The proposal by Watson (1971, UK Patent G6P (G 21 b 3/16) N 1252906) to reduce the cone losses of a plasma in mirror machines depends on creating conditions such that particles with small transverse (with respect to the direction of the magnetic field) speed gain energy from a HF field localised inside a resonant cavity in a region of increasing magnetic field. Watson showed that the interaction between a particle and the HF field is reversible so that the energy expended by the HF field during the passage of the particle inside the cavity is recovered on its return journey after reflection. This possibility becomes less attractive when some peculiarities of the interaction of a real plasma and HF fields are considered which cannot be predicted by the over-simplified single particle model.