A toroidally linked mirror system is proposed as a neutron source. The mirror core has the favourable feature of a high plasma beta in a relatively small volume. A low beta highly elliptical toroidal linkage prevents rapid electron thermal loss and enhances the power efficiency of previous designs of mirror machine based neutron sources to 30-40%. Specific problems related to the following are discussed: low beta toroidal MHD equilibrium, finite beta distortion of the plasma column, radial electric field, particle drift orbits, rotational stability, beam ion kinetics and cross-field transport