The Singularity Reactor was added in patch 3.0 of the Heavensward expansion.
The Singularity Reactor becomes available at level 60 as part of the “Heavensward (Quest)” quest, which is given by Guidance Node – Azys Lla (X:16, Y:22).
The trial has a minimum ilevel of 142 to enter and rewards you with:
Allagan Tomestone of Poetics: 10