This paper proposes a control-oriented approach to the tokamak plasma current profile dynamics. It is established based on a consistent set of simplified relationships, in particular for the microwave current drive sources, rather than exact physical modelling. Assuming that a proper model for advanced control schemes can be established using the socalled cylindrical approximation and neglecting the diamagnetic effects, we propose a model that focuses on the flux diffusion (from which the current profile is inferred). Its inputs are some real-time measurements available on modern tokamaks and the effects of some major actuators, such as the magnetic coils, Lower Hybrid (LHCD), Electron and Ion Cyclotron Frequency (ECCD and ICRH) systems, are particularly taken into account. More precisely, the non-inductive current profile sources are modelled as 3-parameters functions of the control inputs derived either from approximate theoretical formulae for the ECCD and bootstrap terms or from experimental scaling laws specifically developed from Hard X-ray Tore Supra data for the LHCD influence. The use of scaling laws in this model reflects the fact that the operation of future reactors will certainly depend upon a great number of scaling laws and specific engineering parameters. The discretisation issues are also specifically addressed, to ensure the robustness with respect to discretisation errors and the efficiency (in terms of computation time) of the associated algorithm. This model is compared with experimental results and the CRONOS solver for Tore Supra Tokamak.

We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilibria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized nonlinear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas.Here again, this is a straightforward and simple calculation for all mappings except one: the mapping J P,h that is related to the non-linear current profile in the plasma domain. The mapping J P,h is given by

A power-balance model, with radiation losses from impurities and neutrals, gives a unified description of the density limit (DL) of the stellarator, the L-mode tokamak, and the reversed field pinch (RFP). The model predicts a Sudo-like scaling for the stellarator, a Greenwald-like scaling, , for the RFP and the ohmic tokamak, a mixed scaling, , for the additionally heated L-mode tokamak. In a previous paper (Zanca et al 2017 Nucl. Fusion 57 056010) the model was compared with ohmic tokamak, RFP and stellarator experiments. Here, we address the issue of the DL dependence on heating power in the L-mode tokamak. Experimental data from high-density disrupted L-mode discharges performed at JET, as well as in other machines, are taken as a term of comparison. The model fits the observed maximum densities better than the pure Greenwald limit.