Plasma breakdown and current formation in single core and doublet configurations on TCV

This thesis presents an experimental investigation of the plasma formation in the TCV tokamak. The primary goal of this work was to program a reliable and smooth plasma formation at several positions within the TCV vessel and then use the gained understanding to revisit the creation of doublet plasma formation. The first part of this thesis is dedicated to understanding and improving the single-axis plasma formation scenario in TCV. A database for the single-axis TCV plasma formation scenario was created for discharges spanning several years of operation to understand the physics of the plasma formation dynamics. The database shows that most of the failed plasma formation in TCV were during the burn-through and ramp-up phase with only 0.5% of the discharges failing at breakdown. The failed plasma breakdowns are mainly attributed to technical issues, such as no injection of neutral gas into the vacuum vessel, absence of the toroidal field or the Ohmic coil current, and issues with the plasma control system. The improvement of the single-axis plasma formation was separated into two parts: improvement of the breakdown scenario and improvement of the plasma burn-through and ramp-up scenario. During the breakdown phase, a large mismatch was exposed between the intended and experimentally obtained vertical breakdown position, for both Z=0.05m and Z=+0.23m standard vertical breakdown positions and for both I_P and B_phi directions. This mismatch was caused by an additional poloidal field mainly due to errors in the back-off of the stray field generated by vessel currents. The use of a vessel resistivity assuming axisymmetry in the TCV discharge preparation procedure to model the vessel currents was identified as the main reason for the mismatch in the breakdown positions. The analysis of the plasma formation database revealed that most of the failed plasma formation during the burn-through and ramp-up phase occurred due to insufficient, albeit often temporary, Ohmic heating to sustain the plasma. The insufficient Ohmic heating was either due an insufficient initial I_P ramp rate, or a combined effect of strong I_P and/or radial position oscillations caused by the feedback control system due to too high initial I_P ramp rate. A bump-less transfer control technique was implemented to improve the reliability of plasma formation by avoiding the strong oscillations in I_P and radial position that resulted in reliable and sufficient Ohmic heating. The second part of this thesis focuses on developing a doublet shaped plasma configuration, which is a highly unconventional plasma configuration, and TCV's modern and unique shaping capabilities warrant an effort to revisit the configuration. Successful simultaneous breakdown at two locations in TCV was achieved by using the improved inductive breakdown scenario. The similar magnetic properties of the two magnetic null points ensured that the plasma current ramp rate in the two droplets were close and the plasma current in both droplets was ramped up to 50 kA each with Ohmic heating alone. A highly reproducible doublet formation scenario was finally achieved and was verified by several diagnostics. A highly reproducible doublet formation scenario was finally achieved and was verified by several diagnostics. A highest plasma current of 130 kA was achieved in each droplet, with a core electron temperature at 1.3keV, core electron density at 1.3e19m^-3, and 30ms duration with ECRH heating.

A Far-Infrared Polarimeter Diagnostic for the Measurement of the Poloidal Magnetic Field in the TCV Tokamak

