Search

This paper reviews the research on the reversed field pinch (RFP) in the last three decades. Substantial experimental and theoretical progress and transformational changes have been achieved since the last review (Bodin 1990 Nucl. Fusion 30 1717–37). The experiments have been performed in devices with different sizes and capabilities. The largest are RFX-mod in Padova (Italy) and MST in Madison (USA). The experimental community includes also EXTRAP-T2R in Sweden, RELAX in Japan and KTX in China. Impressive improvements in the performance are the result of exploration of two lines: the high current operation (up to 2 MA) with the spontaneous occurrence of helical equilibria with good magnetic flux surfaces and the active control of the current profile. A crucial ingredient for the advancements obtained in the experiments has been the development of state-of-art active feedback control systems allowing the control of MHD instabilities in presence of a thin shell. The balance between achievements and still open issues leads us to the conclusion that the RFP can be a valuable and diverse contributor in the quest for fusion electricity.

This paper reports the main results of the RFX-mod fusion science activity since the last 2014 IAEA Fusion Energy Conference. The RFX-mod device is characterized by a unique flexibility in terms of accessible magnetic configurations. Axisymmetric and helically shaped Reversed-field pinch equilibria have been studied, along with tokamak plasmas in a wide range of q(a) regimes (spanning from 4 down to 1.2 values). The full range of magnetic configurations in between the two, the so-called ultra low-q ones, has been explored, with the aim of studying specific physical issues common to all equilibria, such as, for example, the density limit phenomenon. The powerful RFX-mod feedback control system has been exploited for MHD control, which allowed to extend the range of experimental parameters, as well as to induce specific magnetic perturbations for the study of 3D effects. In particular, transport, edge and isotope effect in 3D equilibria have been investigated, along with runaway mitigations through induced magnetic perturbations. The first transitions to H-mode in circular and D-shaped tokamak plasmas have been obtained thanks to an active modification of the edge electric field through a polarized electrode. The experiments are supported by intense modelling with 3D MHD, gyrokinetic, guiding center and transport codes. Proposed modifications to the RFX-mod device, which will enable further contributions to the solution of key issues in the roadmap to ITER and DEMO, are also briefly presented.

We have spectroscopically investigated the Sterling Scientific miniature electrostatic plasma source - a plasma gun. This gun is a clean source of high-density ( - ), low-temperature (5 - 15 eV) plasma. A key result of our investigation is that molybdenum from the gun electrodes is largely trapped in the internal gun discharge; only a small amount escapes in the plasma flowing out of the gun. In addition, the gun plasma parameters actually improve (even lower impurity contamination and higher ion temperature) when up to 1 kA of electron current is extracted from the gun via the application of an external bias. This improvement occurs because the internal gun anode no longer acts as the current return for the internal gun discharge. The gun plasma is a virtual plasma electrode capable of sourcing an electron emission current density of . The high emission current, small size (3 - 4 cm diameter), and low impurity generation make this gun attractive for a variety of fusion and plasma technology applications.

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.

Plasmas in the MST reversed field pinch bifurcate to a helical equilibrium, forming a Single Helical Axis (SHAx) at high plasma current (Ip?500 kA) and low density (ne?0.5 x 1019 m-3). Modeling of these plasmas requires an equilibrium solver that does not assume axisymmetry. The V3FIT 3D equilibrium reconstruction code is applied to helical equilibria with diagnostic measurements as constraints. The 11-chord interferometer-polarimeter, 22-point Thomson scattering system, and 4-camera soft X-ray probes have been included in addition to external magnetics. Inputs have been adapted for MST's close-fitting conducting shell. Investigations into the role of shell eddy currents have been made, including comparison to eigenfunctions generated from the Newcomb equation. At the plasma boundary, ?60{\%} of the static n=5 toroidal field BT seen by magnetic probes is generated by currents in the shell. The generated VMEC equilibrium serves as the input for applications relevant to the 1 MW, 25 keV neutral beam injector. During beam injection, fast ion confinement is reduced in periods with a SHAx compared to axisymmetric plasmas. A single particle orbit code has been applied to calculate particle trajectories in the 3D case, confirming a strong influence of SHAx equilibria on fast ion orbits. EPM magnetic bursts terminate at the transition to SHAx. Alfv\'{e}n continua have been generated to study this phenomenon with the reduced-MHD code STELLGAP. Work Supported by USDoE and NSF.

MST plasmas with a central 3D helical structure are now routinely achievable. As in RFX-mod, the stellarator-like structure arises in otherwise toroidally axisymmetric plasmas when the innermost-resonant m = 1 tearing mode grows to large amplitude and dominates the core-resonant-mode spectrum. The tearing mode spectrum in MST varies strongly with toroidal plasma current. Peaked spectra with a helical structure occur most reliably at high Ip (0.6 MA), while at low Ip (0.2 MA), the spectra are quite flat. This trend is like that in RFX-mod and may reflect a dependence on the Lundquist number. Preliminary MST data also show that manipulation of the inductive electric field has a significant impact, driving the dominant mode to large amplitude more robustly, and reducing the other modes. At high Ip, Te(0) $>$ 1 keV with a possible several-fold increase in the energy confinement time. Supported by USDOE.

