Helical plasma-wall interaction in the RFX reversed-field pinch: toroidal effects, localization and role of sidebands

The magnetic topology of the stochastic edge of a helical reversed-field pinch in the quasisingle helicity state (QSH)\footnote{R. Lorenzini et al., Nature Phys., \textbf{5}, 570574, (2009).}, which is characterized by a dominant tearing mode with helicity $m/n = 1/7$, shows to be deeply influenced by higher harmonics $(m \pm 1)/n$, with the same $n=7$, due to the toroidal coupling of the dominant mode with the Shafranov shift. Recent analyses\footnote{M. Agostini et al., Nucl. Fusion, \textbf{57}, 076033, (2017).} show that even a modest amount ($\sim 5$~mT total) of higher $7 < n \le 23$ harmonics (the so-called ``secondary'' modes) can have sizable effects on the PWI pattern, as it is evident both in measurements of radiated power and particle influxes, and in simulations of 3D maps of parallel field-connection length to the wall $L_{c,w}$. This is a caveat for MP application in tokamaks, showing that toroidal and poloidal sidebands, though smaller than the base mode  by a factor $\epsilon = a/R$, can influence the kinetic response  and related issues (i.e. ELM suppression). On the contrary, an expected halvening of the amplitude of the secondary modes with $n > 7$  in the modified RFX-mod2 experiment could result in a dramatic reduction of PWI in this device.