Realistic multi-machine tokamak profile simulations and numerical ramp-down optimization using the RAPTOR code

Predictive modelling of plasma profiles is an essential part of ongoing research in tokamak plasmas, required for a successful realization of future fusion reactors. This thesis focuses on upgrading the RAPTOR code to extend the area of its applicability for plasma modelling and scenario development. RAPTOR is a light and fast simulator, solving radial transport equations, developed for plasma real-time control. This thesis also demonstrates new strategy for ramp-down optimization. The RAPTOR transport model has been extended to take into account the influence of the time-varying plasma equilibrium geometry and background kinetic profiles on the evolution of the predicted plasma profiles. It allows to get more realistic predictions of the plasma state in case of rapid changes in the plasma shape and equilibrium. Also transport equations for the ion temperature and plasma particles (electrons and ions) have been implemented in the code. Benchmarks have been performed with more sophisticated transport ASTRA and CRONOS codes and with prescribed data for the particle transport in ITER. With successful benchmarks, we confirm that the new transport equations are solved correctly. A new ad-hoc transport model based on constant gradients for core and pedestal regions, that is suitable for simulations of transition between H (high) and L (low confinement) modes, has been implemented into RAPTOR. This model assumes ``stiffness'' of the plasma profiles in the core region, reflecting their relatively weak reaction to changes in the heat flux. Only few transport model parameters have to be prescribed. They are validated with predictive simulations of the time evolution of plasma profiles for TCV, ASDEX Upgrade and JET plasmas. We demonstrate the capabilities of RAPTOR for fast and realistic predictions of plasma state over the entire plasma discharges, i.e. from ramp-up to ramp-down. We have defined characteristic gradients in the ``stiff'' region for each machine and L/H confinement modes and have obtained a very good agreement with experimental measurements. We have also demonstrated several special cases, where the obtained set of the transport parameters does not work, and proposed possible solutions of the problems. An optimization procedure for the plasma ramp-down phase has been developed during this work. Nondisruptive termination scenarios are necessary for safe operation of ITER, since it can withstand only a limited amount of plasma disruptions. Automatic optimization algorithms can be applied for searching the optimal ramp-down trajectory. With RAPTOR, optimization results are obtained in a reasonable time (hours). We define the goal of the optimization as ramping down the plasma current as fast as possible while avoiding any disruptions caused by reaching physical or technical limits. Physical constraints are relevant for most tokamaks, others are technical and related to the specific tokamaks. We show how different goals and constraints can easily be included or updated in order to simulate a new machine. A proper plasma shaping during the current ramp-down can reduce significantly the plasma internal inductance, improving its vertical stability. Specific heating scenarios allow to reduce the drop in βpol during H-L transition, which is important for plasma MHD stability. Results of numerical and experimental ramp-down studies for TCV, AUG and JET plasmas are presented

Current ramps optimization study with the RAPTOR code

Optimization of the plasma discharge is related to determination of the optimal time evolution of the plasma parameters to reach a specific plasma state taken into account certain physical and technical constraints. The set of plasma parameters which should be optimized consists of the parameters significantly changing the plasma state and can be defined from the different tokamak actuator inputs: plasma current, EC, NBI heating or current drive power, density, etc. In this work we carry out the optimization study of the current ramp down. Numerical optimization of this phase can prescribe evolution of the plasma parameters to terminate plasma as fast as possible and in the same time to avoid disruptions in the real experiments. The simulation is performed with the RAPTOR code. It is a light and fast transport code with a simplified transport model which includes transport equations for electron temperature and poloidal flux. However, this code was constructed assuming a fixed plasma equilibrium, whereas plasma geometry might change during ramp-down phase. Therefore RAPTOR has been extended to include time varying terms. In this way, time varying plasma geometry can be used in the optimization procedure and for example plasma elongation can be an additional parameter for the trajectory optimization. The results of the simulation with the extended transport model and optimization procedure of ramp-down phase of AUG-like plasma parameters are presented

Numerical optimization of ramp-down phases for TCV and AUG plasmas

Optimization of the plasma discharge can be defined as determination of an optimal time evolution of the plasma parameters to lead a plasma to a desired state keeping it within the specific limits: physical ones (like the Greenwald density limit, low normalized beta and internal inductance values) and technical ones (like the vertical stability limit). The parameters, time-trajectories of which have to be optimized, are the ones significantly changing the plasma state, and, depending on the optimization goal, can be chosen from a wide range of plasma parameters: plasma current, plasma elongation, EC, NBI heating or current drive power, electron density, etc. Developing non-disruptive termination scenarios is important for safe operation of future tokamaks and especially for ITER since significant heat fluxes to the wall are expected during disruptions because of large amount of energy stored in burning plasmas. Therefore, the main goal of ramp-down optimization is to ramp down a plasma current as fast as possible while avoiding any disruptions. The results of the optimization problem study with the physical and technical limits is presented for TCV and AUG plasmas. The present work was done mainly with the RAPTOR code. The transport model has been extended to include a time-varying plasma equilibrium geometry, increasing the accuracy of full discharge simulations. Due to the design, the RAPTOR code is also an efficient tool for an optimization problem solving. A new ad-hoc transport model has been implemented to the RAPTOR code and tested during this work. Verification of the thermal transport model with simulation of the AUG and TCV full plasma discharges using RAPTOR will be presented

Control of NTMs and integrated multi-actuator plasma control on TCV

The control of 2/1 neoclassical tearing modes (NTMs) with electron cyclotron (EC) waves has been studied both experimentally and numerically on TCV. Dynamic evolutions of NTMs along with time-varying deposition locations of the control beam have been studied in detail. The prevention of NTMs by means of preemptive EC (i.e. the control beam is switched on before the mode onset) has also been explored. A small sinusoidal sweeping with full amplitude of 0.07 (normalized to the minor radius) has been added to the control beam in two of the experiments to facilitate the comparison between NTM stabilization and prevention. It is shown that the prevention of NTMs is more efficient than NTM stabilization in terms of the minimum EC power required. Interpretative simulations with the Modified Rutherford Equation (MRE) have been performed to better quantify various effects, with coefficients well defined by dedicated experiments. Specifically, in order to obtain more insight on the dominant dependencies, a simple ad-hoc analytical model has been proposed to evaluate the time-varying classical stability index Δ' in the test discharges, based on the Δ'-triggered nature of these 2/1 NTMs. This allows simulating well the entire island width evolution with the MRE, starting from zero width and including both NTM stabilization and prevention cases for the first time. The exploration of NTM physics and control has facilitated the development of an NTM controller that is independent of the particular features of TCV and has been included in a generic plasma control system (PCS) framework. Integrated control of 2/1 NTMs, plasma β (the ratio of plasma pressure to magnetic pressure) and model-estimated safety factor q profiles has been demonstrated on TCV

Real-time model-based plasma state estimation, monitoring and integrated control in TCV, ASDEX-Upgrade and ITER

To maintain a high-performance, long-duration tokamak plasma scenario, it is necessary to maintain desired profiles while respecting operational limits. This requires real-time estimation of the profiles, monitoring of their evolution with respect to predictions and known limits, and their active control to remain within the desired envelope. Model-based techniques are particularly suitable to tackle such problems due to the nonlinear nature of the processes and the tight coupling among the various physical variables. A suite of physics-based, control-oriented models for the core plasma proles in a tokamak is presented, with models formulated in such a way that powerful methods from the systems and control engineering community can be leveraged to design ancient algorithms. We report on new development and applications of these models for real-time reconstruction, monitoring and integrated control of plasma proles on TCV, ASDEX-Upgrade and simulations for ITER