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...

With the exploration of the MA plasma current regime in up to 0.5 s long discharges, RFX-mod has opened new and very promising perspectives for the Reversed Field Pinch (RFP) magnetic configuration, and has made a significant progress in understanding and improving confinement and in controlling plasma stability. A big leap with respect to previous knowledge and expectations on RFP physics and performance has been made by RFX-mod since the last 2006 IAEA Fusion Energy Conference. A new self-organised helical equilibrium has been found (the Single Helical Axis-SHAx-state), which is the preferred state at high current. This regime is characterized by strong core electron transport barriers, with electron temperature gradients comparable to those achieved in tokamaks, and by a factor four improvement in confinement time with respect to the standard RFP. RFX-mod is also providing leading edge results on real-time feedback control of MHD instabilities, of general interest for the fusion community.

We have increased substantially the electron and ion temperatures, the electron density, and the total beta in plasmas with improved energy confinement in the Madison Symmetric Torus (MST). The improved confinement is achieved with a well-established current profile control technique for reduction of magnetic tearing and reconnection. A sustained ion temperature >1 keV is achieved with intensified reconnection-based ion heating followed immediately by current profile control. In the same plasmas, the electron temperature reaches 2 keV, and the electron thermal diffusivity drops to about 2 m 2 s −1. The global energy confinement time is 12 ms. This and the reported temperatures are the largest values yet achieved in the reversed-field pinch (RFP). These results were attained at a density ∼10 19 m −3. By combining pellet injection with current profile control, the density has been quadrupled, and total beta has nearly doubled to a record value of about 26%. The Mercier criterion is exceeded in the plasma core, and both pressure-driven interchange and pressure-driven tearing modes are calculated to be linearly unstable, yet energy confinement is still improved. Transient momentum injection with biased probes reveals that global momentum transport is reduced with current profile control. Magnetic reconnection events drive rapid momentum transport related to large Maxwell and Reynolds stresses. Ion heating during reconnection events occurs globally, locally, or not at all, depending on which tearing modes are involved in the reconnection. To potentially augment inductive current profile control, we are conducting initial tests of current drive with lower-hybrid and electron-Bernstein waves.

Pellet fuelling of improved confinement Madison Symmetric Torus (MST) plasmas has resulted in high density and high plasma beta. The density in improved confinement discharges has been increased fourfold, and a record plasma beta (βtot = 26%) for the improved confinement reversed-field pinch (RFP) has been achieved. At higher β, a new regime for instabilities is accessed in which local interchange and global tearing instabilities are calculated to be linearly unstable, but experimentally, no severe effect, e.g., a disruption, is observed. The tearing instability, normally driven by the current gradient, is driven by the pressure gradient in this case, and there are indications of increased energy transport (as compared with low-density improved confinement). Pellet fuelling is also compared with enhanced edge fuelling of standard confinement RFP discharges for the purpose of searching for a density limit in MST. In standard-confinement discharges, pellet fuelling peaks the density profile where edge fuelling cannot, but transport appears unchanged. For a limited range of plasma current, MST discharges with edge fuelling are constrained to a maximum density corresponding to the Greenwald limit. This limit is surpassed in pellet-fuelled improved confinement discharges.

An overview of recent results from the MST programme on physics important for the advancement of the reversed field pinch (RFP) as well as for improved understanding of toroidal magnetic confinement more generally is reported. Evidence for the classical confinement of ions in the RFP is provided by analysis of impurity ions and energetic ions created by 1 MW neutral beam injection (NBI). The first appearance of energetic-particle-driven modes by NBI in a RFP plasma is described. MST plasmas robustly access the quasi-single-helicity state that has commonalities to the stellarator and 'snake' formation in tokamaks. In MST the dominant mode grows to 8% of the axisymmetric field strength, while the remaining modes are reduced. Predictive capability for tearing mode behaviour has been improved through nonlinear, 3D, resistive magnetohydrodynamic computation using the measured resistivity profile and Lundquist number, which reproduces the sawtooth cycle dynamics. Experimental evidence and computational analysis indicates two-fluid effects, e.g., Hall physics and gyro-viscosity, are needed to understand the coupling of parallel momentum transport and current profile relaxation. Large Reynolds and Maxwell stresses, plus separately measured kinetic stress, indicate an intricate momentum balance and a possible origin for MST's intrinsic plasma rotation. Gyrokinetic analysis indicates that micro-tearing modes can be unstable at high beta, with a critical gradient for the electron temperature that is larger than for tokamak plasmas by roughly the aspect ratio.