L. Piron

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.

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.

Influence of external 3D magnetic fields on helical equilibrium and plasma flow in RFX-mod

A spontaneous transition to a helical equilibrium with an electron internal transport barrier is observed in RFX-mod as the plasma current is raised above 1 MA (Lorenzini R et al 2009 Nature Phys. 5 570). The helical magnetic equilibrium can be controlled with external three-dimensional (3D) magnetic fields applied by 192 active coils, providing proper helical boundary conditions either rotating or static. The persistence of the helical equilibrium is strongly increased in this way. A slight reduction in the energy confinement time of about 15% is observed, likely due to the increased plasma–wall interaction associated with the finite radial magnetic field imposed at the edge. A global helical flow develops in these states and is expected to play a role in the helical self-organization. In particular, its shear may contribute to the ITB formation and is observed to increase with the externally applied radial field. The possible origins of this flow, from nonlinear visco-resistive magnetohydrodynamic (MHD) and/or ambipolar electric fields, will be discussed.

Internal and external electron transport barriers in the RFX-mod reversed field pinch

An interesting result of magnetic chaos reduction in RFX-mod high current discharges is the development of strong electron transport barriers. An internal heat and particle transport barrier is formed when a bifurcation process changes the magnetic configuration into a helical equilibrium and chaos reduction follows, together with the formation of a null in the q shear. Strong temperature gradients develop, corresponding to a decreased thermal and particle transport. Turbulence analysis shows that the large electron temperature gradients are limited by the onset of micro-tearing modes, in addition to residual magnetic chaos. A new type of electron transport barrier with strong temperature gradients develops more externally (r/a = 0.8) accompanied by a 30% improvement of the global confinement time. The mechanism responsible for the formation of such a barrier is still unknown but it is likely associated with a local reduction of magnetic chaos. These external barriers develop primarily in situations of well-conditioned walls so that they might be regarded as attempts towards an L–H transition. Both types of barriers occur in high-current low-collisionality regimes. Analogies with tokamak and stellarators are discussed.

Investigation on the relation between edge radial electric field asymmetries in RFX-mod and density limit

In all major confinement devices (tokamaks, stellarators, spheromaks and reversed-field pinches—RFPs), a density limit has been found. Results summarized in a recent work by Puiatti et al (2009 Nucl. Fusion 49 045012) show that in the RFP high density does not cause a disruption, but a sequence of increasingly critical phenomena. First, at intermediate density there is the disappearance of the high-confinement quasisingle helicity/single helical axis regimes. Then, at densities close to the Greenwald limit, toroidally and radially localized density accumulation and radiation condensation are observed, together with a fast resistive decay of the plasma current, which constitutes the real operative limit of the device. In this paper we discuss the effect of the magnetic ripple on test particle motion, showing that the accumulation of electrons in the X-points of the edge m = 0 islands is responsible for a modulation of the radial electric field Er which is at the core of the density limit mechanism. These results can be also relevant for the explanation of X-point multifaceted asymmetric radiation from the edge formation, observed in L-mode density limit discharges of JET.

Dynamic decoupling and multi-mode magnetic feedback for error field correction in RFX-mod

Magnetic field errors can have a significant impact on the confinement properties of magnetized fusion plasmas. In the RFX-mod reversed-field pinch (Sonato et al 2003 Fusion Eng. Des. 33 161) a significant error field is produced during the current ramp by the eddy currents induced in the 3D wall structures, such as the gaps and some large portholes, by the temporal variation of the vertical magnetic field. A set of 192 magnetic sensors and 192 active coils allowed accurate identification of the error field spatiotemporal pattern and its correction. The correction scheme combines pre-programmed current waveforms and multi-mode magnetic feedback. The pre-programmed currents were computed with the dynamic decoupling algorithm developed in Soppelsa et al (2008 Fusion Eng. Des. 83 224). This accounts for the mutual interaction between different feedback coils and magnetic sensors, which is affected by the frequency-dependent response of the 3D wall structures to external magnetic fields. At the same time, multi-mode magnetic feedback is applied to the main error field harmonics. During the current ramp, multiple tearing modes are normally phase-locked and produce a toroidally localized deformation of the plasma column that tends to grow where the error fields are larger. With error field correction, this deformation does not grow at preferred positions, thus avoiding the plasma–wall interaction being too localized there. In general, the decoupling approach used in this work may find applications in other machines.

