A computational study has been made of the energy amplification factor Q to be expected in a toroidally linked mirror (TLM) reactor, using the one-dimensional multi-species Fokker-Planck code ISOTIONS. Because of the uncertainty which exists over the effect of ambipolar electric fields on diffusional losses from TLM systems, two model loss terms have been considered. For each model, Q has been calculated for a range of values of the mirror ratio, the ion injection energy inj, and the 'critical energy' c, of TLM diffusion theory. For values of c/inj ∼ 0.5, Q is very significantly enhanced with respect to the value in a single mirror machine, even in the relatively pessimistic model.