X-ray measurement on ITER with Low Voltage Ionization Chambers 

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Energy generation from nuclear fusion

Due to the topic of this thesis, a special focus is given on generation of energy through nuclear fusion. Fusion reactions of light elements release energy in the form of kinetic energy of the fusion products. The so-called D-T fusion reaction is the most accessible in reactor conditions. D stands for deuterium, which is the 2H isotope of hydrogen, and T stands for tritium, which is the 3H isotope of hydrogen. Nuclei of deuterium and tritium fuse together at high temperature in the following reaction: D¯ ¯T ¯ ! (fi ¯3.5MeV ) ¯(n ¯14.1MeV ) (1.1).
where fi is a He2¯ nucleus and n is a neutron. The total energy generated by a D-T reaction is ¢E ˘ 17.6MeV , which is around 8 times higher than a 235U fission reaction but with reactants around 50 times lighter.
In terms of availability, nuclear fusion exhibits the advantage that deuterium is a very common isotope of hydrogen which can be extracted from seawater at a low cost. At the present energy consumption, enough deuterium can be extracted for several billions of years of electricity production. Tritium is a radioactive isotope of hydrogen with a very short decay period. The naturally generated tritium has decayed long ago and the world tritium inventory has been produced by nuclear reactions of neutrons with heavy water in nuclear reactors or with lithium. Tritium generation can be achieved in nuclear fusion power plants by surrounding the reactor with lithium blankets. This technique is called tritium breeding and requires neutron multiplication in order for the reactor to be self-sufficient tritium-wise. The availability of nuclear fusion therefore depends on lithium, for which the reserves are expected to last for a thousand years. [5] This value is subject to a high uncertainty as lithium use is massive (electronics, batteries, …).
The environmental impact of nuclear fusion is very low compared to the energy sources listed previously. Indeed, the fusion product are neutrons and helium. Helium is an inert gas which is not radioactive. Neutrons however irradiate the fusion reactor which becomes radioactive. The decay period of a fusion reactor at the end of its lifetime is around 100 years, which is a ridiculously low duration in comparison with fission products.
Fusion reactors are inherently safe. Indeed they operate in very specific conditions, and in the case of a disruption fusion reactions just end prematurely. No reaction avalanche leading to the release of the reactor energy content in a short amount of time can therefore be observed. Due to constant fuelling of the reactor, only a small quantity of fuel is present at any given time (a couple of minutes in a fusion reactor compared to several months in a fission reactor). Moreover, the fuelling can be stopped if necessary. Even if the magnetic energy damaging the reactor, it has been demonstrated that no tritium leaking nor confinement failure is expected. [6] And in the case where the reactor is damaged by an outside event, the maximal amount of tritium released is around 1kg which should have limited consequences on health, and only in a small region and period of time.

Key challenges

In this section, the main challenges faced by magnetic confinement fusion are de-scribed. Tritium and nuclear waste management have been discussed in section 1.1.4, this section focuses on tokamak operation issues.
MagnetoHydroDynamics (MHD) instabilities in tokamak plasmas tend to increase radial transport and are therefore detrimental to energy confinement. The main MHD instabilities observed in tokamak plasmas are the so-called sawtooth oscillations, Edge Localised Modes (ELMs), and tearing modes.
Sawtooth crashes are a periodic instability which ejects energy and particles out of the plasma core. The name comes from the shape of the temperature and density profiles during such instabilities. They are characterised by a build-up phase during which the density and temperature profiles get more and more peaked followed by a sudden redistribution which flattens the profiles. This instability strongly affects particle and energy confinement, and can lead to plasma ending. However, evidence suggests that controlled sawtooth oscillations could be used to avoid impurity accumulation and limit fuel dilution by expelling He ashes.
Edge Localised Modes are a MHD instability which is observed in the plasma edge in H-mode plasmas. Tearing modes are a localised instability which changes the magnetic configuration of a plasma region, leading to the creation of magnetic islands. These islands increase radial transport and therefore deteriorate the confinement.
Another challenge is the choice of materials for PFC. Historically, carbon has been the first choice for PFC in tokamaks. It is a cheap material with a high thermal conduc-tivity, a good resilience to heat fluxes and a relatively low atomic number. However, its tritium retention would lead to biological hazard during D-T operation and the high sputtering rate of carbon is concerning for tokamaks such as ITER or DEMO. As a results, tungsten (W) and beryllium (Be) have been chosen for ITER PFC. The ITER main chamber will be made of Be due to its low atomic number and low tritium retention. The divertor as well as other PFC will be made of W due to its good thermal conductivity, very low tritium retention and sputtering capabilities. The study of the W source in the plasma due to sputtering is crucial to ITER as it limits the lifetime of the PFCs and can generate accumulation of impurities in the core.
Most of the eroded PFC particles and filaments are exhausted towards the divertor without reaching the plasma, but a small fraction can enter the SOL and migrate towards the plasma core. In such environment the impurity is ionized and radiates a significant amount of energy which decreases the plasma performance and can even lead to a radiative collapse of the plasma. The radiated losses are in the range of X-rays and the processes leading to their emission are described in section 2.2. The radiated power increases with the atomic number of the impurity. Heavy impurities such as tungsten are therefore more detrimental to the plasma performance than light impurities such as carbon. This is illustrated by figure 1.9 which displays ignition curves for different concentrations of tungsten and carbon. It can be observed that there are three orders of magnitude of difference between the acceptable tungsten and carbon concentrations for a similar ignition curve. On ITER, the reactor performance is affected by impurities for CW ‚ 10 ¡4 in the plasma core. The divertor configuration is expected to keep cW low enough but tungsten-induced radiative losses remain a major concern for ITER nonetheless.

