In the quest for new energy sources, the research on controlled thermonuclear fusion 1 has been boosted by the start of the construction phase of the International Thermonuclear Experimental Reactor (ITER). ITER is based on the tokamak magnetic configuration 3, which is the best performing one in terms of energy confinement. Alternative concepts are however actively researched, which in the long term could be considered for a second generation of reactors. Here, we show results concerning one of these configurations, the reversed-field pinch 4,5 (RFP). By increasing the plasma current, a spontaneous transition to a helical equilibrium occurs, with a change of magnetic topology. Partially conserved magnetic flux surfaces emerge within residual magnetic chaos, resulting in the onset of a transport barrier. This is a structural change and sheds new light on the potential of the RFP as the basis for a low-magnetic-field ohmic fusion reactor.The main magnetic field configurations studied for the confinement of toroidal fusion-relevant plasmas are the tokamak 3 , the stellarator 6 and the reversed-field pinch 4,5 (RFP). In the tokamak, a strong magnetic field is produced in the toroidal direction by a set of coils approximating a toroidal solenoid, and the poloidal field generated by a toroidal current flowing into the plasma gives the field lines a weak helical twist. This is the configuration that has been most studied and has achieved the best levels of energy confinement time. Thus, it is the natural choice for the International Thermonuclear Experimental Reactor, which has the mission of demonstrating the scientific and technical feasibility of controlled fusion with magnetic confinement.The RFP, like the tokamak, is axisymmetric and exploits the pinch effect due to a current flowing in a plasma embedded in a toroidal magnetic field. The main difference is that, for a given plasma current, the toroidal magnetic field in a RFP is one order of magnitude smaller than in a tokamak, and is mainly generated by currents flowing in the plasma itself. This feature is underlying the main potential advantage of the RFP as a reactor concept, namely the capability of achieving fusion conditions with ohmic heating only in a much simpler and compact device. In the past, this positive feature was overcome by the poorer stability properties, which led to the growth and saturation of several magnetohydrodynamic (MHD) instabilities, eventually downgrading the confinement performance. These instabilities, represented by Fourier modes in the poloidal and toroidal angles θ and φ as exp [i(mθ − nφ) were considered as an unavoidable ingredient of the dynamo self-organization process 4,8,9 , necessary for the sustainment of the configuration in time. The occurrence of several MHD modes resonating on different plasma layers gives rise to overlapping magnetic islands, which result in a chaotic region, extending over most of the plasma volume 10 , where the magnetic surfaces are destroyed and the confinement level is modest. This conditi...

A limit for the edge density, ruled by radiation losses from light impurities, is established by a minimal cylindrical magneto-thermal equilibrium model. For ohmic tokamak and reversed field pinch the limit scales linearly with the plasma current, as the empirical Greenwald limit. The auxiliary heating adds a further dependence, scaling with the 0.4 power, in agreement with Lmode tokamak experiments. For a pure externally heated configuration the limit takes on a Sudolike form, depending mainly on the input power, and is compatible with recent Stellarator scalings.A discharge-terminating density limit (DL) is found in all the magnetic confinement fusion devices [1]. One of the main interpretative branches invokes impurity radiation losses, which scale with the square of the density. The consequent cooling of the plasma can become critical at high density, giving rise to a variety of instabilities, both thermal [2][3][4][5][6][7][8], and MHD [9][10][11][12][13]. Given the rich phenomenology, DL seems elusive of an explanation based on a single mechanism. This letter presents a complementary approach to the problem, analysing, in cylindrical geometry, the feasibility of a magneto-thermal equilibrium with realistic temperature profile, rather than addressing specific instabilities. Such a study provides a unified interpretation of the phenomenon, given that a DL ruled by light impurities radiation (experiments show that any significant contamination by heavy impurities is just detrimental towards the achievement of high densities [1]), quantitatively consistent with experimental scalings, emerges naturally for all the magnetic configurations. In particular, we found a Greenwald-like scaling [1] for tokamak and reversed field pinch (RFP), and a Sudo-like scaling [14,15] for a pure externally heated configuration, taken as approximation of the stellarator. We are aware that this analysis cannot 2 exhaust the topic, since some instability mechanism is necessary to describe the dynamical route to the plasma termination. Consequently, we speak of an 'equilibrium DL' and not of the DL in the ultimate sense. This work has been inspired by analyses of the ohmic tokamak presented in[16] (section 7.8) and in [17] (section 8). The differences rely in a more general approach, besides a more accurate treatment of the profile dependent terms.We introduce a minimal cylindrical equilibrium model (each quantity depending on the radial coordinate r only), analytically treated with a formalism able to unify the configurations with an applied electric field, namely the tokamak, both ohmic and with additional heating, and the RFP, considered as purely ohmic. Basically, we will take integral relations from the heat transport equation, in some way similar to those carried out in [18] apart for the simpler geometry, and combine them with Ohm's law at r=0 (on-axis). Ohm's law is replaced by a suitable scaling for the energy confinement time in the case of pure auxiliary heating. [ ]Here, T is the electron temperature and K an effec...

A power-balance model, with radiation losses from impurities and neutrals, gives a unified description of the density limit (DL) of the stellarator, the L-mode tokamak, and the reversed field pinch (RFP). The model predicts a Sudo-like scaling for the stellarator, a Greenwald-like scaling, , for the RFP and the ohmic tokamak, a mixed scaling, , for the additionally heated L-mode tokamak. In a previous paper (Zanca et al 2017 Nucl. Fusion 57 056010) the model was compared with ohmic tokamak, RFP and stellarator experiments. Here, we address the issue of the DL dependence on heating power in the L-mode tokamak. Experimental data from high-density disrupted L-mode discharges performed at JET, as well as in other machines, are taken as a term of comparison. The model fits the observed maximum densities better than the pure Greenwald limit.

Reversed Field Pinches (RFPs) share with Tokamaks and Stellarators the experimental evidence of an upper limit for the maximum value of the electron density at which they can operate. Above a certain density level, well described by the Greenwald law for Tokamaks and RFPs, a radiative collapse with strong plasma cooling is observed, predominantly due to processes occurring at the plasma boundary. In the RFX-mod RFP close to the density limit a radiating belt, poloidally symmetric and toroidally localized, develops in the region where the plasma is shrunk as an effect of the m=0 tearing modes. The phenomenology recalls that of MARFES or plasma detachment, though, unlike Tokamaks, the appearance of the radiating belt is associated to a soft landing of the plasma discharge. The paper reports the experimental pattern of the RFX-mod plasmas close to the density limit, including density and radiation profiles, plasma flow and turbulence. Particles are toroidally conveyed towards the region of maximum shrinking of the plasma column where they accumulate. The interpretation is related to the topology of MHD m=0 and m=1 modes: the reconstruction of the magnetic topology shows that the highly radiating region corresponds to the presence of peripheral m=0 magnetic islands well detached from the wall. The emerging indication is that in RFPs a reduction of the m=0 activity could be a way to overcome the density limit.