MHD limit cycles on FTU

The development of low-order tearing modes during density ramp-up in the high density regime on the Frascati Tokamak Upgrade is characterized by an initial ordinary stage, with a 'one-to-one' relation between mode amplitude and frequency, followed by the formation, on the amplitude/frequency plane, of 'limit cycles' with increasing area up to disruption for density limit if the density continues to grow. A critical mode amplitude for transition from smooth to cyclic behavior has been observed in experiments performed changing the line-averaged density, and the existence of such a threshold has been confirmed in experiments of real time control of tearing mode in the high density regime by means of electron cyclotron resonance heating.The amplitude and frequency modulations of the observed tearing mode (m and n are the poloidal and toroidal mode number, respectively) occur in few milliseconds, which is not in agreement with the diffusion resistive time of about two hundred milliseconds expected on the resonance from the non-linear theory. The origin of such modulations has been investigated, taking into account that in the high amplitude stages of the mode temporal evolution it is difficult to discriminate between non-linear effects and mode coupling mechanisms. Our analysis suggests that the formation of limit cycles could be due to a recursive island fragmentation, with a sort of self-healing phenomenon; in fact the island distortion increases before amplitude drops. Concerning the interaction with modes of different helicity, our experiments seem to indicate that the presence of the resonance in the plasma is necessary for the occurrence of deep and regular limit cycles for the 2/1 tearing mode.