Abstract.A new paradigm is presented to reconstruct the plasma current density profile in a tokamak in real-time. The traditional method of basing the reconstruction on real-time diagnostics combined with a real-time GradShafranov solver suffers from the difficulty of obtaining reliable internal current profile measurements with sufficient spatial and temporal accuracy to have a complete picture of the profile evolution at all times. A new methodology is proposed in which the plasma current density profile is simulated in real-time by solving the first-principle physics-based equations determining its evolution. Effectively, an interpretative transport simulation similar to those run today in post-plasma shot analysis is performed in real-time. This provides realtime reconstructions of the current density profile with spatial and temporal resolution constrained only by the capabilities of the computational platform used and not by the available diagnostics or the choice of basis functions. The diagnostic measurements available in real-time are used to constrain and improve the accuracy of the simulated profiles. Estimates of other plasma quantities, related to the current density profile, become available in real-time as well. The implementation of the proposed paradigm in the TCV tokamak is discussed, and its successful use in plasma experiments is demonstrated. This framework opens up the possibility of unifying q profile reconstructions across different tokamaks using a common physics model and will support a wealth of applications in which improved real-time knowledge of the plasma state is used for feedback control, disruption avoidance, scenario monitoring, and external disturbance estimation.

A computational method is presented to determine the tokamak actuator time evolution (trajectories) required to optimally reach a given point in the tokamak operating space while satisfying a set of constraints. Usually, trajectories of plasma auxiliary heating, current drive and plasma current required during the transient phases of a tokamak shot to reach a desired shape of the plasma temperature and safety factor (q) profiles are determined by trial-and-error by physics operators. In this paper, these trajectories are calculated by solving a non-linear, constrained, finite-time optimal control problem.The optimization problem contains a physics model of the non-linear plasma profile dynamics, a cost function to be minimized, and a set of constraints on the actuators and plasma quantities. The method is tested by optimizing the trajectories of I p , heating and current drive power to obtain a typical hybrid plasma q profile at the end of the current ramp-up phase, while minimizing both the Ohmic flux swing and the distance from a stationary condition, and requiring q > 1 and edge V loop > 0 at all times. The optimized trajectories feature an I p overshoot similar to that used in existing experiments, and are shown to perform significantly better than a set of non-optimized trajectories, allowing stationary profiles to be obtained at the beginning of the flat-top phase. Additional information is obtained, including the parameter sensitivity of the optimal solution, a linear model describing the linearized dynamics of the profiles around the optimal trajectory, as well as a classification of the actuator trajectories based on the critical constraint which limits their value at a given time. This provides a solid basis for subsequent closed-loop feedback controller design. The tools presented in this paper could be useful to improve existing tokamak operational scenarios, to prepare operation of future machines and optimize their design.

Highlights.• Algorithm vertical stabilisation using a linear parametrisation of the current density • Experimentally derived model of the vacuum vessel to account for vessel currents• Real-time contouring algorithm for flux surface averaged 1.5D transport equations• Full real time implementation coded in SIMULINK runs in less than 200µs• Applications: shape control, safety factor profile control, coupling with RAPTOR Abstract. Equilibrium reconstruction consists in identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. The LIUQE code adopts a computationally efficient method to solve this problem, based on an iterative solution of the Poisson equation coupled with a linear parametrisation of the plasma current density. This algorithm is unstable against vertical gross motion of the plasma column for elongated shapes and its application to highly shaped plasmas on TCV requires a particular treatment of this instability. TCV's continuous vacuum vessel has a low resistance designed to enhance passive stabilisation of the vertical position. The eddy currents in the vacuum vessel have a sizeable influence on the equilibrium reconstruction and must be taken into account. A real time version of LIUQE has been implemented on TCV's distributed digital control system with a cycle time shorter than 200µs for a full spatial grid of 28 by 65, using all 133 experimental measurements and including the flux surface average of quantities necessary for the real time solution of 1.5D transport equations. This performance was achieved through a thoughtful choice of numerical methods and code optimisation techniques at every step of the algorithm, and was coded in MATLAB and SIMULINK for the off-line and real time version respectively.

Starting from a standard single null X-point configuration, a second order null divertor (snowflake (SF)) has been successfully created on the Tokamak à Configuration Variable (TCV) tokamak. The magnetic properties of this innovative configuration have been analysed and compared with a standard Xpoint configuration. For the SF divertor, the connection length and the flux expansion close to the separatrix exceed those of the standard X-point by more than a factor of 2. The magnetic shear in the plasma edge is also larger for the SF configuration.

