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Because of the strong beam-beam force at the interaction points in the FCC-$ee$ collider, the charge balance of two beams opposing each other is vitally important. The injection of a high charge beam derives the imbalance of two beams, which causes the instability of the beams. To avoid this imbalance, the bootstrapping injection has been adopted for the FCC-$ee$ collider. The conditioning of the bootstrapping injection is being performed as a part of the design study of FCC-$ee$. For simulating the top-up injection, the quasi-strong-strong beam-beam method is implemented in the full lattice simulation code SAD.
In this report, the charge threshold of the injection beam for each collision mode are presented. Also, the implementation of the quasi-strong-strong simulation are explained.
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