Studies of a purely non-linear method of RF heating are presented. The method combines localization of absorption at the centre of the plasma column with a marked decrease in the pumping frequency compared with the cyclotron frequency. A stationary distribution of the electromagnetic radiation is found, as a result of multiple reflections from the chamber walls. The energy distribution over the toroidal cross-section was calculated with the help of a ray tracing simulation. It is shown that, compared with linear systems, the threshold for the parametric instability decreases because of the return of oscillations to the pumping region after a cycle of the torus. Calculations of the threshold for both isothermal and non-isothermal plasmas are presented. The level of turbulence defined by the non-linear effects is estimated for this regime. The effective collision frequency, describing pump wave conversion into plasma waves, is determined in the framework of weak turbulence theory. The efficiency of the method is discussed and some comparison with traditional methods is presented