ITER

The International Thermonuclear Experimental Reactor (ITER) is an international experimental fusion reactor currently under construction in Saint-Paul-lèz-Durance, France. ITER is a joint effort, funded and run by 7 seven member entities: the European Union (plus Switzerland), China, India, Japan, Russia, South Korea and the United States of America. The project was initiated in 1985 with the aim to demonstrate the scientific and technical feasibility of a fusion reactor. The first plasma on ITER is expected to take place at the end of 2025, for a D-T nuclear phase which should start in 2035. Its current goals are the following [22]:
— Produce 500 MW of fusion power for pulses of 400 s.
— Demonstrate the integrated operation of technologies for a fusion power plant.
— Achieve a deuterium-tritium plasma in which the reaction is sustained through internal heating (alpha power).
— Test tritium breeding.
— Demonstrate the safety characteristics of a fusion device.
ITER will be the largest tokamak in the world, a comparison between the tables 1.1, 1.2, and 1.3 shows the extent of ITER’s magnitude. The ITER X-ray diagnostics geometry is described in section 5.1.

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Corona Equilibrium

The Corona Equilibrium (CE) is base on the assumption that at low electron densi-ties, collisional processes become weak compared to radiative processes. The name of the model comes from the fact that this assumption applies well to the solar corona. In CE an energy level is only populated by electron collision (radiative processes are neglected as the plasma is considered optically thin) and depopulated by radiative decay: d n(z) j ˘ ne ni(z) d t X i ˙j Xi(!z)j ¡n(jz) A(jz!) (2.23).
where A(jz!) is the Einstein coefficient of spontaneous emission from energy level j and Xi(!z)j is the electron excitation coefficient from energy level i to j . The radiative processes are dominant with regards to collisional processes: A(iz!)j À ne Xi(!z) j . As a result, the ground state g is the dominant energy level (ng(z) … n (z)) and the population in higher energy levels only originates from electron collision from the ground state. The population density of energy level j at steady state is thus given by: n(z) ne X (z) j ˘ g !j ¿ 1 (2.24) ng(z) A(z) j !.
In corona equilibrium plasmas, the ionization of an electron is dominated by electron impact ionization and the recombination of a free electron is governed by radiative recombination. The evolution of the population of ions at ionization level z ¯ 1 is therefore given by: d n(z¯1) ˘ ne n(z)Sz ¡ne n(z¯1)fiz¯1 (2.25).
where Sz is the electron impact ionization coefficient and fiz¯1 is the radiative recom-bination coefficient. In steady state the population is given by: n(z¯1) ˘ Sz (2.26) n(z) fiz¯1.
In the frame of the corona equilibrium, the ratio of ions densities only depends on Te (through the S and fi coefficients) and is thus independent of ne . In order to be considered at coronal equilibrium, a plasma must verify the following condition on electron density [30]: 1 10¡4 Z 2 ne ˙ 1.9 ¢1018 ¢ Z 6 ¢p Te ¢exp µ ¢ ¢ ¶ (2.27).
with Te in keV , ne in m¡3 and Z the effective charge of the ion. For a fully-ionized hydrogen plasma at Te ˘ 10keV , the condition is ne ˙ 6 ¢1018m¡3. Similarly as Local Thermodynamic Equilibrium, Corona Equilibrium is not reached in tokamak plasmas.

Collisional Radiative models

Collisional Radiative (CR) models aim at computing the population densities of an ion in the scope of plasmas with electron densities between the LTE and CE limits, by taking into account the following processes: electron collisional transitions and ionizations, radiative decay, and radiative recombination. This leads to the following dynamics for the population of ions in ionization stage z in energy level j : d n(z) j ˘ ¡n(jz) ne X j !i ¯ ni(z)ne Xi(!z) j d t X X ¡n(jz) i 6˘j q6˘p (2.28) X A(jz!)i ¯ ni(z) Ai(z!) j X i ˙j i ¨j n(z)n S j !g ¯ n(z¯1)n fi(z¯1) ¡ j e g e g !j The evolution of the population vector N (z) ˘ n n(z¯1) (z) (z) can be described by the following matrix system: g ,…,n j ,…,ng o ddt N (z) ˘ M ¢ N (z) where the matrix M is defined by: 8 ‡ · > P i ¨j Ai(z!) j ¯ne Xi(!z) j i ˙ j ne X (z) j.

