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

Current ramps in tokamaks: from present experiments to ITER scenarios

In order to prepare adequate current ramp-up and ramp-down scenarios for ITER, present experiments from various tokamaks have been analysed by means of integrated modelling in view of determining relevant heat transport models for these operation phases. A set of empirical heat transport models for L-mode (namely, the Bohm-gyroBohm model and scaling based models with a specific fixed radial shape and energy confinement time factors of H 96-L = 0.6 or H IPB98 = 0.4) has been validated on a multi-machine experimental dataset for predicting the l i dynamics within ±0.15 accuracy during current ramp-up and ramp-down phases. Simulations using the Coppi-Tang or GLF23 models (applied up to the LCFS) overestimate or underestimate the internal inductance beyond this accuracy (more than ±0.2 discrepancy in some cases). The most accurate heat transport models are then applied to projections to ITER current ramp-up, focusing on the baseline inductive scenario (main heating plateau current of I p = 15 MA). These projections include a sensitivity study to various assumptions of the simulation. While the heat transport model is at the heart of such simulations (because of the intrinsic dependence of the plasma resistivity on electron temperature, among other parameters), more comprehensive simulations are required to test all operational aspects of the current ramp-up and ramp-down phases of ITER scenarios. Recent examples of such simulations, involving coupled core transport codes, free-boundary equilibrium solvers and a poloidal field (PF) systems controller are also described, focusing on ITER current ramp-dow