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

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