Study of trigger algorithm performance with phase 2 upgrade for the muon spectrometer of ATLAS experiment.

The Phase 2 upgrade of the Large Hadron Collider (LHC) at CERN will significantly increase the luminosity of proton-proton collisions, providing a new frontier in particle physics research. The Muon Spectrometer is a crucial component of the ATLAS detector, and its trigger system must be upgraded to meet the challenges of the increased luminosity. In this communication, we present the expected trigger performance of the Muon Spectrometer after Phase 2. We discuss the design and operation of the upgraded trigger system, including new hardware components and algorithms implemented in FPGA firmware that enable faster and more efficient muon identification and selection. We present the expected performance of the upgraded muon trigger system, including the trigger efficiency as a function of muon transverse momentum measured using simulated events. Challenges faced by the system include the high background rate and the need to maintain a high trigger efficiency in the presence of pile-up. In conclusion, the upgraded system is expected to achieve higher performance and enable new discoveries, pushing the boundaries of our understanding of the fundamental nature of matter and universe.