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.
56 075020) is used to pave the way towards ITER divertor procurement and operation. It consists in implementing a divertor configuration and installing ITER-like actively cooled tungsten monoblocks in the Tore Supra tokamak, taking full benefit of its unique long-pulse capability. WEST is a user facility platform, open to all ITER partners. This paper describes the physics basis of WEST: the estimated heat flux on the divertor target, the planned heating schemes, the expected behaviour of the L-H threshold and of the pedestal and the potential W sources. A series of operating scenarios has been modelled, showing that ITER-relevant heat fluxes on the divertor can be achieved in WEST long pulse H-mode plasmas.
The 2014–2016 JET results are reviewed in the light of their significance for optimising the ITER research plan for the active and non-active operation. More than 60 h of plasma operation with ITER first wall materials successfully took place since its installation in 2011. New multi-machine scaling of the type I-ELM divertor energy flux density to ITER is supported by first principle modelling. ITER relevant disruption experiments and first principle modelling are reported with a set of three disruption mitigation valves mimicking the ITER setup. Insights of the L–H power threshold in Deuterium and Hydrogen are given, stressing the importance of the magnetic configurations and the recent measurements of fine-scale structures in the edge radial electric. Dimensionless scans of the core and pedestal confinement provide new information to elucidate the importance of the first wall material on the fusion performance. H-mode plasmas at ITER triangularity (H = 1 at βN ~ 1.8 and n/nGW ~ 0.6) have been sustained at 2 MA during 5 s. The ITER neutronics codes have been validated on high performance experiments. Prospects for the coming D–T campaign and 14 MeV neutron calibration strategy are reviewed.
The 2D (radial/poloidal) spatial topology of RF-induced convective cells developing radially in front of ion cyclotron range of frequency (ICRF) antennae is investigated, in relation to the spatial distribution of RF currents over the metallic structure of the antenna. This is done via a Green's function, determined from the ICRF wave coupling equations, and well-suited to open field lines extending toroidally far away on both sides of the antenna. Using such formalism, combined with a full-wave calculation using the 3D antenna code ICANT (Pécoul S. et al 2000 Comput. Phys. Commun. 146 166-87), two classes of convective cells are analysed. The first one appears in front of phased arrays of straps, and depending on the strap phasing, its topology is interpreted using the poloidal profiles of either the RF current or the RF voltage of the strip line theory. The other class of convective cells is specific to antenna box corners and is evidenced for the first time. Based on such analysis, general design rules are worked out in order to reduce the RF-sheath potentials, which generalize those proposed in the earlier literature, and concrete antenna design options are tested numerically. The merits of aligning all strap centres on the same (tilted) flux tube, and of reducing the antenna box toroidal conductivity in its lower and upper parts, are discussed.
In this paper, a strict Lyapunov function is developed in order to show the exponential stability and input-to-state stability (ISS) properties of a diffusion equation for nonhomogeneous media. Such media can involve rapidly time-varying distributed diffusivity coefficients. Based on this Lyapunov function, a control law is derived to preserve the ISS properties of the system and improve its performance. A robustness analysis with respect to disturbances and estimation errors in the distributed parameters is performed on the system, precisely showing the impact of the controller on the rate of convergence and ISS gains. This is important in light of a possible implementation of the control since, in most cases, diffusion coefficient estimates involve a high degree of uncertainty. An application to the safety factor profile control for the Tore Supra tokamak illustrates and motivates the theoretical results. A constrained control law (incorporating nonlinear shape constraints in the actuation profiles) is designed to behave as closely as possible to the unconstrained version, albeit with the equivalent of a variable gain. Finally, the proposed control laws are tested under simulation, first in the nominal case and then using a model of Tore Supra dynamics, where they show adequate performance and robustness with respect to disturbances.
Wall conditioning techniques applicable in the presence of permanent toroidal magnetic field will be required for the operation of ITER, in particular for recovery from disruptions, vent and air leak, isotopic ratio control, recycling control and mitigation of the tritium inventory build-up. Ion Cyclotron Wall Conditioning (ICWC) is one of the most promising options and has been the subject of considerable recent study on current tokamaks. This paper reports on the findings of such studies performed on European tokamaks, covering a range of plasma-facing materials: TORE SUPRA, TEXTOR, ASDEX Upgrade and JET. IntroductionIn ITER and future fusion devices, the magnetic field, generated by superconducting coils, will be continuously maintained. In the presence of such a magnetic field, conventional DC-glow discharges are unstable and can therefore no longer be used between ohmic plasma pulses. During the non-active He or H phase of ITER, with divertor targets made of carbonfibre composite (CFC), interpulse wall conditioning will be required for reliable discharge initiation or recovery after disruptions. In the D:T phase, wall conditioning may also contribute to the control of the tritium inventory in ITER, of which the build-up is a major investigations are needed prior to its validation and its application to ITER, in particular for fuel removal, recovery after disruptions and isotopic ratio control. This paper reviews the results of recent ICWC experiments performed on current tokamaks, covering a range of plasma-facing materials: TORE SUPRA (CFC), TEXTOR (fine-grain graphite), ASDEX-Upgrade (all W-coated wall) and JET (CFC/Be). The relevance of ICWC, specifications for its application to ITER and the operational domain on current tokamaks are introduced in the first part. The optimization of ICWC discharges is the subject of the second part. The third part reports on the assessment of the efficiency of D 2 (or H 2 ) and He-ICWC discharges for isotopic exchange and fuel removal. The benefit of pulsed ICWC discharges is treated in this part. The last part is devoted to the discussions of the I-9 experimental observations. In particular the He retention in metallic plasma-facing components (PFC) and the role of the different species in wall conditioning are discussed.The operation of ICWC and its efficiency for fuel removal are finally extrapolated to ITER.1. ICWC experiments on the four tokamaks and ICWC discharge characterization a. Principle and relevance of ICWC for wall conditioningThe principle of ICWC discharge production, in the presence of the toroidal magnetic field, has been described elsewhere (see e.g. [7]). The coupling of the RF power to the ICWC discharge is non-resonant and mainly results from the absorption of the RF energy by the electrons. Plasmas with densities ranging from 10 16 and 10 18 m -3 (i.e. 4 to 6 orders of magnitude higher than in DC glow discharges) and temperatures 1 < T e < 10 eV can be produced in a "relay-race" regime of slow and fast wave excitation [7] .In the presence of ...
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