[en] The choice of a suitable geometry in designing a radio-frequency cavity for e⁺e^- storage ring allows the reduction of multipacting (MP) discharges. We have studied the behaviour of resonant electron discharges in the RF cavity of the Adone storage ring in Frascati, that shows a broad MP barrier in the 35 to 70 kV range of the accelerating voltage. It can be explained by one point MP on the end-plates of the resonator. Our computer simulations of the trajectories of electrons in the RF fields of the cavity clearly show multipacting trajectories in that region of the cavity at about that field level. On the base of our experimental measurements and simulations, the design of a new RF cavity, multipactor free in the end-plates region, is presented