Information about the poloidal field inside the plasma and about the current density profile is essential for the understanding of the behavior of tokamak plasmas. The poloidal field outside the plasma edge is easily measured by a set of magnetic coils, whereas measurements of the magnetic field distribution inside the plasma requires dedicated and often complex diagnostic systems. One of the methods is polarimetry using beams of electromagnetic waves traversing the plasma. It makes use of the fact that the magnetic field modifies the refractive index of the plasma and as a consequence affects the state of polarization of the passing waves. Specifically, Faraday rotation refers to the case of a linearly polarized wave propagating parallel to a magnetic field. In this case, the rotation of the polarization vector is proportional to the product of electron density and parallel magnetic field component. This thesis is devoted to the design of a specific polarimeter system and its implementation on the TCV tokamak. The conceptual design took into account the particular requirements of the TCV experiments and its experimental program with particular interest in measurements of current density profiles in low-density, EC-heated plasmas. Aiming at optimum performance of the polarimeter in this parameter range, the FIR laser wavelength of 432.5 µm was chosen. Since TCV is already equipped with an interferometer (at 214 µm) for measurements of the line-integrated density along 14 chords, the polarimeter was built as a separate instrument. The number of 10 spatial channels to cover the plasma diameter was found as a compromise between desired spatial resolution, access constraints and cost. The measurement of the Faraday rotation angle is based on a method suggested by Dodel and Kunz [1], which uses optical beams with rotating linear polarization. In this case, the Faraday rotation angle is retrieved from a phase measurement comparing the modulated signals from the probe detectors with that from a reference detector and to first order is insensitive to amplitude variations of the signals. Waveguide detectors based on Schottky barrier diodes are used as detectors for their sensitivity and large electrical bandwidth. Signal processing and analysis is performed in two branches : a) using specifically built analog electronic phase detectors followed by slow (250 kHz) ADCs b) using fast (5 MHz) ADCs and numeric signal processing on a mainframe computer. The thesis covers the description of the design and the various components of the polarimeter, presents initial tests and an evaluation of its performance based on simulations using real plasma configurations of TCV. The analysis of specific tests with the system installed on TCV revealed the presence of perturbations leading to parasitic contributions to the measured phase angles. The results of first measurements of the Faraday rotation angle for different plasma conditions on TCV are presented. Comparing the measured Faraday rotation angles with the results of calculations showed qualitative agreement, in particular the effects of an increase in electron density and of the reversal of the current direction were clearly seen. The system is also capable to detect a radial displacement of the magnetic axis of the plasma, as was demonstrated by comparing measurements from two specific plasma configurations. However, the absolute values still show significant deviations from the expected ones based on calculations. The discrepancies increase with increasing Faraday angle and depend on the direction of the plasma current. At high electron densities beam refraction becomes a problem and may lead to significant errors in the measurements and eventually to complete loss of the signal in several channels. In its present status, the polarimeter cannot yet provide results that are suitable to reconstruct the poloidal field or the current density profile of the plasma. Tentative explanations for this problem are given, but further specific tests are necessary to confirm them. Even in its present state, the polarimeter may be used to detect transient relative changes in the profiles of electron density and current. This was demonstrated by a series of experiments in plasmas with sawtooth activity. Comparing the signals from the polarimeter with those from other multi-chord diagnostics (interferometer and soft X-ray detectors) clearly revealed correlations but also specific differences. These experimental studies showed that the Far-Infrared Polarimetry still requires further improvements, but has potential to become a valuable diagnostic capable of directly measuring the current density profile in the TCV tokamak.

EPFL2011

Exploration of candidate fusion reactor regimes by real time control of tokamak plasma shape

Himank Anand

The potential of nuclear fusion to provide a practically inexhaustible source of energy has motivated scientists to work towards developing nuclear fusion tokamak power plants. Stable operation of a tokamak at high performance requires simultaneous treatment of several plasma control problems. Moreover, the complex physics which governs the tokamak plasma evolution must be studied and understood to make correct choices in controller design. This mutual inter-dependence has informed this thesis, using control solutions as an experimental tool for physics studies, and using physics knowledge for developing new advanced control solutions. The TCV tokamak at SPC-EPFL is ideally placed to explore issues at the interface between plasma physics and plasma control, by combining a state-of-the-art digital real time control system with a flexible and diverse set of actuators including a full set of independently powered shaping coils. The recent deployment of the real time version of the Grad-Shafranov equilibrium reconstruction code LIUQE, with a sub-ms cycle time in the digital control system, has facilitated the design of a new generalised plasma position and shape controller, based on the information on poloidal flux and magnetic field provided by the real-time Grad-Shafranov solver. The first issue addressed in the thesis is the development and experimental testing of a new real time control strategy to construct a generalised control algorithm for not only controlling the position of the plasma but also to aid in the precise control of higher order shape moments, X-points and strike points, particularly in advanced plasma configurations such as negative-triangularity plasmas, snowflake and super-X divertors, and doublets. A controller formulation ensuring flexibility through an ordering of controlled variables from the most easily to the least easily controlled, while respecting the hardware limits on the poloidal field coil currents, is developed. The successful experimental implementation of the control algorithm has been demonstrated for both fixed and time varying plasma position and shape for limiter and divertor plasma discharges. In addition, the controller has provided satisfactory performance with respect to plasma scenarios involving complex changes in the plasma shape and position. The second issue addressed in the thesis is the application of the generalised plasma position and shape controller to a snowflake plasma configuration. A comparison between the optimised generalised plasma position and shape controller with the performance of the TCV hybrid controller for a given reference snowflake plasma discharge showed a marked improvement in various geometrical properties of the snowflake plasma configuration in the vicinity of the null point. However, strong control of the poloidal magnetic field at the two X-points resulted in a tradeoff on the upper part of the plasma boundary, where the overall precision was comparable to that of the legacy controller. In the experimental time available, the snowflake shots developed exhibited a boundary that was too close to the inner wall of the vessel, modifying the edge plasma behaviour (studied with infrared cameras and Langmuir probes) and making it difficult to study the physics properties of the exact snowflake. However, further optimisation should well be possible.

