M. Gobbin

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 100u2009Hz) 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 1.5u2009MA, 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.

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.

Magnetohydrodynamic properties of nominally axisymmetric systems with 3D helical core

Magnetohydrodynamic equilibrium states with a three-dimensional helical core are computed to model the MAST spherical tokamak and the RFX-mod reversed field pinch. The boundary is fixed as axisymmetric. The MAST equilibrium state has the appearance of an internal kink mode and is obtained under conditions of weak reversed central shear. The RFX-mod equilibrium state has seven-fold periodicity. An ideal magnetohydrodynamic stability analysis reveals that the reversal of the core magnetic shear can stabilize a periodicity-breaking mode that is dominantly m/n = 1/8 strongly coupled to a m/n = 2/15 component, as long as the central rotational transform does not exceed the value of 8.

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.

Improved confinement with internal electron transport barriers in RFX-mod

RFX-mod reliably operates at 1.5 MA, the highest current ever achieved on a reversed field pinch device thanks to the the feedback control on multiple magnetohydrodynamic modes.In these high current discharges magnetic topology spontaneously self-organizes in an Ohmic helical symmetry, the quasi single helicity (QSH) state, in which the magnetic dynamics is dominated by the innermost resonant mode, with the new magnetic axis helically twisting around the geometrical axis of the torus.Inside the helical structure energy confinement is enhanced and electron temperatures exceeding 1 keV are measured, with steep gradients, which identify an internal transport barrier. Separatrix expulsion and symmetric electron temperature profiles with high gradients are obtained for ratios between the dominant mode and total B above about 4%. The measured electron temperature peak involves a large fraction of the plasma cross section, corresponding to an improvement in the global electron energy confinement up to a factor 2. The steep temperature profiles obtained in QSH conditions correspond to an electron thermal diffusivity reduced by more than one order of magnitude.Perturbative experiments (pellets and impurity laser blow off injections) have been performed to study particle confinement inside and outside the thermal island. Inside the helical structure experimental evidence of main gas confinement increase has been obtained, while for impurities there is no evidence of confinement increase.

Three-dimensional equilibria and transport in RFX-mod: A description using stellarator tools

RFX-mod self-organized single helical axis (SHAx) states provide a unique opportunity to advance 3D fusion physics and establish a common knowledge basis in a parameter region not covered by stellarators and tokamaks. The VMEC code has been adapted to the reversed-field pinch (RFP) to model SHAx equilibria in fixed boundary mode with experimental measurements as constraint. The averaged particle diffusivity over the helical volume, estimated with the Monte Carlo code ORBIT, has a neoclassical-like dependence on collisionality and does not show the 1/ν trend of un-optimized stellarators. In particular, the helical region boundary, corresponding to an electron transport barrier with zero magnetic shear and improved confinement, has been investigated using numerical codes common to the stellarator community. In fact, the DKES/PENTA codes have been applied to RFP for local neoclassical transport computations, including radial electric field, to estimate thermal diffusion coefficients in the barrier region for...

Magnetohydrodynamic equilibrium and the stability of tokamak and reversed-field pinch systems with 3D helical cores

Bifurcated magnetohydrodynamic (MHD) equilibrium states are computed for ITER hybrid scenario and RFX-mod SHAx configurations with very flat or reversed core magnetic shear conditions. In the ITER studies, the minimum inverse rotational transform qmin is near unity, while for RFX-mod it is 1/8. Two equilibrium states are obtained: one is axisymmetric, the other displays a 3D helical core. In tokamak devices, the structure resembles a saturated ideal MHD internal kink mode. In the reversed-field pinch, the structure is seven-fold toroidally periodic. The equilibrium magnetic field spectrum in the Boozer coordinate frame is calculated in both the ITER and RFX-mod configurations and the implications are discussed. The RFX-mod equilibria are strongly unstable to external ideal MHD kink modes, which become stabilized with a closely fitting conducting shell when the equilibrium state has a weak reversed core shear. It is marginally unstable with a monotonic q-profile. Unstable modes are driven by the Ohmic current, with pressure and Pfirsch–Schl¨uter currents having a very weak effect. The external kink mode spectrum is dominated by coupled

Self-Organized Helical Equilibria in the RFX-Mod Reversed Field Pinch

m = 1