Low Effort L-i Nuclear Fusion Plasma Control Using Model Predictive Control Laws

One of the main problems of fusion energy is to achieve longer pulse duration by avoiding the premature reaction decay due to plasma instabilities. The control of the plasma inductance arises as an essential tool for the successful operation of tokamak fusion reactors in order to overcome stability issues as well as the new challenges specific to advanced scenarios operation. In this sense, given that advanced tokamaks will suffer from limited power available from noninductive current drive actuators, the transformer primary coil could assist in reducing the power requirements of the noninductive current drive sources needed for current profile control. Therefore, tokamak operation may benefit from advanced control laws beyond the traditionally used PID schemes by reducing instabilities while guaranteeing the tokamak integrity. In this paper, a novel model predictive control (MPC) scheme has been developed and successfully employed to optimize both current and internal inductance of the plasma, which influences the L-H transition timing, the density peaking, and pedestal pressure. Results show that the internal inductance and current profiles can be adequately controlled while maintaining the minimal control action required in tokamak operation.This work was supported in part by the University of the Basque Country (UPV/EHU) through Research Projects GIU11/02 and GIU14/07, Research and Training Unit UFI11/07, and by the Ministry of Science and Innovation (MICINN) through Research Project ENE2010-18345. The authors would also like to thank the collaboration of the Basque Energy Board (EVE) through Agreement UPV/EHUEVE23/6/2011, the Spanish National Fusion Laboratory (EURATOM-CIEMAT) through Agreement UPV/EHUCIEMAT08/190, and Jo Lister, Stefano Coda, and the TCV team for its collaboration and help. Authors are also very grateful to the anonymous reviewers that have helped to improve the initial version of the paper

Low Effort Nuclear Fusion Plasma Control Using Model Predictive Control Laws

One of the main problems of fusion energy is to achieve longer pulse duration by avoiding the premature reaction decay due to plasma instabilities. The control of the plasma inductance arises as an essential tool for the successful operation of tokamak fusion reactors in order to overcome stability issues as well as the new challenges specific to advanced scenarios operation. In this sense, given that advanced tokamaks will suffer from limited power available from noninductive current drive actuators, the transformer primary coil could assist in reducing the power requirements of the noninductive current drive sources needed for current profile control. Therefore, tokamak operation may benefit from advanced control laws beyond the traditionally used PID schemes by reducing instabilities while guaranteeing the tokamak integrity. In this paper, a novel model predictive control (MPC) scheme has been developed and successfully employed to optimize both current and internal inductance of the plasma, which influences the L-H transition timing, the density peaking, and pedestal pressure. Results show that the internal inductance and current profiles can be adequately controlled while maintaining the minimal control action required in tokamak operation

Development and Validation of a Tokamak Skin Effect Transformer model

A control oriented, lumped parameter model for the 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 the 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 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 (RBS) have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated in Ohmic conditions between 200kA and 300kA with 30ms rise time, several times faster than its time constant L/R\approx200ms. The model explains the most salient features of the plasma current transients without requiring detailed or explicit information about resistivity profiles. This proves that lumped parameter modeling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least in Ohmic conditions without external heating and current drive sources

Vertical compact torus injection into the STOR-M Tokamak

Central fuelling is a fundamental issue in the neat generation tokamak – ITER (International Thermonuclear Experimental Reactor). It is essential for optimization of the bootstrap current which is proportional to the pressure gradient of trapped particles. The conventional tokamak fuelling techniques, such as gas puffing and cryogenic pellet injection, are considered to be inadequate to fulfill this goal due to premature ionization caused by high plasma temperature and density. Fuelling by injecting a compact torus (CT) may be the only viable method suitable for a reactor-grade tokamak. CTs can be injected at different angles with respect to the tokamak toroidal magnetic field, either horizontally or vertically. In vertical injection, deeper CT penetration is expected due to the absence of the gradient of tokamak toroidal magnetic field in that direction. This thesis contributes to experimental investigation of vertical compact torus injection into the STOR-M tokamak. To perform vertical injection, the original injector- USCTI (University of Saskatchewan Compact Torus Injector) was modified by attaching a segment of 90˚ curved drift tube to bend the CT trajectory from horizontal to vertical. Bench tests have shown that a CT injected horizontally can be deflected effectively to the vertical direction. The velocity of 130 km•s^{-1}has been achieved while the CT passes through the 90˚ curved drift tube. It was found that the CT magnetic field structure kept intact as a typical structure of compact torus plasma. By further optimization of the USCTI configuration, the velocity has been increased to 270 km•s^{-1}. Based on the encouraging bench test results, actual vertical CT injection experiments have been performed in the STOR-M tokamak. Experimental results demonstrated, for the first time, vertical CT injection into a tokamak. Prompt increases both in line averaged electron density and in soft X-ray emission (central cord) are observed following vertical injection. Some H-mode phenomena, characterized by suppression of the m =2 Mirnov oscillation level and drop in Hα radiation level, have also been observed following the vertical injection. Fuelling effects caused by vertical injection and by tangential injection are discussed. The experimental results suggest that vertical CT injection is a feasible tokamak fuelling technique