With reference to toroidal fusion devices, we solve axisymmetric nonlinear evolutionary equilibrium equations, describing the plasma behaviour, self-consistently coupled to eddy currents equations, describing surrounding three-dimensional (3D) structures. This formulation allows the analysis of nonlinear plasma quasi-static evolution in the presence of 3D volumetric conductors. Several validations and test cases are presented, suggesting the potential applications of the proposed method to the analysis of various situations of scientific and technical interest for future fusion devices such as ITER and DEMO, like for instance disruptions.

The vertical stability of the Experimental Advanced Superconducting Tokamak (EAST) is studied in detail in the present paper. It is found that correct modelling of the detailed three-dimensional (3D) features of the conducting structures surrounding the plasma is essential in order to get reliable estimates of the growth rate of vertical displacement events. The numerical model developed, based on the CarMa0 code, can take 3D effects into account, and provides results very close to experimental values for a wide range of plasma configurations. A deep insight about the current density patterns induced in passive structures is gained.

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The TCV tokamak is augmenting its unique historical capabilities (strong shaping, strong electron heating) with ion heating, additional electron heating compatible with high densities, and variable divertor geometry, in a multifaceted upgrade program designed to broaden its operational range without sacrificing its fundamental flexibility. The TCV program is rooted in a three-pronged approach aimed at ITER support, explorations towards DEMO, and fundamental research. A 1 MW, tangential neutral beam injector (NBI) was recently installed and promptly extended the TCV parameter range, with record ion temperatures and toroidal rotation velocities and measurable neutral-beam current drive. ITER-relevant scenario development has received particular attention, with strategies aimed at maximizing performance through optimized discharge trajectories to avoid MHD instabilities, such as peeling-ballooning and neoclassical tearing modes. Experiments on exhaust physics have focused particularly on detachment, a necessary step to a DEMO reactor, in a comprehensive set of conventional and advanced divertor concepts. The specific theoretical prediction of an enhanced radiation region between the two X-points in the low-field-side snowflake-minus configuration was experimentally confirmed. Fundamental investigations of the power decay length in the scrape-off layer (SOL) are progressing rapidly, again in widely varying configurations and in both D and He plasmas; in particular, the double decay length in L-mode limited plasmas was found to be replaced by a single length at high SOL resistivity. Experiments on disruption mitigation by massive gas injection and electron-cyclotron resonance heating (ECRH) have begun in earnest, in parallel with studies of runaway electron generation and control, in both stable and disruptive conditions; a quiescent runaway beam carrying the entire electrical current appears to develop in some cases. Developments in plasma control have benefited from progress in individual controller design and have evolved steadily towards controller integration, mostly within an environment supervised by a tokamak profile control simulator. TCV has demonstrated effective wall conditioning with ECRH in He in support of the preparations for JT-60SA operation.