Table of contents :

Résumé
Abstract
Remerciements
Contents
List of Figures
List of Tables
1 Introduction 
1.1 The challenge of energy
1.1.1 Historical approach
1.1.2 Fossil fuels: availability and consequences
1.1.3 Alternative energy sources
1.1.4 Energy generation fromnuclear fusion
1.2 Nuclear fusion reactor
1.2.1 Fusion reactions
1.2.2 Ignition
1.2.3 Confinement
1.2.4 Tokamak
1.2.5 Existing tokamaks
1.3 Scope of this thesis
2 X-ray radiation 
2.1 Introduction
2.2 X-ray emission
2.2.1 Bremsstrahlung emission
2.2.2 Radiative recombination
2.2.3 Spontaneous emission
2.3 Ionization equilibrium
2.3.1 Local Thermodynamical Equilibrium
2.3.2 Corona Equilibrium
2.3.3 Collisional Radiative models
2.3.4 Effect of impurity transport on the equilibrium
2.4 Total plasma emissivity
2.4.1 X-ray emissivity on ITER
2.4.2 Influence of impurity transport on the X-ray emissivity
2.5 Extraction of plasma parameters from X-ray measurement
2.5.1 Impurity density
2.5.2 Impurity transport coefficients
2.5.3 Electron temperature
3 X-ray measurement 
3.1 Photodiodes
3.1.1 Semiconductor photodiodes
3.1.2 Vacuum photodiodes
3.2 Gas detectors
3.2.1 Ionization chambers
3.2.2 Multi-anodes Low Voltage Ionization Chamber
3.2.3 Gas ElectronMultipliers
3.2.4 X-rays detectors for ITER nuclear phase
3.3 X-ray tomography
3.3.1 Overview
3.3.2 MinimumFisher Information method
3.4 Accuracy of the X-ray emissivity calculation tool
4 Simulation of a Low Voltage Ionization Chamber on ITER 
4.1 Line-integration of the emissivity
4.1.1 Simplified representation of a detector-aperture system
4.1.2 Pixelization of the plasma
4.2 Interaction between X-ray photons and matter
4.2.1 Absorption processes
4.2.2 Inelastic scattering: Compton effect
4.2.3 Elastic scattering processes
4.2.4 Pair production
4.2.5 Relative importance of the different processes
4.3 Synthetic diagnostic
4.3.1 Computation of the different physical processes
4.3.2 Monte Carlo-based synthetic diagnostic
4.3.3 Matrix-based synthetic diagnostic
4.3.4 Comparison of the twomethods
5 X-ray tomography on ITER 
5.1 ITER radial X-ray cameras
5.2 Tomographic capabilities
5.2.1 Figures of merit
5.2.2 Emissivity profiles
5.2.3 Tomographic reconstructions
5.3 Addition of lines-of-sight: proof of concept
5.4 Geometry proposal
5.4.1 60 vertical lines-of-sight configuration
5.4.2 44 vertical lines-of-sight configuration
6 Application of the synthetic diagnostic 
6.1 X-ray measurement on ITER with Low Voltage Ionization Chambers
6.1.1 Influence of the filling gas
6.1.2 Influence of the filter
6.1.3 Influence of the length pressure product
6.2 Calibration of the LVIC measured current
6.2.1 Calibrationmethodology
6.2.2 Line-of-sight dependency of the calibration factor
6.2.3 Application to simulation results
6.3 Tomography using LVIC
6.3.1 Tomographic reconstruction of a SXR-restricted emissivity profile
6.3.2 Influence of the calibration method on the tomographic reconstruction
6.3.3 Tomographic reconstruction over a wide energy range
6.3.4 Influence of perturbative noise on the tomographic reconstruction
6.3.5 Alternative calibration method
7 Application to impurity transport study 
7.1 Reconstruction of the tungsten transport coefficients on ITER
7.1.1 Scenarios
7.1.2 LVIC measurement
7.1.3 Negative V scenario reconstruction
7.1.4 Positive V scenario reconstruction
7.2 Poloidal asymmetries
7.2.1 Collisional regimes
7.2.2 Theory of parallel forces
7.2.3 Poloidal asymmetries on ITER
8 Energy discrimination using LVIC 
8.1 Spectral deconvolution method
8.1.1 Hypothesis on the X-ray spectrum
8.1.2 Minimization algorithm
8.2 Application to ITER
8.2.1 Figures of merit
8.2.2 Spectral deconvolution using argon-filledMA-LVIC
8.2.3 Spectral deconvolution using xenon-filled MA-LVIC
8.2.4 Comparison between argon and xenon
8.2.5 Improving the reconstruction in the [2, 3] keV energy band
8.2.6 Sensitivity analysis
8.3 Energy-resolved X-ray tomography
8.3.1 Figures of merit
8.3.2 Results
8.3.3 Sensitivity analysis
8.4 Reconstruction of the electron temperature
8.4.1 Figures of merit
8.4.2 Results
8.4.3 Sensitivity analysis
9 Conclusion and perspectives 
Bibliography 

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