Ultracold atom-based electron sources have recently been proposed as an alternative to the conventional photo-injectors or thermionic electron guns widely used in modern particle accelerators. The advantages of ultracold atom-based electron sources lie in the fact that the electrons extracted from the plasma (created from near threshold photo-ionization of ultracold atoms) have a very low temperature, i.e. down to tens of Kelvin. Extraction of these electrons has the potential for producing very low emittance electron bunches. These features are crucial for the next generation of particle accelerators, including free electron lasers, plasma-based accelerators and future linear colliders. The source also has many potential direct applications, including ultrafast electron diffraction (UED) and electron microscopy, due to its intrinsically high coherence. In this paper, the basic mechanism of ultracold electron beam production is discussed and our new research facility for an ultracold, low emittance electron source is introduced. This source is based on a novel alternating current Magneto-Optical Trap (the AC-MOT). Detailed simulations for a proposed extraction system have shown that for a 1 pC bunch charge, a beam emittance of 0.35 mm mrad is obtainable, with a bunch length of 3 mm and energy spread 1 %.