Faa Federico Felici

Snowflake divertor plasmas on TCV

Starting from a standard single null X-point configuration, a second order null divertor (snowflake (SF)) has been successfully created on the Tokamak a Configuration Variable (TCV) tokamak. The magnetic properties of this innovative configuration have been analysed and compared with a standard X-point 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.

Real-time physics-model-based simulation of the current density profile in tokamak plasmas

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 Grad–Shafranov 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 real-time 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.

Non-linear model-based optimization of actuator trajectories for tokamak plasma profile control

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 Ip, 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 Vloop > 0 at all times. The optimized trajectories feature an Ip 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.

Real time control of the sawtooth period using EC launchers

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.

Development and validation of a tokamak skin effect transformer model

A lumped parameter, state space model for a tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non-linear interaction of plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as a function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with random binary signals have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated under ohmic conditions between 200 and 300 kA with 30 ms rise time, several times faster than its time constant L/R approximate to 200 ms. A second-order linear differential equation for equilibrium loop voltage is sufficient to describe the plasma current and internal inductance modulation with 70% and 38% fit parameters, respectively. The model explains the most salient features of the plasma current transients, such as the inverse correlation between plasma current ramp rates and internal inductance changes, without requiring detailed or explicit information about resistivity profiles. This proves that a lumped parameter modelling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least under ohmic conditions without external heating and current drive sources.

Real-time feedback control of millimeter-wave polarization for LHD

Electron cyclotron heating (ECH) is widely used in magnetic fusion devices, and the polarization of the injected millimeter-wave beams plays a crucial role in the propagation and absorption of the beam energy by the plasma. This polarization can be adjusted by grating mirror polarizers placed in the transmission lines which carry the microwaves from the power source to the plasma. In long-pulse devices such as the Large Helical Device (LHD) and ITER, it is desirable to track changes in the plasma and adjust the polarization of the ECH in real time such as to keep the absorption as high as possible and avoid shine-through which may lead to overheating of vessel components. For this purpose a real-time feedback control scheme is envisioned in which a measure of the absorption efficiency can be used to adjust the orientation of the polarizing mirrors toward an optimum. Such a setup has been tested in a low-power test stand as preparation for future implementation in the LHD ECH system. It is shown that a simple search algorithm is efficient and can in principle be used to control either the absorption efficiency or the linear polarization angle.

Edge-localized mode control by electron cyclotron waves in a tokamak plasma

Electron cyclotron resonance heating is applied to the edge of a high-confinement (H-mode) plasma featuring type I edge-localized modes (ELMs) in the TCV tokamak. As the deposition location is shifted gradually in a highly controlled manner towards the plasma pressure pedestal, an increase in the ELM frequency by a factor 2 and a decrease in the energy loss per ELM by the same factor are observed, even though the power absorption efficiency is reduced. This unexpected and, as yet, unexplained phenomenon, observed for the first time, runs contrary to the intrinsic type I ELM power dependence and provides a new approach for ELM mitigation.

Architecture and commissioning of the TCV distributed feedback control system

A new modular, digital, distributed feedback control system has been developed and installed to control the TCV plasma. With many more inputs and outputs, it provides the possibility to build control algorithms using far more information on the plasma state than previously possible as well as the ability to control many more actuators, including the multi-megawatt, multi-launcher electron cyclotron heating and current drive system. This paper provides an overview of the new control system, its integration into the TCV systems and its successful application to control the TCV plasma discharge.

From profile to sawtooth control : developing feedback control using ECRH/ECCD systems on the TCV tokamak

Real time control of heating systems is essential to maximize plasma performance and avoid or neutralize instabilities under changing plasma conditions. Several feedback control algorithms have been developed on the Tokamak a Configuration Variable (TCV) tokamak that use the electron cyclotron (ECRH/ECCD) system to control a wide range of plasma properties, including the plasma current, shape, profiles as well as the sawtooth instability. Controllers have been developed to obtain sawteeth of a pre-determined period, to maximize the sawtooth period using an extremum seeking control algorithm and finally to provide simultaneous control of the plasma emission profile peak and width using multiple independent EC actuators.

Feedback control of ECRH polarization on LHD

The polarization of electron cyclotron resonance heating (ECRH) waves, set by the orientation of a pair of corrugated mirror polarizers in the transmission line, determines the degree of coupling to O- and X-modes in the plasma and has an important effect on the first-pass absorption. Existing methods for determining the required polarization have been found adequate in most experiments. However, as the pulse length is increased it becomes increasingly important to maximize the first-pass absorption while the plasma or injection conditions change or when there can be significant O- to X-mode power coupling during propagation, particularly in the edge plasma region of a stellarator. This has motivated the development of a dedicated feedback control system which is able to adjust the polarizers angles settings during the discharge in order to maintain the highest possible absorption. An extremum seeking controller is shown to successfully recover the optimum polarization setting during long-pulse ECRH experiments on the Large Helical Device (LHD).Corrections were made to this article on 02 September 2010. The was removed before LHD in several places.