presented.