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.

Reversed field pinch (RFP) sustainment is studied in the framework of three dimensional magnetohydrodynamic (MHD) numerical simulations. The scaling law for the magnetic fluctuation amplitude with Lundquist number S is delta B approximately=S-0.22, which can be understood if the basic dynamic processes are governed by current sheet reconnection. Quasi-periodic oscillations are in fact found to be correlated with the presence of localized sheet currents, which for sufficiently large S make the major contribution to the average power dissipated by fluctuations. Special attention is paid to numerical convergence in the simulations. The results are compared with experimental observations

A scaling approach to the simplest viscoresistive MHD model reveals that the Prandtl number acts only through the inertia term. When this term is negligible the dynamics is ruled by the Hartmann number H only. This occurs for the reversed field pinch dynamics as seen by numerical simulation of the model. When H is large the system is in a multiple helicity state. In the vicinity of H = 2500 the system displays temporal intermittency with laminar phases of quasi-single-helicity (SH) type. For lower H's two basins of SH are shown to coexist. SH regimes are of interest because of their nonchaotic magnetic field.

The resilience to chaotic perturbations of one-parameter one-degree-of-freedom Hamiltonian dynamics is shown to increase when its corresponding separatrix vanishes due to a saddle-node bifurcation. This is first highlighted for the magnetic chaos related to quasisingle helicity (QSH) states of the reversed field pinch. It provides a rationale for the confinement improvement of helical structures experimentally found for QSH plasmas; such a feature would not be expected from the classical resonance overlap picture as the separatrix disappearance occurs when the amplitude of the dominant mode increases.

Within the framework of MHD modelling the RFP is shown to develop turbulent or laminar regimes switching from the former to the latter in a continuous way depending on the strength of dissipative forces (the higher they are the more laminar is the corresponding regime). In either of these cases interesting features can be observed such as the occurrence of quasiperiodic relaxation events involving reconnection processes, or the formation of stationary helical symmetric configurations. The first case corresponds to the conventional turbulent dynamo in the RFP where perturbations with multiple helical harmonic content are present. The second case corresponds to a global single helical deformation of the current channel. This simpler configuration is associated with a laminar electrostatic dynamo field and may also be found as a solution of a helical Ohmic equilibrium problem where a finite beta is necessary. The continuity of the transition between the two regimes suggests that the simple helical symmetric solution can provide a fruitful intuitive description of the RFP dynamo in general. Many of the MHD predictions are in good agreement with experimental findings and suggest possible improvements for the confinement properties of the RFP configuration.

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.

In this paper numerical results of three-dimensional (3-D) resistive magnetohydrodynamic (MHD) plasma simulations are presented. A system of coupled nonlinear differential equations is evolved in time over a significant fraction of the macroscopic resistive diffusion time scale. The dynamical evolution resembles the main features of the famous Lorenz system. In fact, sensitivity of MHD equations on initial distribution of spectral energy and stochastic oscillations in phase space have been found. At least two dynamic attractors of the motion have been identified. Moreover, in analogy with Lorenz’s system, the stochastic motion can be damped by an enhanced dissipation and the fixed point can be recovered. In this paper more specific topics are also considered, which are relevant to the reversed field pinch (RFP), such as the role of different modes in the ‘‘dynamo’’ mechanism for plasma sustainment and the associated transport due to stochastic diffusion.