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...

The reversed field pinch (RFP) is a configuration for plasma magnetic confinement. It has been traditionally viewed as dominated by a bath of MHD instabilities producing magnetic chaos and high energy transport. We report experimental results which go beyond this view. They show a decrease of magnetic chaos and the formation of a coherent helical structure in the plasma, whose imaging and temperature profile are provided for the first time. These quasi-single-helicity states are observed both transiently and in stationary conditions. The last case is consistent with a theoretically predicted bifurcation. Our results set a new frame for improving confinement in high current nonchaotic RFP's.

The mechanisms of nonlinear interaction of external helical fields with a rotating plasma are investigated analyzing the results of recent systematic experiments on the Joint European Torus (JET) [A. Gibson et al., Phys. Plasmas 5, 1839 (1998)] that widen the previous data base collected on Compass-D [T. C. Hender et al., Nucl. Fusion 32, 2091 (1992)], Doublet III-D [R. J. La Haye et al., Nucl. Fusion 32, 2119 (1992)] and JET. The empirical scaling laws governing the onset of “error field” locked modes are re-assessed and interpreted in terms of existing driven reconnection theories and with new models. In particular the important mechanisms of plasma rotation braking, and spin up, associated with error fields are analyzed in detail and interpreted.

to their discrete nature a grid of active coils for the feedback control produces an infinite sequence of sideband harmonics in the magnetic field. If the sensors have the same periodicity as the coils, as in the Intelligent Shell scheme, the aliasing of the sidebands determines a systematic error on the Fourier analysis of the measurements. This is a drawback for the control of those perturbations that cannot be suppressed by the feedback, but only reduced in their saturation level, as the non-linear tearing modes of reversed field pinches. We have derived analytical formulas for the subtraction of the sidebands, implemented in a real-time correction algorithm of the Fourier analysis. The Fourier harmonics so obtained are used as feedback variable of a new control scheme named Clean-Mode-Control (CMC). The first tests of CMC in RFX-mod have given interesting results in the tearing modes control: besides a reduction of the edge radial field and the plasma surface distortion, systematic rotations with frequencies up to 100Hz are seen. These phenomena will be interpreted using a MHD model of the CMC.

A new method to obtain the radial profile of the magnetic perturbation in a toroidal force-free plasma having a circular cross section is developed. The toroidal geometry produces poloidal harmonics in the equilibrium quantities (at the leading order m = ±1, n=0), which act as mediators between perturbations with the same toroidal number and different poloidal numbers. The approach proposed here, based on the contravariant representation of the magnetic field in flux co-ordinates, is formally simple and rigorous and maintains a nice similarity with the cylindrical treatment. The method is quite general and can be applied to any circular low-beta plasma. In this work we describe its application to the Reversed Field eXperiment (RFX) plasma. It is customary in reversed field pinches to approach the analysis of MHD instabilities by using a cylindrical geometry. Nonetheless, the effect of a more realistic toroidal geometry can play an important role, and indeed we found that the toroidal effects on the magnetic perturbations are not negligible.

The transition to a new magnetic topology, characterized by a quasi-single-helicity state with a single helical magnetic axis has been experimentally observed for the first time in a reversed-field-pinch plasma. The occurrence of the new state, which has been dubbed a single-helical-axis state, was found to provide magnetic chaos healing and enhanced thermal content of the plasma. The helical structure extends on both sides of the vessel geometric axis, and is related to exceeding a threshold in the ratio between the amplitude of the dominant MHD mode and the amplitude of the secondary ones.

Active feedback stabilization of multiple independent resistive wall modes is experimentally demonstrated in a reversed-field pinch plasma. A reproducible simultaneous suppression of several nonresonant resistive wall modes is achieved. Coupling of different modes due to the limited number of the feedback coils is observed in agreement with theory. The feedback stabilization of nonresonant RWMs also has an effect on tearing modes that are resonant in the central plasma, leading to a significant prolongation of the discharge pulse.

The RFX-mod machine (Sonato et al 2003 Fusion Eng. Des. 66 161) recently achieved, for the first time in a reversed-field pinch, high plasma current up to 1.6 MA with good confinement. Magnetic feedback control of magnetohydrodynamic instabilities was essential to reach the goal. As the current is raised, the plasma spontaneously accesses a new helical state, starting from turbulent multi-helical conditions. Together with this raise, the ratio between the dominant and the secondary mode amplitudes increases in a continuous way. This brings a significant improvement in the magnetic field topology, with the formation of helical flux surfaces in the core. As a consequence, strong helical transport barriers with maximum electron temperature around 1 keV develop in this region. The energy confinement time increases by a factor of 4 with respect to the lower-current, multi-helical conditions. The properties of the new helical state scale favourably with the current, thus opening promising perspectives for the higher current experiments planned for the near future.