The stored energy and neutron yields of TFTR plasmas have been modelled, with small dispersion, by considering a parameter associated with the peakedness of the beam fuelling profile as an independent variable. Scalings with fixed multiplicative constants and exponential powers determined from the experimental data are applied to deuterium discharges at different major radii in TFTR, and also to deuterium-tritium (DT) plasmas. The domain of the data considered includes the supershot, high poloidal beta, L mode and limiter H mode operational regimes, as well as discharges with a reversed shear (RS) magnetic configuration. The role of plasma parameters, such as plasma current Ip, edge safety factor qa and toroidal field Bt, are considered in this study. Improved energy confinement and neutron production are relatively insensitive to these parameters compared with the beam fuelling peakedness parameter when considering plasmas that are stable to magnetohydrodynamic modes. In contrast, plasma stability is dependent on these quantities and also on parameters describing the peakedness of the equilibrium profiles. On the basis of externally controllable plasma parameters, the limitation and optimization of fusion power production of the present TFTR is investigated and a path towards a discharge condition with fusion power gain Q>1 is suggested