Nonlocal analyses of electrostatic and electromagnetic waves in hot, magnetized, nonuniform, bounded plasmas

Heating of tokamak plasmas up to temperatures of the order of 10 keV (≈ 108 0K) is one of the main subjects in plasma physics research. Much experimental and theoretical effort has been devoted to the improvement of the heating efficiency and to the understanding of the beam-particle or wave-particle interactions. We have studied the latter subject. Many models describing the linear wave-particle interaction already exist, allowing one to analyze the absorption of the wave by the electrons and/or the ions. They can be separated into two main classes: ray-tracing models [Brambilla, 1986] and global wave models [Willard et al., 1986]. The latter describe the "global" wave field (sum of incident, transmitted and reflected fields) taking into account the finiteness of the plasma, the boundary conditions, the plasma-vacuum interfaces and the antenna. With this global wave approach, one is able to study scenarii where cut-off, reflected, resonant, mode converted and/or evanescent wave fields are present. Note also that this work is principally devoted to the ion cyclotron range of frequencies. The most advanced global wave models are the "local" models which use a second-order expansion in k⊥ρσ, where k⊥ is the perpendicular wavenumber and ρσ the Larmor radius of species σ [Appert et al., 1986a and 1987; Jaeger et al., 1988; Fukuyama et al., 1986; Edery and Picq, 1986; Brambilla and Krücken, 1988b]. In this way, one obtains a system of three second-order differential equations [Martin and Vaclavik, 1987]. However, the local models are limited to Larmor radii small compared with the wavelength or with the characteristic length of the inhomogeneous density and temperature profiles. Moreover, they are limited to frequencies lower than the third harmonic of the cyclotron frequency. In present day experiments, the temperature of the particles is very high, especially if tails of high energy particles are created. Also, the first experiments with D-T plasmas, generating alpha particles having a temperature of the order of 1 MeV, have been performed in JET. Moreover, increasing numbers of experiments use heating scenarii at high harmonic frequencies. Because these cases can no longer be studied using a local model, we have developed a "nonlocal" model which is not limited by the size of the Larmor radii nor by the harmonic considered. This model is based on the global wave approach and therefore can treat the variety of problems mentioned above. Nevertheless, we have limited our work to uni-dimensional geometry, Maxwellian equilibrium distribution functions and slowly-varying equilibrium magnetic field. We have also neglected ky in the conductivity tensor, where y is the direction normal to the direction of the inhomogeneity and to the magnetostatic field. Starting from the linearized Vlasov-Maxwell equations, we have derived the equations in the Fourier and the configuration spaces (Chaps.3 and 4), which consist, in the latter case, of a system of three second-order integro-differential equations. We have also derived a formulation of the local power absorption allowing us to determine the profile of absorption of the wave by the particles. The equations are solved numerically using the finite element method (Chap.5). We have developed two codes, SEAL and SEMAL, which calculate the wave field in the electrostatic and electromagnetic cases, respectively. These codes have been tested, and SEAL has been used to simulate an experiment which studies the interaction of a Bernstein wave with a cylindrical plasma (Chap.6). SEMAL has mainly been used to study the effects of the alpha particles on ion cyclotron heating. We have shown that the local model was inadequate and have studied in more detail the effect of temperature and the strong influence of the alpha particle concentration (Chap.7). We have also studied the excitation of an ion Bernstein wave through mode conversion at the lower-hybrid frequency in the scrape-off layer (Chap.7).

Étude du transport d'énergie thermique dans les plasmas du tokamak à configuration variable au moyen de chauffage électronique cyclotronique

