How to Colonize an Asteroid
Once there are more mirrors than can be focused on the main shaft, a second solar concentration system can be set up on the opposite pole of the asteroid to begin cutting the smaller shaft.
The smaller shaft will be of the same length as the main shaft, but berhaps only a few feet in diameter. This shaft will connect the main docking bays and the burried ship modules with the main core, and will in fact be the primary entry and exit for the interior of the asteroid. This shaft will probaly come to an end 50 or 100 feet before the core of the asteroid so that there can be a solid mount at that end of the sphere for the diffusion mirrors.