Recently, a new mechanism was proposed by Fisch and Rax (1992) which could lead to the amplification of lower hybrid (LH) waves (LHWs) at the expense of alpha particle energy, thus improving the LH current drive efficiency. The method of quasi-linear lines of diffusion constraints used in the present contribution yields a more complete description of the above mentioned effect; the role of additional terms that are revealed is discussed. One of the necessary prerequisites for the mechanism to become operative is a sufficiently deep penetration of LHWs into the plasma column. A simple numerical analysis performed shows that this condition is more likely to be met in more conventional tokamaks than in those with a bean shaped cross-section