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

Non-local heat transport, rotation reversals and up/down impurity density asymmetries in Alcator C-Mod ohmic L-mode plasmas

Several seemingly unrelated effects in Alcator C-Mod ohmic L-mode plasmas are shown to be closely connected: non-local heat transport, core toroidal rotation reversals, energy confinement saturation and up/down impurity density asymmetries. These phenomena all abruptly transform at a critical value of the collisionality. At low densities in the linear ohmic confinement regime, with collisionality ν[subscript *] ≤ 0.35 (evaluated inside of the q = 3/2 surface), heat transport exhibits non-local behaviour, core toroidal rotation is directed co-current, edge impurity density profiles are up/down symmetric and a turbulent feature in core density fluctuations with k[subscript θ] up to 15 cm[superscript −1] (k[subscript θ]ρ[subscript s] ~ 1) is present. At high density/collisionality with saturated ohmic confinement, electron thermal transport is diffusive, core rotation is in the counter-current direction, edge impurity density profiles are up/down asymmetric and the high k[subscript θ] turbulent feature is absent. The rotation reversal stagnation point (just inside of the q = 3/2 surface) coincides with the non-local electron temperature profile inversion radius. All of these observations suggest a possible unification in a model with trapped electron mode prevalence at low collisionality and ion temperature gradient mode domination at high collisionality.United States. Dept. of Energy (Contract DE-FC02-99ER54512)United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program

Hysteresis and fast timescales in transport relations of toroidal plasmas

This article assesses current understanding of hysteresis in transport relations, and its impact on the field. The rapid changes of fluxes compared to slow changes of plasma parameters are overviewed for both core and edge plasmas. The modulation ECH experiment is explained, in which the heating power cycles on-and-off periodically, revealing hysteresis and fast changes in the gradientflux relation. The key finding is that hystereses were observed simultaneously in both the the gradientflux and gradientfluctuation relations. Hysteresis with rapid timescale exists in the channels of energy, electron and impurity densities, and plausibly in momentum. Advanced methods of data analysis are explained. Transport hysteresis can be studied by observing the higher harmonics of temperature perturbation ??Tm in heating modulation experiments. The hysteresis introduces the term ??Tm, which depends on the harmonic number m in an algebraic manner (not exponential decay). Next, the causes of hysteresis and its fast timescale are discussed. The nonlocal-in-space coupling works here, but does not suffice. One mechanism for the heating heats turbulence is that the external source S in phase space for heating has its fluctuation in turbulent plasma. This coupling can induce the direct input of heating power into fluctuations. The height of the jump in transport hysteresis is smaller for heavier hydrogen isotopes, and could be one of the origins of isotope effects on confinement. Finally, the impacts of transport hysteresis on the control system are assessed. Control systems must be designed so as to protect the system from sudden plasma loss

ASTRA Automated System for TRansport Analysis in a Tokamak

A code, based on the MHD equations for the plasma current and the magnetic field, the Grad-Shafranov equilibrium equation, and the transport equations with the boundary conditions for densities, temperatures, and the poloidal flux, for the simulation of plasma transport is described. (HSI)Available from TIB Hannover: RA 71(5/98) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

ASTRA - an automatic system for transport analysis in a tokamak

SIGLEAvailable from TIB Hannover: RA 71(5/42) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

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