Measurement of the Radial Profile of the Plasma Isotopic Composition in JET Plasmas Using Alfven Eigenmodes

The measurement of the plasma isotopic composition is necessary in future burning plasma devices such as ITER and DEMO as a tool for optimizing the DT fusion performance. This paper reports on the results of experiments performed on the JET tokamak where Toroidal Alfven Eigenmodes (TAEs) with toroidal mode number (N) up to |N|=12 were actively driven with a set of in-vessel antennas, and were then used to infer the value of the plasma isotopic composition at different radial positions. A novel and important result with respect to previous work on JET is that by correctly including the effect of plasma impurities in the calculation of the Alfven frequency, through its dependence on the plasma mass, it has become now possible to distinguish plasmas with different majority ion species but with the same charge-to-mass ratio, notably majority Deuterium and Helium4 plasmas. Furthermore, and combined with modelling of AEs in JET discharges, these experimental results indicate that a diagnostic system based on the detection of AEs with different toroidal mode numbers and at different frequencies, could provide profile measurements of the plasma isotopic composition in future burning plasma devices such as ITER and DEMO.

Astrophysics and Fusion Plasmas: application of the SparSpec algorithm to the data analysis and design of the ITER high-frequency Mirnov coil diagnostic system

René Chavan, Ambrogio Fasoli, Jonathan Bryan Lister, Jean-Marc Moret, Theodoros Panis, Francisco Sanchez, Duccio Testa, Matthieu Toussaint

Analysis of magnetic fluctuations is important for understanding the magneto-hydrodynamic (MHD) properties of fusion plasmas. These properties affect nearly all aspects of behaviour of magnetic confinement, and thus are of interest in topics ranging from global plasma stability, control, and disruption avoidance, to more subtle areas such as MHD spectroscopy. Mode number analysis is generally accomplished by interpreting signals from a finite number of Mirnov coils, which typically are unevenly spaced in the spatial coordinates. Many aspects of the MHD spectroscopy technique rely specifically on the precise determination of the toroidal (n) and poloidal (m) mode numbers. Moreover, in fusion plasmas it is often of further benefit to be able to perform such analysis in “real–time”, i.e. using a clock-rate of the order of 1ms. The variety of methods in common use to determine the spatial structure of MHD phenomena in fusion plasmas from magnetic measurements is quite small. Traditionally, the linear phase fitting, the Fourier decomposition, the Lomb periodogram and fitting techniques such as the Wigner and Choi-Williams distributions have been proposed. More recently, Singular Value Decomposition and wavelets have also been used regularly. However, all these techniques suffer variously from at least one between these four main limitations: (1) the phase relation between the in-phase and quadrature (I/Q) components of the measured (complex) fluctuations is not always conserved (Wigner, Choi-Williams distributions); (2) multiple degenerate harmonics are not correctly treated (linear phase fitting, Fourier decomposition, Lomb periodogram, Wigner and Choi-Williams distributions); (3) uniform sampling is assumed (Fourier decomposition, Lomb periodogram); (4) a truly blind analysis is very CPU-time consuming, hence it is not suitable for real-time applications (wavelets, SVD). On the other hand, the problem of finding periodic waveforms in unevenly sampled data is ubiquitous in the field of astronomy, where much work has been done. It is easily seen that temporal frequencies in astronomical data correspond to spatial mode numbers in fusion plasmas, and that unevenly sampled data in time domain are the analog of data from unevenly distributed Mirnov sensors in the toroidal and poloidal coordinates. However, in astronomy, the frequencies sought are allowed to take on any value, while periodic boundaries in fusion devices ensure that only modes with integer mode numbers exist. Since all astronomical data is unevenly sampled (due to weather conditions and the earth rotation), considerable effort has gone into the problem of improving upon the limitations of the classic Lomb periodogram. Recently, a new method for fitting sinusoids to irregularly sampled data was proposed, based on the principle of sparse representation of signals: this is implemented in the SparSpec code (available at: http://www.ast.obs-mip.fr/softwares). As the analysis of MHD fluctuations data from the JET tokamak will show, this method has proven to be far superior to other methods in terms of accuracy and computational speed of the calculation, so much so that in fact it has recently been implemented for real-time detection of toroidal mode numbers for the active MHD spectroscopy diagnostic system in JET. Further application of the SparSpec analysis method to the design of the high-frequency magnetic diagnostic system for ITER will be discussed, with a view to develop ideas for future collaborative activities.

2008

Direct Measurements of the Damping of Alfvén Eigenmodes for an Assessment of their Stability Limits in Tokamak Plasmas

