The performance of tokamaks is usually described in terms of plasma temperature, density and confinement time. The term temperature implies that the plasma is in thermal equilibrium and its particles have maxwellian (normal) velocity distribution. However, in several conditions, the plasma contains a significant number of suprathermal or 'fast' particles, whose energy is several times higher than thermal energy. The number of such particles can be significantly higher than that corresponding to the maxwellian distribution. Such electrons produced by different acceleration mechanisms in the TCV tokamak have been analyzed in the course of this thesis. This thesis consists of three parts. The first part describes the design, construction and implementation of a new 24-channel Electron Cyclotron Emission (ECE) radiometer, viewing the plasma from the Low Field Side (LFS) in the frequency range 65-100 GHz. The new LFS ECE radiometer, together with the existing 24-channel ECE radiometer viewing the plasma from the High Field Side (HFS) in the frequency range 78-114 GHz are the main diagnostics used in the analysis. The second part includes the development of a numerical code to simulate the ECE signals. The code is based on the WKB approach and solves the equation of radiation transport to calculate ECE signals using a numerically defined Electron Distribution Function (EDF). A method to reconstruct EDF from HFS and LFS ECE, based on the ECE code, is presented. The third part discusses the experimental data obtained on the TCV tokamak. In regimes with Electron Cyclotron Current Drive (ECCD), a quantitative explanation of the anomalously high absorption of the RF power at 118 GHz and a validation of the power balance analysis based on Thomson scattering measurements are provided. An analysis of the EDF during sawtooth instability shows that suprathermal electrons are generated in ohmic, Electron Cyclotron Heated (ECH) and ECCD plasmas. In ECH plasmas, typical energies and densities are found to be E = 15–30 keV and nst = 2·1017 m–3. This corresponds to 30-40 % of the energy lost during the crash, which proves that acceleration of electrons is an important mechanism for the dissipation of energy released during magnetic reconnection in a tokamak plasma. The observed fast electron dynamics suggests a high radial diffusion in the plasma during and just after the sawtooth crash (Dst = 25 m2/s), which dominates over the classical slowing down process.

Reconstruction of the electron distribution function during ECRH/ECCD and magnetic reconnection events in a tokamak plasma

Fokker‐Planck modeling of the absorption of third harmonic electron cyclotron waves is presented. In the TCV tokamak an advanced electron cyclotron heating system is used to both heat the plasma (ECRH) and drive current (ECCD). Two frequencies are available for heating, 3 MW at 82.7 GHz in X‐mode matching the second harmonic of the cyclotron frequency(X2), and 1.5 MW at 117.7GHz which couples to the third harmonic (X3). The X3 waves have a smaller absorption coefficient as the optical thickness of the plasma strongly decreases with the harmonic number. In order to maximize the damping, waves are launched vertically from the top of the vacuum vessel, following the cold X3 resonance. This method alone has been measured to lead to 66% absorption. The Fokker‐Planck (F‐P) modeling is in agreement with the linear ray tracing code TORAY‐GA and both satisfactory reproduce the experimental results. A second method is based on nonlinear enhancement of the absorption coefficient. A suprathermal electron population with a temperature of about 5 times the bulk temperature is created with the X2 waves. The X3 waves are efficiently damped by this electron population, leading to the measured full absorption of the X3 waves. In this scenario, nonlinear modeling is required, and the F‐P calculations are in qualitative agreement with the experiments. However, the simulations suffer from numerical difficulties, and require a large number of mesh points in 3 dimensions (velocity, pitch angle, and radial coordinates). Work is in progress for a better quantitative comparison with the experiment.

Fokker‐Planck simulations of X3 EC wave absorption experiments in the TCV tokamak

Introduction In order to properly describe the physics of electron cyclotron resonance heating (ECRH) and current drive (ECCD), it is essential to include relativistic effects, especially when the wave propagation is nearly perpendicular to the magnetic field. Trubnikov [1] solved the fully relativistic, linearized, Fourier-transformed Vlasov-Maxwell system of equations which allowed him to express the dielectric tensor elements in two forms, the second of which has been the basis of a widely used approximation [2; 3]. This formulation (referred to in this paper as weakly relativistic) relies on an expansion in several small parameters, two of which are the electron temperature normalized to the electron rest mass (i.e. large μ = mec/Te), and the electron Larmor radius normalized to the wavelength (i.e. small λ = (n⊥ω/Ωce)/μ). Thus for a given n⊥, the approximation becomes worse for larger frequencies (higher harmonics) and higher temperature. Recent papers by Swanson [4] and Melrose [5] have cast doubt on the accuracy of the weakly relativistic dielectric tensor. There was a fairly simple fully relativistic formulation derived in 1985 by Weiss [6] which seems to have been overlooked since then in the literature. His solution of the Vlasov-Maxwell equations resulted in a double integral but with no infinite sums over harmonics (all orders λ are also automatically included). Recently, Swanson [4], starting from Trubnikov’s first form and using the Newberger sum rule to eliminate the infinite sums arrived at a form exactly equivalent to Weiss’. In Ref. [4], Swanson also introduces an expression for the dielectric tensor elements that he calls “moderately relativistic”. However, these are in fact identical to the weakly relativistic expressions mentioned above [2; 3]. The results in this paper are based on a code developed using Weiss’ dielectric tensor elements (correcting the sign error in the off-axis tensor elements σ+‖ and σ−‖), and his suggested numerical integration method (Gauss-Legendre and Gauss-Laguerre quadrature). The dispersion relation is solved for complex n⊥ given real n‖ and ω, using Muller’s algorithm for finding complex roots of an analytic function. X3 absorption on X2 pre-heated plasmas The TCV tokamak at the CRPP has two sets of gyrotrons for auxilliary heating. One set at 82.7 GHz, which for a typical toroidal field of 1.45 T heats electrons at the 2nd harmonic X-mode (X2) near the center of the plasma. The other set is at a frequency of 118 GHz, which for the same field heats electrons at the 3rd harmonic (X3) near the center. A series of experiments was carried out on TCV for studying X3 absorption in the presence of X2

http://epsppd.epfl.ch/StPetersburg/PDFS/P3_210.PDF

A Comparison of Weakly and Fully Relativistic Electron Cyclotron Wave Damping in the Presence of High Energy Electrons

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A Comparison of Weakly and Fully Relativistic Electron Cyclotron Wave Damping in the Presence of High Energy Electrons