With the exploration of the MA plasma current regime in up to 0.5 s long discharges, RFX-mod has opened new and promising perspectives for the Reversed Field Pinch (RFP). 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. We present results, which are relevant for the understanding of the RFP physics and confinement performance, and contribute to the solution of issues for the optimization of ITER construction and operation. RFX-mod is a large ohmically heated RFP (R = 2 m, a = 0.457 m, volume 10 m3), equipped with an advanced system for feedback control of MHD instabilities, based on 192 independently driven coils covering the whole plasma boundary. An axisymmetric magnetic boundary is produced, with differential rotation of tearing modes and full stabilization of multiple RWM. The operation above 1 MA (up to 1.6 MA reported at this conference) has revealed a new self-organised helical equilibrium (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. The electron temperature shows peak values in the 1 keV range, linearly increasing with plasma current with no degradation of beta. The RFP dominated by magnetic chaos belongs to the past, and the new findings open an exciting and clear path, which deserved to be explored. The achievements in the field of MHD stability real-time control have been of high quality. Progresses in control of tearing modes and RWM have been reported. Besides providing an improved magnetic boundary for the high current operation, the feedback experiments address general issues like multi-mode control, tools for mode unlocking and for forcing mode rotation, implementation of advanced control theory, development of a plant model including features of the plasma, wall, sensors, actuators, field error environment, noise environment and controller dynamics, incorporation of 3-d effects due to a non-axisymmetric wall, benchmarking of numerical stability codes also used for ITER. All these results give strong confidence in the RFX-mod future programme.

An overview of recent results from the MST reversed field pinch programme is presented. With neutral beam injection, bursty energetic particle (EP) modes are observed. The profiles of the magnetic and density fluctuations associated with these EP modes are measured using a far infrared interferometer-polarimeter. Equilibrium reconstructions of the quasi-single-helicity 3D helical state are provided by the V3FIT code that now incorporates several of MST's advanced diagnostics. The orientation of the helical structure is controlled using a new resonant magnetic perturbation technique. Gyrokinetic simulations based on experimental equilibria predict unstable trapped-electron modes (TEMs), and small-scale density fluctuations are detected in improved-confinement plasmas with TEM-like features. Upgraded pellet injection permits study of density and beta limits over MST's full range of operation, and an MST-record line-average density of 0.9 ×1020 m3 (n/nG = 1.4) has been obtained. Impurity ion temperature measurements reveal a charge-to-mass-ratio dependence in the rapid heating that occurs during a sawtooth crash. Runaway of NBI-born fast ions during the impulsive sawtooth event agrees with test-particle theory. Magnetic self-organization studies include measurements of the dynamo emf with an applied ac inductive electric field using oscillating field current drive.

Experimental results using active methods in order to control the locked mode and to improve the confinement in the TPE-RX (R/a = 1.72/0.45) RFP, are presented. A phase- and wall-locked mode (LM) was found in the case of high plasma current (> 300 kA) and/or high filling pressure. The rotation of the LM has been attempted using an auxiliary rotating toroidal magnetic field. By applying the auxiliary field, the LM can be successfully delayed or even eliminated in the case of low plasma current (200 kA) with high filling pressure for the first time. As one of the active operations for an improvement of the confinement, pulsed poloidal current drive (PPCD) has been conducted by the auxiliary and main reversal toroidal field system. The soft X-ray in the PPCD becomes an order of magnitude larger than that in the standard case. The electron temperature, density and ion temperature increase during the PPCD. These results show considerable improvement of energy confinement. Another operation is the high electron density discharge using the fast gas puffing. The highest values of poloidal beta and energy confinement time are estimated to be obtained at the highest electron density case.

A strongly sheared radial electric field is observed in enhanced confinement discharges in the MST reversed-field pinch. The strong shear develops in a narrow region in the plasma edge. Electrostatic fluctuations are reduced over the entire plasma edge with an extra reduction in the shear region. Magnetic fluctuations, resonant in the plasma core but global in extent, are also reduced. The reduction of fluctuations in the shear region is presumably due to the strong shear, but the causes of the reductions outside this region have not been established.

We have spectroscopically investigated the Sterling Scientific miniature electrostatic plasma source-a plasma gun. This gun is a clean source of high density (10{sup 19} - 10{sup 20} m{sup -3}), low temperature (5 - 15 eV) plasma. A key result of our investigation is that molybdenum from the gun electrodes is largely trapped in the internal gun discharge; only a small amount escapes in the plasma flowing out of the gun. In addition, the gun plasma parameters actually improve (even lower impurity contamination and higher ion temperature) when up to 1 kA of electron current is extracted from the gun via the application of an external bias. This improvement occurs because the internal gun anode no longer acts as the current return for the internal gun discharge. The gun plasma is a virtual plasma electrode capable of sourcing an electron emission current density of 1 kA/cm{sup 2}. The high emission current, small size (3 - 4 cm diameter), and low impurity generation make this gun attractive for a variety of fusion and plasma technology applications.