In all major confinement devices (tokamaks, stellarators, spheromaks and reversed-field pinches—RFPs), a density limit has been found. Results summarized in a recent work by Puiatti et al (2009 Nucl. Fusion49 045012) show that in the RFP high density does not cause a disruption, but a sequence of increasingly critical phenomena. First, at intermediate density there is the disappearance of the high-confinement quasisingle helicity/single helical axis regimes. Then, at densities close to the Greenwald limit, toroidally and radially localized density accumulation and radiation condensation are observed, together with a fast resistive decay of the plasma current, which constitutes the real operative limit of the device. In this paper we discuss the effect of the magnetic ripple on test particle motion, showing that the accumulation of electrons in the X-points of the edge m = 0 islands is responsible for a modulation of the radial electric field Er which is at the core of the density limit mechanism. These results can be also relevant for the explanation of X-point multifaceted asymmetric radiation from the edge formation, observed in L-mode density limit discharges of JET.