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As part of an upgrade to the LHC collimation system, 8 TCTP and 1 TCSG collimators are proposed to replace existing collimators in the collimation system. In an effort to review all equipment placed in the accelerator complex for potential side effects due to collective effects and beam-equipment interactions, beam coupling impedance simulations are carried out in both the time-domain and frequency-domain of the full TCTP design. Particular attention is paid to trapped modes that may induce beam instabilities and beam-induced heating due to cavity modes of the device.

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