Linear theory of electron-plasma waves at arbitrary collisionality

The dynamics of electron-plasma waves is described at arbitrary collisionality by considering the full Coulomb collision operator. The description is based on a Hermite–Laguerre decomposition of the velocity dependence of the electron distribution function. The damping rate, frequency and eigenmode spectrum of electron-plasma waves are found as functions of the collision frequency and wavelength. A comparison is made between the collisionless Landau damping limit, the Lenard–Bernstein and Dougherty collision operators and the electron–ion collision operator, finding large deviations in the damping rates and eigenmode spectra. A purely damped entropy mode, characteristic of a plasma where pitch-angle scattering effects are dominant with respect to collisionless effects, is shown to emerge numerically, and its dispersion relation is analytically derived. It is shown that such a mode is absent when simplified collision operators are used, and that like-particle collisions strongly influence the damping rate of the entropy mode.

Chauffage de plasma par ondes électromagnétiques à la troisième harmonique de la fréquence cyclotron des électrons dans le tokamak TCV

Gilles Arnoux

The Tokamak à Configuration Variable (TCV) programme is based on flexible plasma shaping capabilities together with a powerful electron cyclotron wave (ECW) additional heating for studies of stability, confinement, transport, control and power exhaust. In particular, ECW heating system allows an extended study of the β limit, defined as the ratio between the plasma kinetic pressure and the magnetic pressure, which is attributed to MHD (MagnetoHydroDynamic) instabilities. The ECW heating (ECH) is based on the resonant interaction between the electrons and an electromagnetic (EM) wave in a region of the plasma where the wave frequency is an harmonic of the electron cyclotron frequency. The TCV ECH system is composed of 6 gyrotrons (high power radio frequency sources), at the frequency of 82.7 GHz for second harmonic X-mode heating (X2) and 3 gyrotrons at the frequency of 118 GHz for third harmonic X-mode heating (X3), providing each a nominal power of 0.5 MW. In the moderate magnetic field of TCV (1.45 T), the X2 system is able to heat plasmas up to the X2 cutoff density (4.2 · 1019 m-3) above which the wave cannot propagate. The X3 system extends the accessible density range for ECH up to the X3 cutoff density (11.2 · 1019 m-3) and allows in particular the heating of plasmas in high confinement regime (H mode), most appropriate candidates to reach the β limit. The X2 wave is totally absorbed (plasma optically thick) being launched from the lateral side of TCV and crossing the vertical resonance layer. With this launching configuration, the X2 wave can also be used for non-inductive generation of the plasma current. Since the X3 absorption coefficient is weaker than the X2 absorption coefficient, the X3 wave is injected vertically in order to increase the beam path within the resonance layer, therefore maximizing the X3 optical depth. The present work, based on experiments and simulation, is the first detailed study of the X3 absorption properties in a top-launch configuration. The X3 absorption is shown to mainly depend on the wave injection conditions and the electron temperature. Full single-pass absorption is measured increasing nearly threefold the central electron temperature (1 keV –> 2.7 keV) when 1.35 MW of RF power is injected in low confinement regime plasmas (L-mode) with a central density of 4.0·1019 m-3. Experimental evidences show that a fraction of the power is absorbed on suprathermal electrons generated by the X3 wave itself. An absorption level of 85% is measured increasing threefold the central temperature by injecting 1.35 MW of X3 in H-mode plasmas with a central density of 8.2 · 1019 m-3. A new plasma dynamics is observed for the first time on TCV in these experiments. The X3 absorption is shown to depend strongly on the wave injection angle. In order to maximize the absorption during a plasma discharge by optimizing the injection angle, a real time feedback control has been developed and used. The system is based on the synchronous demodulation technique and uses a PI controller. In order to simulate the X3 wave propagation and absorption, the linear ray-tracing code TORAY-GA is used. These simulations predict an absorption dependence on the temperature and the injection conditions in agreement with the experimental results. Since TORAY-GA does not take into account the diffraction effects on the beam propagation, a comparison with the beam tracing code ECWGB which includes diffraction is discussed. The present results on X3 absorption properties demonstrate the efficiency of the X3 heating system on TCV, therefore extending the β limits study capabilities in elongated plasmas.