Theodoros Panis

Direct damping rate measurements of AEs are obtained using the active MHD spectroscopy system installed on the JET tokamak. The system was recently equipped with new antennas, designed to study especially the modes of intermediate toroidal mode number n, |n| = 3 – 15, as the AEs of this range are most prone to destabilization by the fast particles in JET and in future burning plasma experiments such as ITER. The broad n-spectrum that is driven by the new antennas and the more localized structure of intermediate-n AEs has important implications for the ability to measure damping rates of intermediate n. To obtain an extended database of high accuracy individual-n measurements, experimental work on technical and engineering aspects was indispensable both on the excitation side and on the detection side. On the excitation side, the electrical model of the AE exciter has been constructed during this thesis. The model is used to determine the operational capabilities of the exciter with the new antennas, to optimize the antenna currents and to design the relevant impedance matching circuits. On the detection side, the excitation of multiple-n, degenerate AEs at close frequencies prompted for a sophisticated method to correctly estimate the n-spectrum of the plasma response. To this end, a sparse spectrum representation method was adapted to deal with the complex and real-time data produced by the active MHD spectroscopy system. The n-decomposition of the plasma response requires an accurate relative calibration of the magnetic pick-up coils. An in situ method was developed and applied for the calibration of the coils using the direct coupling to the new AE antennas. A large collection of damping rate measurements of, mainly, toroidal AEs (TAEs) was obtained during the 2008/2009 JET experimental campaigns following the technical optimization of the antenna system. Selected measurements of |n| = 3, 4 and |n| = 7 TAEs are compared to the plasma models of the numerical codes LEMan and CASTOR. The robustness of the results of the simulations is tested against uncertainties in density and safety factor profiles. The antenna-driven modes are characterized and the dominant damping mechanisms are identified in a number of cases, and confirm in general for a wide n- range the stabilizing role played by the edge magnetic shear. These comparisons underline the importance of the kinetic effects in order to achieve a realistic estimation of the TAE damping. A database of approximately 3000 TAE damping rate measurements in ohmic plasmas is studied. The dependence of the damping rate measurements of |n| = 2 – 7 TAEs on the edge magnetic shear, the edge elongation and the q profile is investigated. The analysis provides experimental evidence that the damping properties of TAEs with |n| = 2 – 7 change as the toroidal mode number n increases, showing that medium-n modes tend to be less damped than low-n modes. In JET plasmas, the turning point for the damping properties to change from low-n to medium-n behavior is found to be at |n| ≈ 3 – 4.

EPFL2010

Edge Localized Mode Control in TCV

Jonathan Rossel

The Tokamak concept, based on magnetic confinement of a hydrogen plasma, is one of today's most promising paths to energy production by nuclear fusion. The experimental scenarios leading to the largest fusion rate are based on a high confinement plasma regime, the H-mode, in which the energy and particle confinement are enhanced by a transport barrier located at the plasma edge and forming a pedestal in the plasma pressure profile. In standard axisymmetric magnetic configurations, stationary H-mode regimes suffer from instabilities of the plasma edge, the so-called edge localized modes (ELMs), leading to potentially damaging repetitive ejections of heat and particles toward the plasma facing components. In ITER, a Tokamak currently being built to demonstrate net power production from fusion, type I ELMs are expected to occur during high performance discharges. It is expected that the power flux released by these ELMs will cause an intolerable erosion and heat load on the plasma facing components. The control of ELMs, in terms of frequency and energy loss, is therefore of primary importance in the field of magnetic fusion and is subject to an intense research effort worldwide. This thesis, in line with this effort, focuses on two particular ELM control methods: local continuous or modulated heating of the plasma edge, and application of resonant magnetic perturbations (RMP). In this thesis, the effects of plasma edge heating on the ELM cycle have been investigated by applying electron cyclotron resonant heating (ECRH) to the edge of an H-mode plasma featuring type I ELMs in the Tokamak à Configuration Variable (TCV). As the power deposition location is shifted gradually toward the plasma pressure pedestal, an increase of the ELM frequency by a factor 2 and a decrease of the energy loss per ELM by the same factor are observed, even though the power absorption efficiency is reduced. This unexpected and, as yet, unexplained phenomenon, observed for the first time, runs contrary to the intrinsic type I ELM power dependence and provides a new approach for ELM mitigation. The effects of heating power modulation on the ELM cycle have also been experimentally investigated. It showed that power modulation synchronized in real-time with the ELM cycle is able to pace the ELMs with low deviation from a given frequency. Experimental results also clearly indicate that the ELM frequency purely remains a function of the heating power averaged over the ELM cycle, so that power modulation itself is not able to drive the ELM frequency and only has a stabilization effect. These results are in qualitative agreement with a simple 0D finite confinement time integrator model of the ELM cycle. RMP consists in applying a magnetic field perpendicular to the plasma magnetohydrodynamic equilibrium flux surfaces with a spatial variation tuned to align with the equilibrium magnetic field lines. If each coil of an RMP coil system (i.e. a set of toroidally and poloidally distributed coils) is powered with an independent power supply, the coil current distribution can be tuned to optimize the RMP space spectrum. In the course of this thesis, a multi-mode Lagrange method, with no assumption on the coil geometry or spatial distribution, has been developed to determine this optimum, in the limit of the vacuum magnetic field approximation. This method appears to be an efficient way to minimize the parasitic spatial modes of the magnetic perturbation, and the coil current requirements, while imposing the amplitude and phase of a set of target modes. A figure of merit measuring the quality of a perturbation spectrum with respect to RMP independently of the considered coil system or plasma equilibrium is also proposed. To facilitate the application of the Lagrange method, a spectral characterization of the coil system, based on a generalized discrete Fourier transform applied in current space, is performed to determine how spectral degeneracy and side-bands creation limit the number of simultaneously controllable target modes. Finally, this thesis sets the foundations of experimental research in the particular subject of RMP at CRPP by proposing a physics-based design for a multi-purpose saddle coil system (SCS) for TCV, a coil system located and powered such as to create a helical magnetic perturbation. Using independent power supplies, the toroidal periodicity of this perturbation is tunable, allowing simultaneously ELM control, error field correction and vertical control. Other experimental applications, like resistive wall mode and rotation control, are also in view. In this thesis, the adequacy of two SCS designs, an in-vessel one and an ex-vessel one, is assessed with respect to the desired experimental applications. The current requirements and the system performances are also characterized. The conducting vessel wall is accounted for in a model used to determine the coupled response functions of the SCS, the screening of the magnetic perturbation by the wall, the induced voltages and currents during a plasma disruption and the maximal magnetic forces exerted on the SCS. A scaling of the SCS parameters with the number of coil turns is presented and the issue of coil heating and cooling is discussed.

EPFL2012