It is shown that efficient RF current generation using lower hybrid slow waves is possible in the presence of fusion generated alpha particles. Wave accessibility and the condition for strong quasi-linear electron Landau damping restrict propagation of the slow wave to r/a ⪆ 0.5 in a thermonuclear plasma. This turns out to be a beneficial effect in terms of avoiding significant absorption of the injected waves via alpha particle damping, because of the spatial peaking of the alpha particle density profile near the plasma centre. Numerical results for RF current generation and wave absorption, relevant to the reactor regime, are obtained using a combined Fokker-Planck and toroidal ray tracing calculation.