MHD origin of the density limit

The density limit constraints the parameter space of toroidally confined fusion plasmas. In this work we explain the physical mechanism responsible for the large power input required to sustain a reversed-field pinch (RFP) discharge over a threshold in the Greenwald parameter n/n_G (n_G = I_P / πa² with I_P the plasma current). In fact, in the RFX-mod RFP, by increasing n/n_G, first a transition from the high-confinement, helical state (QSH) to the low-confinement, chaotic multiple-helicity state (MH) is observed: by increasing density further, at n/n_G ≈ 0.5 a poloidally symmetric (m=0), toroidally localized annulus of high density and high radiation forms, in all respect similar to the tokamak MARFE. For larger n/n_G, operating the machine becomes difficult, and very few discharges with n/n_G ≈ 1 are obtained, though no disruptions are seen. The RFP MARFE is caused by a convective cell which accumulates density in an annulus, whose size is proportional to the edge resonant m/n=0/1 magnetic island.

From MHD theory it is known that the m=0 mode amplitude is governed by the Hartmann number H, which plays a fundamental role in visco-resistive 3D simulations. By calculating H in a large RFX database, we show that the threshold in n/n_G corresponds to critical values in the Hartmann number.