Plasma oscillation | EPFL Graph Search

Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon. Langmuir waves were discovered by American physicists Irving Langmuir and Lewi Tonks in the 1920s. They are parallel in form to Jeans instability waves, which are caused by gravitational instabilities in a static medium. Mechanism Consider an electrically neutral plasma in equilibrium, consisting of a gas of positively charged ions and negatively charged electrons. If one displaces by a tiny amount an electron or a group of electrons with respect to the ions, the Coulomb force pulls the electrons back, acting as a restori

Apertureless SNOM

Rubén Esteban Llorente

This thesis studies apertureless Scanning Near Field Optical Microscopy, a technique that uses the apex of a very sharp tip to obtain local optical information with lateral resolution much beyond the diffraction limit. Both theoretical and experimental results are discussed. The theoretical work is a significant advance towards the quantitative convergence of experiments and theoretical predictions, and should be useful in aiding the interpretation of measured images. Extended tips and substrates are used, and the detector is also carefully modeled. A static tip in vacuum serves to study the influence of the tip and illumination geometry on the far fields and on the near fields in the proximity of the tip apex, the volume used to probe the sample. Including a gold substrate and the commonly used demodulation scheme allows to study the discrimination of the components carrying the local information. A very good discrimination is verified for silicon tips and small oscillation amplitudes, as far as the tip interacts closely with the substrate and the oscillation remains highly sinusoidal. The imaging process is studied by including patterned substrates. The obtained signal is mostly sensitive to a few nanometers of depth into the sample, and the influence of the scanning conditions on the level of signal, background suppression and lateral resolution is characterized. Further, a closer look into the behavior of the extended physical detector reveals the influence of the spatial inhomogeneities of the scattered fields and, for interferometric measurements, the large significance of the optical phase. Experimentally, different techniques are first described that can facilitate images with clear local information. A cross polarization scheme is introduced which is very useful for non-perturbative measurements. It is applied to the mapping of the the field distribution surrounding plasmonic structures, for both the phase and the amplitude. Beyond dipolar resonances, I also study coupled dipoles and quadrupole field distributions. When imaging artifacts are avoided, the obtained images closely resemble theoretical expectations.

EPFL2007

Analysis of plasma dynamic response to modulated electron cyclotron heating in TCV tokamak

Ilya Pavlov

The need of durable, economically acceptable and safe energy sources continues to stimulate studies in a field of thermonuclear fusion. The most successful solution for controlled magnetic fusion is the tokamak. The improvement of tokamak performance depends on the optimization of pressure and current density spatial distributions which can be modified by means of an auxiliary heating and a current drive. Electron cyclotron heating, in particular is a very important tool for the study and control of basic physical processes governing plasma confinement and stability, particularly because it allows the injection of highly localized intense power. ECH power deposition location plays a crucial role in sawtooth control and suppression, it is also important for tearing mode stabilization, and for implementation of closed loop systems for automatic control/suppression of magnetohydrodynamic activity. A part of the ECH power can be modulated (MECH), and used to identify where the ECH power has been deposited, and can also be useful in the experimental analysis of the electron transport in general. Nevertheless, despite the goal of MECH being a diagnostic and analysis tool, MECH can couple to plasma oscillations, such as sawteeth. MECH-sawtooth phase coupling adds significant complications in ECH deposition location and transport analysis, in some cases making the interpretations of results misleading. This is why it is important to get an insight into the phenomenon of MECH-sawtooth interaction, and to establish the boundaries where conventional types of modulation analysis can be successfully implemented. This thesis presents the analysis and interpretation of perturbative MECH experiments performed in the TCV tokamak with particular attention paid to the non-linear phase coupling of heat waves. TCV is equipped with a very flexible and high power ECH system. Two independent ECH systems permit MECH to be deposited at two different spatial locations, with two different types of modulating signals. This set-up was used to study simultaneous propagation of heat waves induced by MECH in non-sawtoothing plasmas, and in discharges with sawtooth activity. A new analysis method for the characterization of the plasma non-linear dynamic response to modulated heating was developed on the basis of Higher Order Spectral Analysis (HOSA) technique. This method applied to signals from different diagnostics, such as electron cyclotron emission and soft X-ray measurements, was extensively used to quantitatively characterize the effect of nonlinear phase coupling. In sawtooth free discharges a detailed analysis of the propagation of heat waves demonstrated that their phase coupling is solely related to properties of heat sources. It was demonstrated that if two heat waves are induced by non-coupled power sources (multi-beam MECH) then no phase coupling occurs. In the opposite case, when a source of perturbation (MECH) contains coupled harmonics, the corresponding heat waves demonstrate phase coupling. It was shown that these coupled heat waves loose their phase coherence while propagating in plasma. The dissipation of phase coupling is due to different phase velocities of heat waves and their diffusive damping. The new type of ECH power modulation accompanied with bicoherence analysis was proposed as a candidate for a reliable identification of EC power deposition location in a case of high frequency and low modulation depth MECH, including multi-beam heating. This type of MECH can be particularly important for real time control applications. In cases when MECH is applied to sawtoothing plasmas a direct experimental evidence of MECH-sawtooth non-linear phase coupling has been demonstrated using HOSA techniques, in particular bispectrum and bicoherence profiles. The detailed analysis presented here demonstrates a direct proof of periodic modification of sawtooth behavior by modulated ECH. It was shown that a simple diffusive model for the perturbed electron temperature with MECH source term can not be used for transport analysis in the presence of MECH-sawtooth coupling. Self-consistent time dependant transport simulations including a sawtooth relaxation model is capable of properly reproducing the effect of MECH-sawtooth phase coupling and can be used for transport analysis. On the basis of these simulations, an hypothesis for MECH-sawtooth coupling based on periodic modifications of magnetic shear was proposed. Additional information provided by HOS analysis enabled a correct interpretation of the plasma dynamic response to modulated heating in the presence of MECH-sawtooth coupling.

EPFL2008

The impact of the Boussinesq approximation on plasma turbulence in the scrape-off layer

Baptiste Jimmy Frei, Federico David Halpern, Félix Benedito Clément Musil, Paola Paruta, Paolo Ricci, Fabio Riva, Morgan Siffert, Christoph Wersal

Plasma turbulence in the tokamak scrape-off layer (SOL) region, where magnetic field lines are open and intersect the reactor inner walls, determines the heat loads on the limiter or divertor targets. This is one of the most crucial issues on the way towards a fusion reactor. Since SOL plasma is colder compared to the tokamak core, it is reasonable to use a fluid approximation to describe its dynamics. In particular the drift-reduced Braginskii equations are chosen to study the SOL plasma turbulence. To further simplify the drift-reduced Braginskii equations, the Boussinesq approximation is also applied in a number of numerical codes. This approximation consists in considering the plasma density constant in the evaluation of the divergence of the polarisation current, which simplifies substantially the solution of the Poisson equation necessary to evaluate the electric potential. In this study a new formulation of the drift-reduced Braginskii equations is presented together with a new numerical implementation that allow us to relax the Boussinesq approximation in the plasma turbulent code GBS. We show the energy conservation properties of the new system of equations. Also we compare the results of three-dimensional turbulent simulations with and without the Boussinesq approximation.