Progress on the 10 TeV center-of-mass energy muon collider

A 10 TeV center-of-mass muon collider could serve as a next-generation high-energy lepton collider with substantial physics potential while offering a more compact footprint than other proposed machines. However, this collider presents unique challenges, largely due to the short lifetime of muons and their decay products. Specifically, the collider ring requires specialized designs to protect the magnets and detectors while ensuring negligible neutrino radiation at Earth's surface. The high required luminosity also imposes stringent constraints, including very small beta functions at the interaction points that lead to strong chromatic effects. To meet these challenges, high-field combined-function magnets are used to create a compact layout with minimal straight sections. Flexible momentum compaction arc cells are used to maintain short bunch lengths and local chromatic correction sections to address the chromatic aberrations from the interaction regions. This work presents recent advancements in the 10 TeV muon collider ring, including interaction region improvements to reduce beam-induced background and a study that investigates the impact of $\beta^*$ on the dynamic and momentum acceptance.