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

Extrapolation of ASDEX Upgrade H-mode discharges to ITER

In this paper we discuss a procedure to evaluate the fusion performance of ASDEX Upgrade discharges scaled up to ITER. The kinetic profile shape is taken from the measured profiles. Multiplication factors are used to obtain a fixed Greenwald fraction and an ITER normalized thermal pressure as in the corresponding ASDEX Upgrade discharge. The toroidal field and the plasma geometry are taken from the ITER-FEAT design (scenario 2), whereas q(95) is taken from the experiment. The confinement time is inferred assuming that the measured H-factor with respect to several existing scaling laws also holds for ITER. While retaining the information contained in the multi-machine databases underlying the different scaling laws, this approach adds profile effects and confinement improvement with respect to the ITER baseline, thus including recent experimental evidence such as the prediction of peaked density profiles in ITER. Under this set of assumptions, of course not unique, we estimate the ITER performance on the basis of a wide database of ASDEX Upgrade H-mode discharges, in terms of fusion power, fusion gain and triple product. According to the three scalings considered, there is a finite probability of reaching ignition, while more than half of the discharges require less auxiliary power than the one foreseen for ITER. For all the scaling laws, high values of the thermal beta(N) up to 2.4 are accessible. A sensitivity study gives an estimate of the accuracy of the extrapolation. The impact of different levels of tungsten concentration on the fusion performance is also studied in this paper. This scaling method is used to verify some common 0D figures of merit of ITER's fusion performance

Paraxial WKB solution of a scalar wave equation

An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)Available from TIB Hannover: RA 71(4/260) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman