Ecole Centrale Marseille JET (CCFE)Plasma Boundary Group

Abingdon, OxfordshireUnited Kingdom

Travail de Fin d’EtudesDu 31/03 au 12/09

Analysis of Divertor Profiles for TestingPhysics Assumptions

Axel Jardin3eme année promotion 2014

Parcours "IRIS"

Tuteur école :

Laurent Gallais

Tuteurs Entreprise :

Christophe GuillemautBruce Lipschultz

Acknowledgement

First, I would want to thank Christophe Guillemaut for being an amazing supervisor, forhis availability, his advice and his participation in my work.

• I thank Bruce Lipschultz and Guy Matthews for allowing this internship to happenin the JET Plasma Boundary Group and for their precious advice.

• I thank my teachers Mireille Commandré and Laurent Gallais from the EcoleCentrale Marseille and my referent Laetitia Abel-Tiberini.

• I thank Peter Beyer and Rémy Guirlet from the Master Fusion and EmmanuelJoffrin for helping me to find this internship, and Jan Dalton for welcoming me atJET.

• I thank Adrien Autricque, Gilles Arnoux and Stéphane Devaux for their assistanceand their very useful work.

• I would also want to thank Didier Mazon for our discussions and the introductionto Soft X-ray measurements, in the framework of my future PhD thesis at CEACadarache.

• Finally, I thank the people with whom I have worked: Jan Horacek, RenaudDejarnac, Thomas Eich, Andrea Scarabosio, Elena De La Luna, Mike Stamp,Sebastijan Brezinsek, David Moulton, Alexander Huber, Emilia Solano, MeikeClever, Jurrian Boom, and Peter Drelelow and Nicolas Fedorczak for our interest-ing conversations.

• Special thanks to Adrien, Boubou, Cas-Lu, Alexandrine, Zozo, Zaza, Mama,Manu, Coco, Alexandre, and Jess, Gwen and all the people from the MFO, forthe great mood and the wonderful time we spent together.

Summary

In the framework of controlled magnetic confinement fusion, this internship took placein the Joint European Torus (JET) Plasma Boundary Group, Culham, UK. The toka-mak experiments can involve up to 40MW of heating power. Once exhausted from theplasma core, this power reaches the divertor surfaces which are especially designed tosustain high heat fluxes. ITER divertor will be designed to sustain heat flux density upto 10MW/m2 in steady state. High power discharges in JET allow operations in highconfinement mode (H-mode) which comes with regular short and intense edge instabil-ities called Edge Localized Modes (ELMs). Erosion by ELMs of JET divertor targetsmade of tungsten (W) is a crucial issue to study since ITER divertor will also be madeof W and small concentrations of this material are sufficient to degrade strongly the per-formances of the plasma core. This project consists in using edge plasma diagnostics- Langmuir probes (LP) for the most part, and also infrared cameras (IR) or ElectronCyclotron Emission (ECE) - in order to analyse divertor profiles and correlate them withupstream plasma.During these 5 months of internship, a user interface has been created and is now usedas a standard tool to display and analyse divertor targets profiles from LP measurements(ion saturation current, electron temperature, heat flux and electron density). This GUIhas first been used to determine the power decay length on the outer target, for both Land H-mode using an ELM-removal algorithm. Then, divertor and pedestal dynamicsduring type-I ELMy on JET-ILW have been observed. Intra-ELM LP measurements va-lidity is discussed and LP/IR measurements are compared in order to estimate the targetimpact energy per particule during ELMs. It appears for the moment that the usual as-sumption considering that the target electron temperature during an ELM is equal to theelectron temperature at the pedestal is valid for the JET-ILW discharges studied here.This is an important result since the evaluation of the W sputtering source during ELMsrelies on this assumption.

KeywordsMagnetic confinement fusion, Joint European Torus (JET), plasma boundary group, di-vertor, JET-ILW, Langmuir probe, SOL Power decay length, Edge Localized Modes(ELMs), Tungsten (W) sputtering

Résumé

Dans un contexte de recherche sur la fusion contrôlée par confinement magnétique, cestage s’est déroulé au sein du groupe des plasmas de bord du tokamak Joint EuropeanTorus (JET), Culham, Royaume-Uni. Lors des expériences réalisées sur JET, jusqu’à40MW de puissance de chauffage sont fournis au plasma. Cette puissance éjectée horsdu plasma de coeur atteint les surfaces du diverteur spécialement conçues pour résisterà de hauts flux de chaleur. Le diverteur d’ITER sera conçu de manière à soutenir unedensité de flux de chaleur jusqu’à 10MW/m2. Lors des décharges à haute puissance,JET opère en mode de haut confinement (H-mode), qui entraîne l’apparition de courteset intenses instabilités appelées Modes Localisés de Bord (ELMs). L’érosion des ciblesdu diverteur en tungstène (W) lors des ELMs est un enjeu majeur, puisque le diverteurd’ITER sera également en W et que même de très faibles concentrations de W dansle plasma de coeur suffisent à dégrader considérablement ses performances. Ce projetconsiste en l’utilisation de diagnostics de plasma de bords dans le but d’analyser lesprofils de diverteur et les corréler avec le plasma en amont.Durant ces 5 mois de stage, une interface utilisateur à été créée pour afficher et traiterde manière standardisée les profils de divertor à partir des données des sondes de Lang-muir. Un module de détermination de l’épaisseur de dépôt de puissance sur le diverteura été implémenté et utilisé lors de récente expériences. La dynamique du diverteur et dupiédestal durant les ELMs de type I ont été étudiées. Enfin, les mesures des sondes deLangmuir et infrarouges ont été couplées dans le but d’estimer l’énergie d’impact desparticules sur les cibles du diverteur pendant les ELMs. Les premiers résultats montrentque l’hypothèse courante selon laquelle la temperature electronique sur les cibles dudiverteur est égale à celle du piédestal pendant les ELMs est valide pour les déchargesétudiées sur JET-ILW. Ce résultat est important puisque la prédiction de la source de Wpar érosion dépend de cette hypothèse.

Mots-clefsFusion par confinement magnétique, Joint European Torus (JET), Groupe des plasmasde bord, diverteur, JET-ILW, sonde de Langmuir, épaisseur de dépôt de puissance, Modede bord localisé, Erosion du tungstène

Glossary

• Plasma. Plasma is the fourth fondamental state of matter and corresponds toan ionized gas, composed of both positive ions and negative electrons. Thesecharge carriers make the plasma electrically conductive and strongly sensitive toelectromagnetic fields.

• Tokamak. A tokamak is a torus containing a strong magnetic field created bymagnetic field coils. The purpose is to confine hot plasma and prevent it fromtouching vacuum vessel walls.

• Divertor. The divertor is the surface inside the vacuum vessel specifically de-signed for handling plasma wall interaction, sustaining high heat fluxes and pre-venting cold particles and impurities from going back in the plasma core anddegrading its performances.

• Separatrix. The separatrix is the last closed magnetic surface, between the con-finement region (plasma core) and open magnetic field lines (Scrape-off layer).

• Scrape-off layer (SOL). The SOL is the thin region where magnetic field linesof open and connected to divertor targets, outside the confinement region.

• Sheath The sheath is the thin layer between plasma and plasma facing surfacesinduced by the Debye shield effect. The local electrostatic field in the sheathaccelerates incoming ions and repels electrons from the plasma.

• Pedestal. Pedestal is a transport barrier at the edge of the plasma core that im-proves confinement and plasma core performances.

• Edge Localized Mode (ELM). ELMs are regular short and intense edge instabil-ities that occur in high confinement regime and make the pedestal collapse.

• Sputtering. Sputtering characterizes erosion of plasma facing materials irradiatedby hot plasma particles (ions).

• Langmuir probe (LP). LPs are edge plasma diagnostics that measure the incom-ing ion flux on plasma facing surfaces.

Contents

Acknowledgement 2

Summary (EN) 3

Résumé (FR) 4

Glossary 5

Introduction 8

I. Fusion Challenges and Main Issues of my Internship 10

1. Fusion, Tokamaks and JET 11

2. Divertor, Edge Plasma and Diagnostics 13

3. Simple Understanding of SOL Physics 17

4. Introduction to H-mode and ELMs 20

II. Technical Part of the Project 22

5. A New Tool for LP Profile Analysis on Divertor Targets 235.1. Data processing from JET experiments . . . . . . . . . . . . . . . . . . 235.2. Divertor Profiles Reconstruction . . . . . . . . . . . . . . . . . . . . . 245.3. Implementation in a Python GUI Interface . . . . . . . . . . . . . . . . 25

6. LP Profiles fitting for Determining the SOL Power Decay Length 276.1. Power decay length challenges and fitting models for IR data . . . . . . 276.2. Power Width Fitting with LP Measurements . . . . . . . . . . . . . . . 28

7. Divertor and Pedestal Dynamics During type I ELMy on JET-ILW 307.1. Intra-ELM Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 307.2. Cold Pulse Regime after Type-I ELMs . . . . . . . . . . . . . . . . . . 327.3. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

8. Estimation of Target Impact Energy per Particule during ELMs 348.1. LP measurements validity . . . . . . . . . . . . . . . . . . . . . . . . . 34