In the standard scenario of tokamak plasma operation, sawtooth crashes are the main perturbations that can trigger performance-degrading, and potentially disruption-generating, neoclassical tearing modes. This Letter demonstrates sawtooth pacing by real-time control of the auxiliary power. It is shown that the sawtooth crash takes place in a reproducible manner shortly after the removal of that power, and this can be used to precisely prescribe, i.e., pace, the individual sawteeth. In combination with preemptive stabilization of the neoclassical tearing modes, sawtooth pacing provides a new sawtooth control paradigm for improved performance in burning plasmas.PACS numbers: 52.35Py,52.50. Sw,52.55.Fa In high performance tokamaks, the plasma β (the ratio of plasma pressure to magnetic pressure) is often limited by metastable magnetohydrodynamic (MHD) instabilities known as neoclassical tearing modes (NTMs) [1]. These modes are of special concern for fusion-reactorgrade tokamak plasmas since the islands generated in the confining magnetic topology grow to a size, even at relatively low β, that they must be mitigated, or avoided altogether, to allow sufficiently economic power generation. Fortuitously, these modes will self-stabilize if the island is reduced below a certain size, and moreover they require a seed island to begin to grow. The main perturbation that triggers these modes in the standard tokamak scenario is the sawtooth core relaxation event [2,3] that can occur when the safety factor q is below one (q is the rate of change of the toroidal flux with the poloidal flux). At the "crash" of the sawtooth, particle and magnetic energy are redistributed from inside to outside the surface where q = 1 and the liberation of this energy can seed MHD modes at resonant surfaces where q = m/n is rational (m and n are the integer poloidal and toroidal mode numbers, respectively), in particular at the q = 3/2 and q = 2/1 surfaces. Large 2/1 modes can also lead to plasma current disruptions, which might damage a reactor.NTM avoidance is concerned with eliminating or reducing the triggering mechanisms. The scenario foreseen in ITER to reach the optimal fusion power, the socalled standard scenario, is a sawtoothing plasma with long sawtooth periods resulting from the strong fastpartical stabilization inherent in burning plasmas [4,5]. It has been shown in many tokamaks that the crashes of long-period sawteeth can trigger NTMs even at low β [6,7]. Therefore, the control of the sawtooth period is crucial for NTM avoidance and emphasis has been placed on shortening the period. It has been demonstrated in the tokamakà configuration variable (TCV) [8] and Tore Supra [9] that the sawtooth period can be controlled by feedback-positioning very-locally absorbed EC waves relative to the q = 1 surface. However, the dependence of the sawtooth period on the the absorption location is extremely non-linear. We propose a new approach for the control of the sawtooth period, that of sawtooth pacing by power control. The method provides a...

Simultaneous real-time control of multiple MHD instabilities is experimentally demonstrated in the TCV tokamak. Multiple sources of EC heating and current drive, injected through real-time controlled launchers, are used to stabilize 3/2 and 2/1 neoclassical tearing modes (NTMs) rapidly after their appearance. Control of the sawtooth instability using a new sawtooth-pacing technique is demonstrated, providing precise control of the time of appearance of the sawtooth crash. Efficient NTM preemption can then be performed by applying pulsed power on the mode rational surface at the time of the seed-island generating sawtooth crash. These three elements are combined into one integrated control system which can simultaneously control the sawtooth period, preempt the formation of NTMs and suppress these if they appear.

Abstract. Tokamak plasmas operating at high performance are limited by several MHD instabilities. The sawtooth instability limits the core plasma pressure and can drive the neoclassical tearing mode unstable, but also prevents accumulation of impurities in the core. Electron cyclotron heating and current drive systems can be used to modify the local current profile and therefore tailor the sawtooth period. This paper reports on demonstrations of continuous real time feedback control of the sawtooth period by varying the EC injection angle.

SUMMARYThe trend with offshore wind turbines is to increase the rotor diameter as much as possible to decrease the costs per kWh. The increasing dimensions have led to the relative increase in the loads on the wind turbine structure. Because of the increasing rotor size and the spatial load variations along the blade, it is necessary to react to turbulence in a more detailed way: each blade separately and at several separate radial distances. This combined with the strong nonlinear behavior of wind turbines motivates the need for accurate linear parameter-varying (LPV) models for which advanced control synthesis techniques exist within the robust control framework. In this paper we present a closed-loop LPV identification algorithm that uses dedicated scheduling sequences to identify the rotational dynamics of a wind turbine. We assume that the system undergoes the same time variation several times, which makes it possible to use timeinvariant identification methods as the input and the output data are chosen from the same point in the variation of the system. We use time-invariant techniques to identify a number of extended observability matrices and state sequences that are inherent to subspace identification identified in a different state basis. We show that by formulating an intersection problem all states can be reconstructed in a general state basis from which the system matrices can be estimated. The novel algorithm is applied on a wind turbine model operating in closed loop.