R. Lorenzini

Magnetic order and confinement improvement in high-current regimes of RFX-mod with MHD feedback control

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.

The plasma boundary in single helical axis RFP plasmas

Single helical axis states obtained in high current reversed field pinch plasmas display, aside from a dominant mode in the m = 1 spectrum, also a dominant m = 0 mode, with the same toroidal mode number as the m = 1 one. The two modes have a fixed phase relationship. The island chain created by the m = 0 mode across the reversal surface gives rise, at shallow reversal of the toroidal field, to an X-point structure which separates the last closed flux surface from the first wall, creating a divertor-like configuration. The plasma–wall interaction is found to be related to the connection length of the field lines intercepting the wall, which displays a pattern modulated by the dominant mode toroidal periodicity. This configuration, which occurs only for shallow toroidal field reversal, could be exploited to realize an island divertor in analogy to stellarators.

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.

On the energy transport in internal transport barriers of RFP plasmas

Single helical axis (SHAx) states obtained in high current reversed field pinch (RFP) plasmas feature an internal transport barrier delimiting the hot helical core region. The electron temperature jump across this region, and the related temperature gradient, display a clear relationship with the normalized amplitude of the secondary MHD modes. A transport analysis performed with the ASTRA code, taking into account the helical geometry, yields values of the thermal conductivity in the barrier region as low as 5 m 2 s −1 . The thermal conductivity is also related to the secondary mode amplitude. Since such amplitude is reduced when plasma current is increased, it is expected that higher current plasmas will display even steeper thermal gradients and hotter helical cores. (Some figures may appear in colour only in the online journal)

Equilibrium reconstruction for single helical axis reversed field pinch plasmas

Single helical axis configurations are emerging as the natural state for high-current reversed field pinch plasmas. These states feature the presence of transport barriers in the core plasma. Here we present a method for computing the equilibrium magnetic surfaces for these states in the force-free approximation, which has been implemented in the SHEq code. The method is based on the superposition of a zeroth-order axisymmetric equilibrium and of a first-order helical perturbation computed according to Newcombs equation supplemented with edge magnetic field measurements. The mapping of the measured electron temperature profiles, soft x-ray emission and interferometric density measurements on the computed magnetic surfaces demonstrates the quality of the equilibrium reconstruction. The procedure for computing flux surface averages is illustrated, and applied to the evaluation of the thermal conductivity profile. The consistency of the evaluated equilibria with Ohms law is also discussed.