Modelling of electron transport and of sawtooth activity in tokamaks
Transport phenomena in tokamak plasmas strongly limit the particle and energy confinement and represent a crucial obstacle to controlled thermonuclear fusion. Within the vast framework of transport studies, three topics have been tackled in the present thesis: first, the computation of neoclassical transport coefficients for general axisymmetric equilibria and arbitrary collisionality regime; second, the analysis of the electron temperature behaviour and transport modelling of plasma discharges in the Tokamak à Configuration Variable (TCV) ; third, the modelling and simulation of the sawtooth activity with different plasma heating conditions. The work dedicated to neoclassical theory has been undertaken in order to first analytically identify a set of equations suited for implementation in existing Fokker-Planck codes. Modifications of these codes enabled us to compute the neoclassical transport coefficients considering different realistic magnetic equilibrium configurations and covering a large range of variation of three key parameters: aspect ratio, collisionality, and effective charge number. A comparison of the numerical results with an analytical limit has permitted the identification of two expressions for the trapped particle fraction, capable of encapsulating the geometrical effects and thus enabling each transport coefficient to be fitted with a single analytical function. This has allowed us to provide simple analytical formulae for al1 the neoclassical transport coefficients valid for arbitrary aspect ratio and collisionality in general realistic geometry. This work is particularly useful for a correct evaluation of the neoclassical contribution in tokamak scenarios with large bootstrap current fraction, or improved confinement regimes with low anomalous transport and for the determination of the plasma current density profile, since the plasma conductivity is usually assumed neoclassical. These results have been included in the plasma transport code PRETOR. This code has been further extended and applied to the simulation of electron transport in TCV. In simulating the electron temperature profile of Ohmic sawtoothing plasmas, the proper description of the current density profile and the sawtooth activity play the dominant role and not the specific transport model, provided that a single parameter in the model is adjusted to match the global plasma performance. In TCV discharges with electron cyclotron heating (ECH), the behaviour of the electron temperature exhibits some characteristics which have been recently observed to be common to several tokamaks. In particular, with central heating the electron temperature profile is stiff outside the power deposition region, that is the gradient scale length is independent of the heating power and essentially constant along the minor radius. With off-axis heating, transport is strongly reduced in the central region of the plasma, whereas a steep increase of the heat conductivity is observed at the power deposition location. Although the semi-empirical Rebut-Lallia-Watkins (RLW) transport model does not involve a critical gradient scale length, as the experimental observations would suggest, rather a critical electron temperature gradient, we have shown that it allows simulations which reproduce the described experimental features with very good agreement. Due to the relatively low toroidal magnetic field of TCV, the experimental temperature gradient with ECH exceeds by far the threshold included in the model. It can thus be stated that the parametric dependence of the electron heat conductivity of this transport model is adequate to reproduce the electron transport for plasma parameters in the operation domain of TCV. PRETOR, interfaced with the experimental data and the code TORAY-GA for the computation of the ECH source, has hence been used as a reliable tool for transport analysis and planning of new experiments. This has contributed to the identification of an improved central electron confinement (ICEC) regime in TCV, characterized by a precise heating scheme (strong electron cyclotron current drive in the counter-direction in the plasma center, and localized off-axis heating), with a specific time sequence. Transport simulations and investigations of this regime, in particular dedicated to the reconstruction of the current density profile during the high performance phase, have motivated further experiments which have confirmed numerical predictions. As a consequence, the magnetic shear reversa1 has been identified as the crucial ingredient for ICEC. The powerful ECH system in TCV does not allow only strong global current profile modifications but also local tailoring which has significant effects on sawtooth activity. A model introduced for the prediction of the sawtooth period in the proposed International Thermonuclear Experimental Reactor (ITER) has been extended to be applicable to Ohmic and ECH discharges in TCV. The model has been found in agreement with the experimental observations and thereby we were able to identify the physical mechanisms which make ECH capable of controlling the sawtooth period. The parameter dependence of the relevant stability threshold has been found consistent with dedicated experiments demonstrating the effects of localized heating and current drive on the sawtooth period. The simulations have pointed out the effects of the magnetic shear and of the pressure gradient at the q = 1 surface. Moreover, the most efficient heating location to stabilize the sawtooth period has been identified as located outside the q = 1 surface before the sawtooth crash. The same period model has been used for the simulation of the sawtooth period in recent discharges with neutral beam injection (NBI) in the Joint European Torus (JET), performed to assess the role of beam ions on sawtooth stabilization. With the inclusion of an analytical expression for the fast ion contribution to the internal kink potential energy, validated by the hybrid kinetic/MHD code NOVA-K, the simulations have been found in remarkable good agreement with the experimental observations. This work has demontrated the role of beam ions in sawtooth stabilization and validated the stability threshold for the resistive internal kink which was predicted to be the sawtooth crash trigger relevant for ITER operation.
Faculté des sciences de base
Centre de recherches en physique des plasmas
Jury: Jean Buttet, Rakesh Chawla, Tuong Hoang, Jean-Marc Moret, Arthur Peeters, Minh Quang Tran, Laurent Villard
Public defense: 2001-12-14
Record created on 2005-03-16, modified on 2016-08-08