Like the Speaker of the House, the Sergeant at Arms is a position that applies only to Senate meetings. While the Speaker is the administrator of the Senate meetings, the Sergeant at Arms is the strong arm. It is up to him to ensure that the meetings remains under control, don't get out of hand and remain on topic.
The Sergeant at Arms needs to be able to drown out all others in the meeting and be a respected member who commands attention when needed. If all goes well during a Senate meeting, people should not even know he is there. However, the second things start to get out of hand, it is up to the Sergeant at Arms to step in, stop the situation and get everything back on track.
During a Senate meeting, the Sergeant at Arms is the supreme authority. When he says stop, everyone needs to stop what they're doing. This includes the Chancellor and the Council. (We need to add something here about the repercussions for not listening to the Sergeant at Arms)