Contents

8.2. Target Electron Temperature Estimates by Coupling LP/IR . . . . . . . 368.3. Comparison with Pedestal Temperatures . . . . . . . . . . . . . . . . . 38

Conclusion 40

Bibliography 42

III. Appendix 43

A. Internship Description 44

B. ELM detection 45

C. Hyperbolic Tangent Fit Function 46

D. LP Target-Profile GUI 47

E. Pedestal dynamics with ECE 50

F. Outer/Inner Target Comparison during ELMs 51

G. Spectroscopy during ELMs 52

H. Langmuir Probes Calibration 53

I. Mirnov Coils collapse during type I ELM 54

J. Sheath Heat Transmission Coefficient 55

K. Physical Sputtering 56

L. Free Streaming Model 57

7

Introduction

Energy supply is a crucial issue for mankind in a context of continuous growth. Whilethe world energy production relying on fossil fuels (oil, gas, coal) is expected to peak,the world energy consumption is still increasing, particularly because of the economicgrowth of emerging countries. This energetic crisis already has a significant impact onour economy and urges us to find new sources of energy and/or how to contain ourenergy consumption. That is why engineers and researchers focus on finding new pos-sibilities to increase and optimise the energy supply.In this context, nuclear fusion could be a good alternative energy source for the future.Nuclear fusion powers the stars (like the sun) and could also be used on Earth in a con-trolled way, to provide large quantities of energy over a very long time scale. The mostfeasible nuclear reaction relies on the use of deuterium-tritium (D-T) fuel mix. Largequantities of deuterium are available in sea water (enough for ∼ 1010 years of presentworld energy consumption) and tritium can be produced from lithium which is alsoquite abundant in salt flats and sea salt (potentially ∼ 108 years of reserves). There isenough deuterium in one cubic meter of sea water to satisfy the lifetime energetic needsof one person. Fusion is cleaner and safer than nuclear fission since there is no chainreaction and no direct production of long term radiotoxic elements. Moreover, it willnot be intermittent like solar energy or wind.

Two paths are being explored in fusion research centres worldwide: inertial con-finement fusion (ICF) and magnetic confinement fusion (MCF). The first one is led byprojects like the National Ignition Facility (NIF) in the USA and the Laser MégaJoule(LMJ) in France, and consists in igniting small high density D-T targets for a very shorttime (∼ 10−9s) with a laser pulse. MCF involves the confinement of low density fusionplasmas with magnetic fields in devices like tokamaks or stellarators mainly. The maininternational project in MCF is the International Thermonuclear Experimental Reactor(ITER) under construction in Southern France. For the moment, the fusion research isconducted all around the world, on different (smaller) tokamak experiments like JET [1]and MAST [2] in the UK, ASDEX-Upgrade in Germany, DIII-D and NSTX in the USA,SST-1 in India, EAST in China, K-STAR in Korea and possibly JT60-SA in Japan, andWEST [3] (Tore-Supra) in France.The main current technological limitations of the development of commercial fusionreactors are the power exhaust, high energy neutrons and production of tritium. As thetokamak chamber has to sustain high power exhaust (up to 40MW in JET), a specificsurface called the divertor has been designed for handling the plasma wall interaction,sustaining high heat fluxes and preventing expelled and sputtered particles from goingback to the plasma core and degrading its performances.

Contents

In this context of divertor resistance to high heat flux and sputtering (mostly inducedby Edge Localize Modes), my internship in the JET Plasma Boundary Group has beenfocused on diagnostic data analysis - Langmuir probes for the most part - and correla-tion of divertor profiles with upstream data for testing physics assumptions. First, a userinterface has been created in order to extract Langmuir probes data from experimentsand display automatically divertor profiles - ion saturation current, electron tempera-ture, electron density and heat flux. This interface has been used to determine the strikepoints positions and study detachment, but mostly to estimate the power decay lengthon divertor targets in recent power scaling experiments, which shows if the power staysin a thin layer or spreads out onto the divertor. Divertor and pedestal dynamics duringtype-I ELMy on JET-ILW have been observed. Then, Langmuir probes measurementshave been compared to infrared data in order to estimate the target impact energy perparticule during ELMs and compare it to upstream values, as the target electron tem-perature during an ELM is usually assumed equal to the electron temperature at thepedestal. The validity of this assumption is an important issue since the evaluation ofthe W sputtering source during ELMs relies on it.

9

Part I.

