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The aim of this paper is to define the optimal couple of the total pressure and the magnetization of the permanent magnets for self-maintaining under optimal conditions an asymmetric magnetron radio frequency (RF) discharge. Electro-dynamics discharge simulations are based on a self-consistent particle model using Monte Carlo method for the treatment of collisions between charged particle and background gas. The simulations are performed at a fixed mixture of 90% Ar/10% O2 by simultaneously decreasing the total pressure P and increasing the magnetization σ. In the case of a sinusoidal RF power supply with 200 V for peak voltage and 13.56 MHz for frequency, the magnetization of the permanent magnets varies between 500 Gauss at 25 mTorr to 1400 Gauss at 5 mTorr. We use a semianalytical method for calculating the applied magnetic field generated by two permanent magnets that are composed of concentric rings. This enables generating, in a specific region of the interelectrode gap near the cathode, an optimal magnetic field crossing the RF electric field for application to magnetron discharges. The simulation results of RF magnetron discharge shown that, in the case of the lowest considered pressure (5 mTorr), a high magnetization of 1400 Gauss is the most favorable for self-maintaining the discharge and generating a quasi-ion beam energy distribution near the cathode that is interesting for cathode sputtering processes.