Yann Camenen

The development of controlled thermonuclear fusion, a quasi-unlimited energy source suitable for large scale electricity production, is one of the main goals of plasma physics research. Among the directions explored to date, the use of toroidal devices called tokamaks to create and confine hot plasmas using strong magnetic fields is particularly promising. The energy used to heat the plasma must remain well confined in order to achieve plasma temperatures higher than one hundred millon degrees for a sufficiently long period to obtain numerous fusion reactions. In the frame of efficient electricity production, maximising the energy confinement is also essential to achieve the required temperature with the lowest heating power. In tokamak plasmas, energy losses are mainly due to radiation and radial energy transport from the plasma core to the edge. A significant fraction of plasma physics research is therefore dedicated to the study of radial transport in tokamaks and the exploration of new operation regimes characterised by a low transport level. The development and optimisation of diagnostics used to observe plasmas is also part of this work. This thesis work, performed on the Tokamak à Configuration Variable (TCV) in Lausanne, covers the implementation and exploitation of a multi-channel soft X-ray detector with high spatial and temporal resolution, together with the development of the tomographic inversion routines used for data analysis. The detector, comprised of two superposed wire chambers, has been tested and calibrated using an X-ray source and then installed onto the tokamak. The position of the detector was chosen such as to observe the whole plasma cross-section with maximum spatial resolution leading to high quality tomographic inversions. A mobile absorber holder was installed between the plasma and the wire chambers. The energy range of the soft X-ray emission observed by the detector was thus chosen by selecting the appropriate absorber. These various features have made possible the use of the detector for numerous studies and in particular for the spatial and temporal characterisation of the plasma internal transport barrier formation. Plasma shaping abilities covering a wide range of plasma elongations and triangularities, including negative values, are one of the strengths of the TCV tokamak. For instance, plasmas with elongated cross-sections offer higher energy confinement as well as higher plasma current and pressure limits. However, the increase of the plasma vertical instability growth rate with elongation makes the vertical control of elongated plasmas difficult, in particular if the plasma current profile is too peaked. As the current profile is usually peaked for low plasma currents, current profile broadening is required there to achieve high elongation. During this thesis, a current profile broadening method based on temperature profile modification by localised EC heating has been studied in detail. The mechanism of this method has been documented and the optimal conditions for the EC power deposition determined. Using these conditions, the TCV operational space has been extended towards higher elongation at low current. The highest elongation obtained at low current has been increased by over 25% permitting the exploration of the plasma transport properties in this regime. The flexibility of the TCV EC heating system has also been used to investigate radial electron heat transport in L-mode plasmas. For the first time, the normalised temperature gradient has been varied by a factor of four and its influence on electron heat transport has been separated from that of the electron temperature. Electron heat transport increases strongly with the normalised temperature gradient, for values between 6 and 10, and then becomes independent of this parameter. In addition, electron heat transport increases with increasing electron temperature, decreasing density and increasing effective charge. The electron heat transport dependence on these three parameters can be cast as a single dependence on the plasma collisionality. TCV shaping abilities have then been used to test the influence of plasma triangularity. The main variations of the level of electron heat transport are described by a decrease of the electron heat diffusivity towards negative triangularity and high collisionality. At constant collisionality, electron heat transport is two times lower at a negative triangularity of –0.4 than at a positive triangularity of +0.4. Concerning micro-instabilities, gyro-fluid and gyro-kinetic simulations indicate that TEM and ITG instabilities are at play in these plasmas. The good qualitative agreement between the observed experimental dependencies and the predictions of simulations suggests strongly that the TEM instabilities are involved in the transport of electron heat. The experimental study provides dependable scaling of the electron heat transport on plasma parameters that can now be used to test the prediction of transport simulations. New elements such as the saturation of electron heat transport at high values of the normalised temperature gradient and the decrease of electron heat transport towards negative triangularities have been demonstrated.

EPFL2006

Overview of alfven eigenmode experiments in jet

Ambrogio Fasoli, Pierre Lavanchy, Jonathan Bryan Lister, Jean-Marc Moret, Laurie Porte, Laurent Villard

Results from the first experiments to drive Alfven Eigenmodes (AEs) with antennas external to a tokamak plasma are presented. In ohmically heated plasma discharges, direct experimental measurements of the damping of toroidicity induced AEs (TAEs) have allowed an identification of different regimes corresponding to different dominant TAE absorption mechanisms with a wide range of damping rates, 10(-3) less than or equal to gamma/omega less than or equal to 10(-1). In plasmas heated by ion cyclotron resonance heating, neutral beam injection heating, lower hybrid heating and high plasma current ohmic heating, a new class of weakly damped Alfven eigenmodes, the kinetic Alfven eigenmodes, predicted in theoretical models that include finite Larmor radius and finite parallel electric field effects, has been identified experimentally.

1995

Overview of results and possibilities for fast particle research on JET

Olivier Sauter, Duccio Testa

The large physical size of the JET tokamak, its heating systems and diagnostics, and its capability to operate with full deuterium-tritium (D-T) plasmas, including high-power tritium neutral beam injection (NBI), give it unique possibilities in fast particle research in fusion plasmas. These have already been used to generate significant (2-3 MW level) power in fusion a-particles in the 1997 D-T campaign. Recent JET experiments have concentrated on two important scenarios of relevance to next-step tokamak devices: the ELMy H-mode plasmas and plasmas with strong internal transport barriers (ITBs). The achieved progress will help in preparation for a possible second D-T experiment on JET. Fast particle studies have also been carried out recently using ion cyclotron resonance heating (ICRH)-accelerated particles and external-excitation methods to study Alfven eigenmodes (AEs). Looking towards the future, the capability of JET will be enhanced by upgrades to the NBI system, ICRH system and various diagnostics. Results of the first JET D-T experiment (DTE1) form a basis on which to elaborate a second D-T experiment (DTE2) which could be proposed after these enhancements. The alpha-physics part of this programme would be divided between the investigation of alpha-particle confinement, heating and loss processes in the 'integrated scenarios' (where the discharge is as close as possible to an ITER-relevant scenario), and dedicated 'alpha-physics' experiments, with specially prepared plasmas. In ELMy H-mode plasmas the fusion performance could roach Q(=P-fusion/P-input) of similar to0.33 at the highest combined heating powers, corresponding to similar to 6x10(-4), allowing a test of the margins of TAE stability in quasi-steady-state conditions. The integrated-scenario fast particle programme could concentrate on the instabilities and heating in plasma regimes with strong steady-state ITBs, with expected Q values similar to0.58 and similar to2x10(-3), demonstrating the compatibility of these operating scenarios with alpha-effects. Excitation of TAEs by alpha-particles in the plasma core could also be studied in such integrated scenarios. An issue which will receive attention is the confinement of MeV energy ions in the centre of ITB plasmas with strongly reversed shear, where the low current density in the centre may lead to the alpha-particles entering loss orbits. In preparation for a D-T campaign, studies of triton burn-up in deuterium ITB plasmas will begin in the 2002 experimental campaigns. Special 'afterglow' experiments to measure TAEs after the termination of the (stabilizing) NBI have already been explored in JET deuterium ITB scenarios and would be planned for DTE2. It is intended to develop special versions of ITB plasmas with dominant ion heating which would maximize the sensitivity to degradation of alpha-heating effects.