EPFL2017

Stability of Tokamak and RFP Plasmas with an Extended Region of Low Magnetic Shear

Daniele Brunetti

It has been observed experimentally that magnetically confined plasmas, characterised by the safety factor q with a small or slightly inverted magnetic shear, have good confinement properties. Such plasmas typically have no internal transport barrier, operate with q95 around 4 and are good candidates for long pulse operation at high fusion yield in the reactor ITER. These hybrid scenarios are an intermediate step between the reference standard H-mode (high confinement) scenario with monotonic q and inductive current, and advanced scenarios with strongly reversed magnetic shear in which the entire plasma current is ideally generated non-inductively. This thesis focuses on the study of the dynamics of hybrid plasmas, with weak or almost zero magnetic shear, in tokamak and Reversed Field Pinch (RFP) configurations, when q in the central region assumes values close to one (tokamaks) or to a rational number (tokamaks, RFPs), though the exact resonance is avoided. The first part of this thesis is focused on the study of tokamak and RFP equilibria with slightly reversed shear when an extremum in the safety factor is close to a low order rational. These equilibria are characterised by the possible presence of internal helical cores, although the plasma edge is symmetric in the toroidal direction. Such 3D structures can be understood as the result of the nonlinear saturation of ideal MHD modes. The amplitude of large scale m=1 helical displacements in tokamak and RFP plasmas is investigated using contrasting approaches, namely 3D equilibrium and non-linear stability codes. The non-linear amplitude of such saturated modes obtained with the stability code is compared both with the helical core structure resulting from equilibrium numerical calculations, and with analytic predictions which extend the nonlinear treatment of reversed q plasmas to arbitrary toroidal mode numbers. A preliminary study of the impact of a n=1 RMP on the equilibrium helical distorsion is also presented. The second part of the thesis is devoted to the analytical and numerical study of the stability of an initially axisymetric tokamak configuration when the safety factor is almost flat and very close to a rational value over a macroscopically extended region in the plasma centre. Such conditions typically occur either in hybrid scenarios or following reconnection of a global instability such as a sawtooth. This configuration is characterised by non-negligible coupling between a fundamental mode and its Fourier adjacent modes. A dispersion relation has been derived both for ideal and resistive modes, with additional non-MHD effects such as plasma diamagnetism, viscosity and equilibrium velocity flows. The analytical results show that the resistive sidebands coupled to a core kink-like mode exhibit extremely fast growth, though additional non-MHD effects tend to moderately reduce the extreme growth rate of the resistive modes. The existence of such modes has been confirmed numerically, where the sensitivity of the growth rate to changes in resistivity and two-fluid effects has been demonstrated, and thus in turn provides generally good agreement with the analytical theory developed. A family of modes are obtained, including modes with novel scaling against plasma resistivity, some of which rotate in the electron diamagnetic direction, and others in the ion diamagnetic direction, consistent with experimental observations in e.g. TCV during hybrid-like operation.

EPFL2015