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...

Energy confinement comparable with tokamak quality is achieved in the Madison Symmetric Torus (MST) reversed field pinch (RFP) at a high beta and low toroidal magnetic field. Magnetic fluctuations normally present in the RFP are reduced via parallel current drive in the outer region of the plasma. In response, the electron temperature nearly triples and beta doubles. The confinement time increases tenfold (to ∼10 ms), which is comparable with Land H-mode scaling values for a tokamak with the same plasma current, density, heating power, size and shape. Runaway electron confinement is evidenced by a 100-fold increase in hard x-ray bremsstrahlung. Fokker-Planck modelling of the x-ray energy spectrum reveals that the high energy electron diffusion is independent of the parallel velocity, uncharacteristic of magnetic transport and more like that for electrostatic turbulence. The high core electron temperature correlates strongly with a broadband reduction of resonant modes at mid-radius where the stochasticity is normally most intense. To extend profile control and add auxiliary heating, rf current drive and neutral beam heating are in development. Low power lower-hybrid and electron Bernstein wave injection experiments are underway. Dc current sustainment via ac helicity injection (sinusoidal inductive loop voltages) is also being tested. Low power neutral beam injection shows that fast ions are well-confined, even in the presence of relatively large magnetic fluctuations.

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.

Abstract.Optimization of machine operation, including plasma position control, density control, and especially feedback control on multiple magnetohydrodynamic modes has led RFX-mod to reliably operate at 1.5 MA, the highest current ever achieved on a Reversed Field Pinch (RFP). At high current and low density the magnetic topology spontaneously self-organizes in an Ohmical helical symmetry, with the new magnetic axis helically twisting around the geometrical axis of the torus. The separatrix of the island disappears leaving a wide and symmetric thermal structure with large gradients in the electron temperature profile. The new topology still displays an intermittent nature but its overall presence has reached 85 % of the current flat top period. The large gradients in the electron temperature profile appear to be marginal for the destabilization of Ion Temperature Gradient modes on the assumption that ions and electrons have the same gradients. There are indications that higher currents could provide the conditions where to prove the existence of a true helical equilibrium as the standard RFP configuration

This paper summarizes the main achievements of the RFX fusion science program in the period between the 2008 and 2010 IAEA Fusion Energy Conferences. RFX-mod is the largest reversed field pinch in the world, equipped with a system of 192 coils for active control of MHD stability. The discovery and understanding of helical states with electron internal transport barriers and core electron temperature >1.5 keV significantly advances the perspectives of the configuration. Optimized experiments with plasma current up to 1.8 MA have been realized, confirming positive scaling. The first evidence of edge transport barriers is presented. Progress has been made also in the control of firstwall properties and of density profiles, with initial first-wall lithization experiments. Micro-turbulence mechanisms such as ion temperature gradient and micro-tearing are discussed in the framework of understanding gradient-driven transport in low magnetic chaos helical regimes. Both tearing mode and resistive wall mode active control have been optimized and experimental data have been used to benchmark numerical codes. The RFX programme also provides important results for the fusion community and in particular for tokamaks and stellarators on feedback control of MHD stability and on three-dimensional physics. On the latter topic, the result of the application of stellarator codes to describe three-dimensional reversed field pinch physics will be presented.

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.

The Helicity Injected Torus [HIT-II: T. Jarboe et al., Phys. Plasmas 5, 1807 (1998)] is a low-aspect-ratio tokamak capable of both inductive (ohmic) and Coaxial Helicity Injection (CHI) current drive. HIT-II is modest in size (major radius R=0.3 m, minor radius a=0.2 m, and on-axis toroidal field of up to 0.5 T), but has demonstrated 200 kA of toroidal plasma current, using either CHI or induction separately. The loop voltage, boundary flux, and plasma equilibrium are controlled by a real-time flux feedback system. HIT-II ohmic plasmas exhibit reconnection events during both the current ramp-up and decay, events that relax the current profile while conserving the magnetic helicity. A new operating regime for CHI plasmas, using a double-null divertor (DND) boundary flux, has been explored. DND CHI plasmas exhibit good shot-to-shot reproducibility, low impurity content, minimal shorting current in the absorber region, and EFIT-reconstructed equilibria consistent with significant closed-flux core regions [EFIT: L. Lao et al., Nucl. Fusion 25, 1611 (1985)]. HIT-II DND CHI discharges also exhibit a continuous n=1 mode at the outer midplane, a mode that has been correlated experimentally with current-profile relaxation. A detailed explanation of helicity injection current drive has been developed, which is consistent with experimental observations of HIT and HIT-II discharges. According to this mechanism, asymmetric distortion of the n=1 mode structure generates current drive in the core plasma by dynamo action, relaxing the CHI-driven current profile.

To aid in diagnosis of 3D equilibria in the Madison Symmetric Torus, it has become necessary to control the orientation of the equilibria. In reversed field pinch experiments a transition to a 3D equilibrium is common with sufficiently large plasma current (and Lundquist number). Diagnosis of this state is hampered by the fact that the helical structure is stationary but with an orientation that varies shot-to-shot. A resonant magnetic perturbation (RMP) technique has been developed to vary controllably the orientation of the 3D equilibria and optimized to minimize the plasma wall interaction due to its use. Application of an RMP now allows alignment of the structure with key diagnostics, including Thomson scattering and an interferometer-polarimeter.