F. Felici

Numerical optimization of actuator trajectories for ITER hybrid scenario profile evolution

Optimal actuator trajectories for an ITER hybrid scenario ramp-up are computed using a numerical optimization method. For both L-mode and H-mode scenarios, the time trajectory of plasma current, EC heating and current drive distribution is determined that minimizes a chosen cost function, while satisfying constraints. The cost function is formulated to reflect two desired properties of the plasma q profile at the end of the ramp-up. The first objective is to maximize the ITG turbulence threshold by maximizing the volume-averaged s/q ratio. The second objective is to achieve a stationary q profile by having a flat loop voltage profile. Actuator and physics-derived constraints are included, imposing limits on plasma current, ramp rates, internal inductance and q profile. This numerical method uses the fast control-oriented plasma profile evolution code RAPTOR, which is successfully benchmarked against more complete CRONOS simulations for L-mode and H-mode mode ITER hybrid scenarios. It is shown that the optimized trajectories computed using RAPTOR also result in an improved ramp-up scenario for CRONOS simulations using the same input trajectories. Furthermore, the optimal trajectories are shown to vary depending on the precise timing of the L–H transition.

A mimetic spectral element solver for the Grad-Shafranov equation

In this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in 56 to the solution of the Grad-Shafranov equation. This approach combines a finite volume discretization with the mixed finite element method. In this way the discrete differential operators (?, ?×, ??) can be represented exactly and metric and all approximation errors are present in the constitutive relations. The result of this formulation is an arbitrary order method even on highly curved meshes. Additionally, the integral of the toroidal current J ? is exactly equal to the boundary integral of the poloidal field over the plasma boundary. This property can play an important role in the coupling between equilibrium and transport solvers. The proposed solver is tested on a varied set of plasma cross sections (smooth and with an X-point) and also for a wide range of pressure and toroidal magnetic flux profiles. Equilibria accurate up to machine precision are obtained. Optimal algebraic convergence rates of order p + 1 and geometric convergence rates are shown for Soloviev solutions (including high Shafranov shifts), field-reversed configuration (FRC) solutions and spheromak analytical solutions. The robustness of the method is demonstrated for non-linear test cases, in particular on an equilibrium solution with a pressure pedestal.

Simultaneous closed-loop control of the current profile and the electron temperature profile in the TCV tokamak

Two key properties that are often used to define a plasma operating scenario in nuclear fusion tokamak devices are the current and electron temperature (Te) profiles due to their intimate relationship to plasma performance and stability. In the tokamak community, the current profile is typically specified in terms of the safety factor (q) profile or its inverse, the rotational transform (ι = 1/q) profile. The plasma poloidal magnetic flux (Ψ) and Te dynamics are governed by an infinite-dimensional, nonlinear, coupled, physics-based model that is described by the magnetic diffusion equation and the electron heat transport equation. In this work, an integrated feedback controller is designed to track target ι (proportional to the spatial gradient of Ψ) and Te profiles by embedding these partial differential equation models into the control design process. The electron thermal conductivity profile is modeled as an uncertainty, and the controller is designed to be robust to an expected uncertainty range. The performance of the integrated ι + Te profile controller in the TCV tokamak is demonstrated through simulations with the simulation code RAPTOR by first tracking a nominal target, and then modulating the Te profile between equilibrium points while maintaining the ι profile in a stationary condition.

Closed-loop control of the safety factor profile in the TCV tokamak

A key property that has a close relationship to both the performance and stability of the plasma in nuclear fusion tokamak devices is the safety factor profile (q-profile). As a result, extensive research has been conducted to develop algorithms to actively control the q-profile evolution with the goal of optimizing the tokamak approach to fusion energy production. The actuators that can be used to control the q-profile are the total plasma current, the auxiliary heating/current-drive system and the line-average electron density. In this work, we first investigate the effect that pure plasma auxiliary heating has on the q-profile in low performance (L-mode) operating scenarios in the TCV tokamak. This study indicates that pure auxiliary heating has a small effect on the q-profile in the examined scenarios. Therefore, feedback controllers that utilize the total plasma current and exclusively the auxiliary current-drive capabilities are designed for q-profile control in TCV. The controllers are designed to put emphasis on achieving the target q-profile in different spatial regions and to respond differently to errors in the q-profile. The control performance of each controller is tested with the simplified physics-based plasma profile simulation code RAPTOR. The comparison of the closed-loop performance of these controllers is done in preparation for future q-profile control experiments in the TCV tokamak.

Individual Sawtooth pacing by synchronized ECCD in TCV

Previous real-time sawtooth control scenarios using EC actuators have attempted to shorten [1] or lengthen [2] the sawtooth period by optimally positioning the EC absorption near the q=1 surface. In new experiments we demonstrate for the first time that individual sawtooth crashes can be repetitively induced at predictable times by reducing the stabilizing ECCD power after a predetermined time from the preceding crash. Other stabilizing actuators ( e. g. ICRF, NBI) are expected to produce similar effects. Armed with these results, we present a new sawtooth / NTM control paradigm for improved performance in burning plasmas. The potential appearance of neo-classical tearing modes, triggered by long period sawtooth crashes even at low beta, becomes predictable and therefore amenable to preemptive ECCD. The ITER Electron Cyclotron Upper Launcher (EC-UL) design incorporates the needed functionalities for this method to be applied. The methodology and associated TCV experiments will be presented.