EPFL2005

Turbulence studies in TCV using the Correlation ECE diagnostic

Matteo Fontana

In this thesis work, the flexibility of the Tokamak à Configuration Variable (TCV) is exploited to study the influence of plasma parameters on turbulent fluctuations. The correlation electron cyclotron emission (CECE) diagnostic is used to measure low amplitude, large bandwidth radiative temperature fluctuations, associated with the anomalous transport terms that constitute the largest contribution to heat and particle loss in tokamak plasmas. In a series of L-mode limited plasmas, fluctuations are characterized over a large range of plasma parameters, obtained varying collisionality, Te/Ti and plasma triangularity. The influence of negative triangularity on confinement and fluctuations is also investigated. Temperature fluctuations profiles have been measured in low density, ohmic, positive and negative triangularity discharges, with matched current and density profiles. Strong suppression of fluctuations is observed in negative triangularity discharges from the plasma edge to the plasma mid radius. This is despite triangularity quickly decreasing when moving away from the edge. The existence of a region of low stiffness at the plasma edge is postulated to be responsible for this. Negative triangularity is confirmed having beneficial effects on confinement and reducing fluctuations amplitude in regimes with high Te/Ti. The neutral beam injector (NBI) has been used on positive and negative triangularity discharges in order to study the effect of negative triangularity on plasmas where Te/Ti~1. This condition is of particular interest since future reactor-like tokamaks are expected to work with thermalized electrons and ions. A pair of discharges with positive and negative triangularity has been realized, where matched temperature profiles are attained with ~385 kW and ~145 kW of NBI power respectively for the two shapes. This is evidence of negative triangularity improving plasma confinement also in conditions of low Te/Ti. In these discharges, CECE measurements find suppressed fluctuations in the negative triangularity discharges. Linear, flux tube, gyrokinetic simulations show that, in the same plasmas, the dominant turbulent regime is a mix of ion temperature gradient (ITG) instabilities and trapped electron modes (TEM). This is different with respect to all previous works in TCV, in which no ion heating had been available and only pure TEM regimes were observed. The results of the linear simulations indicate that, also in this mixed turbolence regime, negative triangularity has a stabilizing effect on instabilities, more visible for radial positions closer to the plasma edge, where the magnitude of triangularity is higher. A database of fluctuations measurements has been constructed from a series of discharges with positive and negative triangularity covering a large range of plasma conditions, particularly focusing on the effects of different combinations of collisionality and the Te/Ti ratio. Collisionality is found to be the main parameter to control the relative suppression of fluctutations in negative triangularity plasmas. No direct effect of Te/Ti on the fluctuation amplitudes is observed in the explored parameter range. Measurements taken in positive and negative triangularity plasmas, with comparable conditions and matched normalized temperature scale lengths still show reduced fluctuation levels for negative triangularity, suggesting influence on the threshold gradients for the onset of fluctuations.

EPFL2018

An efficient treatment of the full Coulomb collision operator with applications

Rogério Manuel Cabete De Jesus Jorge, Baptiste Jimmy Frei, Paolo Ricci

A formulation of full Coulomb (or Landau) collision operator is provided that allows for an efficient numerical implementation, both in unmagnetized and magnetized plasmas. The method is based on projecting the Boltzmann equations and the collision operator onto a Hermite-Laguerre velocity-space polynomial basis, obtaining a moment-hierarchy. This approach is implemented in a numerical simulation code and studies of systems of increasing complexity are being carried out, shedding light on the importance of retaining the full Coulomb collision operator, with respect to widely used simplified operators. First, the dynamics of electron-plasma waves is described at arbitrary collisionality for the first time by considering the full Coulomb collision operator. In particular, a purely damped entropy mode, characteristic of a plasma where pitch-angle scattering effects are dominant with respect to collisionless effects, is shown to emerge numerically, and its dispersion relation is analytically derived. This mode is absent when simplified collision operators are used, and like-particle collisions strongly influence its damping rate. Second, the linear properties of drift-waves are investigated, which allows for the comparison of the Coulomb collision operator to collision operators used in state-of-the-art turbulence simulation codes. Established collisional and collisionless limits are retrieved and an analysis on both the growth rate and eigenmode spectrum shows the need for retaining the Coulomb collision operator, specially at the intermediate levels of collisionality relevant for present and future magnetic confinement fusion devices.