Improved dynamic response of magnetic feedback in RFX-mod and DIII-D

The wall of any magnetic fusion device is characterized by the presence of several 3D structures, such as portholes for diagnostics and for heating and current drive systems, coil feeds and other features. Time-varying magnetic fields induce eddy currents in the wall, whose pattern is modified by these structures, giving rise to magnetic field errors that can be amplified or shielded by the plasma. Two examples will be given on how the dynamic response of a 3D wall to external magnetic fields can be identified and used to optimize magnetic feedback. In the RFX-mod reversed-field pinch, a dynamic decoupler algorithm has been developed, which allows for the production of pure radial magnetic field harmonics inside the wall, reducing the harmonic distortion due to the 3D wall structures. This is applied here to the problem of producing helical boundary conditions to control helical RFP equilibria. In the DIII-D tokamak, a frequency-dependent scheme for the compensation of the magnetic sensors from spurious n = 1 fields due to the coupling with the feedback and axisymmetric coils has been recently implemented in real time and tested with plasma. The possible relevance of these 3D effects for high performance scenarios is discussed.

Model-based design of multi-mode feedback control in the RFX-mod experiment

Interest in real-time control of magnetic field errors and magnetohydrodynamic (MHD) instabilities has been growing in the last decades due to the demanding stability requirements of high-performance scenarios in fusion devices. In this framework, the RFX-mod experiment (Sonato et al 2003 Fusion Eng. Des. 66 161) plays an important role. One of the main goals of RFX-mod is to explore high-plasma current regimes up to 2 MA for the first time in a reversed-field pinch. To this aim, RFX-mod is equipped with an advanced active coil system for the control of error fields and MHD modes, such as tearing and resistive-wall modes. As far as tearing modes are concerned, both controlling their edge radial magnetic field and maintaining them into slow (~10–100 Hz) rotation are crucial to reduce both the plasma–wall interaction and the core magnetic stochasticity. In this paper, a model-based optimization of the RFX-mod feedback control is presented. The aim is to find an optimal gain set for a spectrum of multiple tearing modes, which produces the lowest possible value of the edge radial magnetic field, maintaining at the same time the modes into slow rotation and avoiding coil current saturations. These optimal gains have first been calculated offline by simulating the non-linear dynamics of a spectrum of tearing modes interacting through viscous and electromagnetic torques, using an adaptation to the RFX-mod multiple-shell layout of the model described in Zanca (2009 Plasma Phys. Control. Fusion 51 015006). This gain set has been obtained by scanning the proportional and derivative gains and has been tested in an extensive experimental campaign, showing good agreement with the model. With this approach, a reduction in the edge radial magnetic field up to 15%, with respect to discharges in which an empirical optimization was used, has been obtained. The above model proved to be a powerful tool to tune a multi-mode controller offline, which allowed us to save a large amount of experimental time.

Feedback-assisted extension of the tokamak operating space to low safety factora)

Recent DIII-D and RFX-mod experiments have demonstrated stable tokamak operation at very low values of the edge safety factor q(a) near and below 2. The onset of n = 1 resistive wall mode (RWM) kink instabilities leads to a disruptive stability limit, encountered at q(a) = 2 (limiter plasmas) and q95 = 2 (divertor plasmas). However, passively stable operation can be attained for q(a) and q95 values as low as 2.2. RWM damping in the q(a) = 2 regime was measured using active MHD spectroscopy. Although consistent with theoretical predictions, the amplitude of the damped response does not increase significantly as the q(a) = 2 limit is approached, in contrast with damping measurements made approaching the pressure-driven RWM limit. Applying proportional gain magnetic feedback control of the n = 1 modes has resulted in stabilized operation with q95 values reaching as low as 1.9 in DIII-D and q(a) reaching 1.55 in RFX-mod. In addition to being consistent with the q(a) = 2 external kink mode stability limit, the...