The appearance of multipaction discharges in diode gaps of the linear accelerator of ions without the system for stabilization of electrodynamic parameters of the multicell cavity structure is considered to be one of the serious factors of excitation, at which it is impossible to attain not only the required characteristics of accelerating fields but also stable RF oscillations in its system of the complexly coupled oscillation loops. At suppression of the conditions of secondary electrons multiplication and elimination of the possibility of their number growing in time up to the size of multipaction discharges, the conditions of stability of RF oscillations and operation of the entire system of accelerator excitation can be, in general, satisfactory. And for many start-up and commissioning works and technological problems on the accelerator, solving of the suppression problem of spurious multipaction discharges and achieving of stable mode of the excited RF voltages is considered to be the final stage. It is experimentally shown the control of low-voltage multipaction processes from their maximal influence upon establishment of the RF voltages on the elements of high-Q accelerating structure up to the complete suppression of multiplication of the secondary electrons from the material of the electrodes and obtaining of the stable electrodynamic characteristics.