A method of stabilizing an electrolysis cell with a boundary, a liquid metal layer and an electrolyte layer having specific operational and geometric parameters, and comprises the steps of determining amplitude and frequency values for a desired external, time-varying and/or alternating magnetic field through wave reflection analysis on a theoretical wall whose parameters are representative of the cell wall's parameters; and imposing on said cell an external, time-varying and/or alternating magnetic field having substantially the same amplitude and frequency values determined in the wave reflection analysis so that the resultant magnetic field imposed on the cell tends to parametrically and dynamically desynchronize the occurrence of resonance instability near the cell's walls.