In the quest for new energy sources, the research on controlled thermonuclear fusion 1 has been boosted by the start of the construction phase of the International Thermonuclear Experimental Reactor (ITER). ITER is based on the tokamak magnetic configuration 3, which is the best performing one in terms of energy confinement. Alternative concepts are however actively researched, which in the long term could be considered for a second generation of reactors. Here, we show results concerning one of these configurations, the reversed-field pinch 4,5 (RFP). By increasing the plasma current, a spontaneous transition to a helical equilibrium occurs, with a change of magnetic topology. Partially conserved magnetic flux surfaces emerge within residual magnetic chaos, resulting in the onset of a transport barrier. This is a structural change and sheds new light on the potential of the RFP as the basis for a low-magnetic-field ohmic fusion reactor.The main magnetic field configurations studied for the confinement of toroidal fusion-relevant plasmas are the tokamak 3 , the stellarator 6 and the reversed-field pinch 4,5 (RFP). In the tokamak, a strong magnetic field is produced in the toroidal direction by a set of coils approximating a toroidal solenoid, and the poloidal field generated by a toroidal current flowing into the plasma gives the field lines a weak helical twist. This is the configuration that has been most studied and has achieved the best levels of energy confinement time. Thus, it is the natural choice for the International Thermonuclear Experimental Reactor, which has the mission of demonstrating the scientific and technical feasibility of controlled fusion with magnetic confinement.The RFP, like the tokamak, is axisymmetric and exploits the pinch effect due to a current flowing in a plasma embedded in a toroidal magnetic field. The main difference is that, for a given plasma current, the toroidal magnetic field in a RFP is one order of magnitude smaller than in a tokamak, and is mainly generated by currents flowing in the plasma itself. This feature is underlying the main potential advantage of the RFP as a reactor concept, namely the capability of achieving fusion conditions with ohmic heating only in a much simpler and compact device. In the past, this positive feature was overcome by the poorer stability properties, which led to the growth and saturation of several magnetohydrodynamic (MHD) instabilities, eventually downgrading the confinement performance. These instabilities, represented by Fourier modes in the poloidal and toroidal angles θ and φ as exp [i(mθ − nφ) were considered as an unavoidable ingredient of the dynamo self-organization process 4,8,9 , necessary for the sustainment of the configuration in time. The occurrence of several MHD modes resonating on different plasma layers gives rise to overlapping magnetic islands, which result in a chaotic region, extending over most of the plasma volume 10 , where the magnetic surfaces are destroyed and the confinement level is modest. This conditi...

Using the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), the single fluid resistive MHD plasma response to applied n = 2 resonant magnetic perturbations is computed, for a plasma discharge in the ASDEX-Upgrade tokamak. The computation predicts strong kink amplification, as previously predicted in DIII-D (Haskey et al 2014 Plasma Phys. Control. Fusion 56 035005), which is strongly dependent on the toroidal phase shift between the upper and lower coils, ϕ Δ ul . In particular, edge localised low n peeling modes with poloidal mode numbers just above pitch resonance-a subset of the kink response-are amplified. The robustness of the amplified peeling response with respect to truncation of the X point is investigated, by recomputing the plasma response for a range of edge geometries. It is found that the computed peeling response, when plotted against the safety factor, is not sensitive to the numerical truncation near the X point. It is also predicted that near the plasma edge where resistivity is large, the pitch aligned components are finite and also strongly dependent on ϕ Δ ul . A previous proposal that the amplified peeling response may indirectly drive the pitch aligned components by spectral proximity (Lanctot et al 2013 Nucl. Fusion 53 083019), is investigated by numerically applying magnetic perturbations of a single poloidal harmonic, as a boundary condition at the plasma edge. It is found that poloidal harmonic coupling causes harmonics to couple to and drive harmonics directly beneath them spectrally, and also that the pitch aligned components can be driven by this mechanism. This suggests that it is quite possible that the amplified low n peeling response can drive the pitch aligned components when it is strongly amplified, which would alter the coil configuration for optimum plasma stochastization, with implications for ELM control by RMPs.

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications.

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.

Toroidal computations are performed using the MARS-F code [Liu Y Q et al 2000 Phys.Plasmas 7 3681], in order to understand correlations between the plasma response and the observed mitigation of the edge localized modes (ELM) using resonant magnetic perturbation fields in ASDEX Upgrade. In particular, systematic numerical scans of the edge safety factor reveal that the amplitude of the resonant poloidal harmonic of the response radial magnetic field near the plasma edge, as well as the plasma radial displacement near the X-point, can serve as good indicators for predicting the optimal toroidal phasing between the upper and lower rows of coils in ASDEX Upgrade. The optimal coil phasing scales roughly linearly with the edge safety factor 95 q , for various choices of the toroidal mode number n=1-4 of the coil configuration. The optimal coil phasing is also predicted to vary with the upper triangularity of the plasma shape in ASDEX Upgrade. Furthermore, multiple resonance effects of the plasma response, with continuously varying 95 q , are computationally observed and investigated.