D. Terranova

Overview of quasi-single helicity experiments in reversed field pinches

We report the results of an experimental and theoretical international project dedicated to the study of quasi-single helicity (QSH) reversed field pinch (RFP) plasmas. The project has involved several RFP devices and numerical codes. It appears that QSH spectra are a robust feature common to all the experiments. Our results expand and reinforce the evidence that the formation of self-organized states with one dominant helical mode (Ohmic SH state) is an approach complementary to that of active control of magnetic turbulence to improve confinement in a steady state RFP.

Quasi-single helicity states in the reversed field pinch: Beyond the standard paradigm

This paper reports experimental results showing that coherent helical structures are formed in the reversed field pinch (RFP) self-organizing plasma core as a result of transitions to states where the n-spectrum of the m=1 modes is dominated by a single (1,nmax) geometrical helicity. These states are dubbed quasi-single helicity (QSH) states. Their magnetic and thermal properties measured in the reverse field experiment (RFX) [G. Rostagni, Fusion Eng. Des. 25, 301 (1995)] device are described. The present theoretical understanding of QSH states is discussed and some recent theoretical results are presented. The role of aspect ratio is discussed. These results represent a significant step to open a path beyond the standard paradigm that a bath of magnetohydrodynamic (MHD) modes is intrinsic to the RFP.

Reconstruction of the magnetic perturbation in a toroidal reversed field pinch

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.

A new paradigm for RFP magnetic self-organization: results and challenges

This paper reports the most recent experimental results on quasi-single helicity (QSH) reversed field pinch (RFP) plasmas. QSH is considered a key element towards the full experimental realization of the theoretically predicted single helicity (SH) RFP. The SH RFP, where an individual resistive kink mode and its harmonics drive the dynamo electric field, is predicted to have superior confinement performance with respect to the standard multiple helicity (MH) state. Magnetic chaos is in fact strongly reduced in the SH RFP, which therefore retains all the positive features of the RFP configuration without the problems connected with the magnetic turbulence typical of the MH scenario. Data from the RFX-mod device, presented here, provide a more complete description of QSH states, indicate a positive synergy between the growth of the dominant resistive mode and the decrease in the secondary modes (with reduction of magnetic chaos and hints of confinement improvement outside the helical domain), and show a promising scaling with plasma current. Initial experiments on active control of QSH states in RFX-mod are presented.

Overview of RFX-mod results

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 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-organized helical equilibrium has been experimentally achieved (the Single Helical Axis—SHAx—state), which is the preferred state at high current. Strong core electron transport barriers characterize this regime, with electron temperature gradients comparable to those achieved in tokamaks, and by a factor of 4 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.

Magnetic self organization, MHD active control and confinement in RFX-mod

RFX-mod is a reversed field pinch (RFP) experiment equipped with a system that actively controls the magnetic boundary. In this paper we describe the results of a new control algorithm, the clean mode control (CMC), in which the aliasing of the sideband harmonics generated by the discrete saddle coils is corrected in real time. CMC operation leads to a smoother (i.e. more axisymmetric) boundary. Tearing modes rotate (up to 100 Hz) and partially unlock. Plasma–wall interaction diminishes due to a decrease of the non-axisymmetric shift of the plasma column. With the ameliorated boundary control, plasma current has been successfully increased to 1.5 MA, the highest for an RFP. In such regimes, the magnetic dynamics is dominated by the innermost resonant mode, the internal magnetic field gets close to a pure helix and confinement improves.

High density physics in reversed field pinches: comparison with tokamaks and stellarators

Reversed field pinches (RFPs) share with tokamaks and stellarators the experimental evidence of an upper limit for the maximum value of the electron density at which they can operate. Above a certain density level, well described by the Greenwald law for tokamaks and RFPs, a radiative collapse with strong plasma cooling is observed, predominantly due to processes occurring at the plasma boundary. In the RFX-mod RFP close to the density limit a radiating belt, poloidally symmetric and toroidally localized, develops in the region where the plasma is shrunk as an effect of the m = 0 tearing modes. The phenomenology recalls that of MARFES or plasma detachment, though, unlike tokamaks, the appearance of the radiating belt is associated with a soft landing of the plasma discharge.The paper reports the experimental pattern of the RFX-mod plasmas close to the density limit, including density and radiation profiles, plasma flow and turbulence. Particles are toroidally conveyed towards the region of maximum shrinking of the plasma column where they accumulate. The interpretation is related to the topology of MHD m = 0 and m = 1 modes: the reconstruction of the magnetic topology shows that the highly radiating region corresponds to the presence of peripheral m = 0 magnetic islands well detached from the wall. The emerging indication is that in RFPs a reduction of the m = 0 activity could be a way to overcome the density limit.

Helical equilibria and magnetic structures in the reversed field pinch and analogies to the tokamak and stellarator

The reversed field pinch configuration is characterized by the presence of magnetic structures both in the core and at the edge: in the core, at high plasma current the spontaneous development of a helical structure is accompanied by the appearance of internal electron transport barriers; at the edge strong pressure gradients, identifying an edge transport barrier, are observed too, related to the position of the field reversal surface.The aim of this paper is the experimental characterization of both the internal and edge transport barriers in relation to the magnetic topology, discussing possible analogies and differences with other confinement schemes.

High current regimes in RFX-mod

Optimization of machine operation, including plasma position control, density control and especially feedback control on multiple magnetohydrodynamic modes, has led RFX-mod to operate reliably 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 under which to prove the existence of a true helical equilibrium as the standard RFP configuration.

High density limit in Reversed Field Pinches

The fusion triple product depends on density, which is therefore a key parameter for the future fusion reactor. In this paper the high density limit is studied in the reversed field experiment (RFX-mod) device in Padova, Italy. A rather complete experimental picture of the high density regimes is provided, showing a series of features, such as, plasma flow inversion in the edge, density accumulation, radiation condensation (poloidally symmetric and toroidal asymmetric) which resemble the MARFE phenomenon characteristic of tokamak discharges. However, in RFX-mod high density does not cause a disruption, as often observed in tokamaks, but a soft landing of the plasma current. According to a new 1D transport/radiative code applied to analyze the high density discharges, the current decay is due to an increased need for dynamo in these highly resistive, edge-cooled discharges. The relation between the radiative pattern of RFX-mod high density plasmas, the magnetic topology, and edge radial electric field is discussed.