Fusion Challenges and MainIssues of my Internship

1. Fusion, Tokamaks and JET

Fusion energy is produced by getting together two light atomic nuclei to create heavieratoms, in opposition with nuclear fission. The deuterium-tritium (D-T) fusion reactionshown in figure 1.1 is the most feasible and the one foreseen for controlled nuclearfusion on Earth:

21D +3

1 T →42 He(3.5MeV ) +1

0 n(14.1MeV ) (1.1)

Figure 1.1.: Fusion reaction and different reaction rates [4]

Deuterium (D) is extractible from sea water; tritium (T) can be produced in situ byreaction between a lithium blanket and the neutrons directly or indirectly produced bythe fusion reactions (1.2) as follows:

63Li+1

0 n→31 T (2.75MeV ) +4

2 He(2.05MeV ) (1.2)

Presently, tokamaks are the most performant devices for controlled fusion. A toka-mak is a torus containing a strong magnetic field created by toroidal and poloidal mag-netic field coils as shown in the figure 1.2 below. The hot fusion plasma (T ∼ 108Kand n ∼ 1020m−3 ) composed of both ions and electrons is confined inside the cham-ber by a strong helicoidal magnetic field, preventing them from touching the wall sincethey follow magnetic field lines. The toroidal component of this field is induced bytoroidal coils, while the poloidal component is generated by the plasma current. Thecentral solenoid acts as the primary transformer circuit and induces this plasma current.Poloidal coils are used to control the shape and position of the plasma. The Europeanmagnetic confinement fusion project [1] and ITER’s predecessor [4], the Joint Euro-pean Torus (JET) is the current world’s largest and most powerful tokamak with a majorradius of 3m, ∼ 100m3 of plasma and 40MW heating.

1. Fusion, Tokamaks and JET

Figure 1.2.: Tokamak elements (left) [5] / layout of JET (right) [6]

The tokamak JET is hosted in Culham Centre for Fusion Energy (CCFE), which isthe UK’s national laboratory for fusion research. CCFE (formerly known as UKAEACulham) is based at Culham Science Centre in Oxfordshire, and is owned and operatedby the United Kingdom Atomic Energy Authority. Since the 1960s, Culham has mademany major contributions to international fusion research and development.

Figure 1.3.: Culham Science Center for Fusion Energy

The JET facilities are collectively used by European fusion scientists, co-ordinated bya program management unit at Culham. JET is situated next to the UK fusion labora-tory. Around 500 people are employed at the JET facilities, with around 350 Europeanscientists visiting each year to conduct research, and many from outside Europe.

12

2. Divertor, Edge Plasma andDiagnostics

The portion of the 40MW heating that is not radiated by the plasma core is exhaustedout of the confinement region (beyond the separatrix) in the scrape-off layer (SOL), andhits directly the divertor behaving as a plasma sink. The divertor is the surface insidethe vacuum vessel specifically designed for handling plasma wall interaction, sustain-ing high heat fluxes and preventing cold particles and impurities from going back in theplasma core and degrading its performances.

Figure 2.1.: JET ITER-Like Wall components [7]

Initially, most of divertors were made in Carbon Fiber Components (CFC), which hasnow been replaced by tungsten (W), like in Tore-Supra (WEST). ITER main chamberwall will rely on W and Beryllium (Be) and is being tested in JET with the ITER-LikeWall project (JET-ILW), as shown in figure 2.1. Among its advantages, W has a betterresistance to heat fluxes, a smaller sputtering yield in hot plasmas and a smaller tritiumretention rate. Unfortunately, sputtered W particles are a source of concern due to theirhigh atomic number. Indeed, they radiate a lot of plasma energy when ionized in thecore and W has a higher self-sputtering yield than CFC. Thus, predicting the heat fluxand W sputtering on divertor targets are a crucial issue for future tokamaks and havebeen the baseline of my internship.

2. Divertor, Edge Plasma and Diagnostics

Divertor Diagnostics: Langmuir probes, InfraredCameras, Spectroscopy

Figure 2.2.: JET divertor tiles (left) / Example of magnetic equilibrium (right)

The main diagnostics in the divertor are Langmuir probes (LP), infrared cameras (IR)and spectroscopy. They have been used in the present work in order to study power loadand particles flux and radiation on the JET divertor targets. LP are conducting "tips"electrically isolated from the divertor plates. By biasing the probe’s electric potential,positive ions can be drawn to the probe and electrons repelled, such that we can deter-mine both ion flux and electron temperature analysing the probe current as a functionof its voltage, following the equation (2.1) below with 3-parameter fit: Jsat, Te and Vf .The next equation (2.2) introduces a fourth parameter dI

dV, taking into account the sheath

expansion as the voltage decreases (see [8]).

J = Jsat(1− exp(V − VfTe

)) (2.1)

J = Jsat(1− exp(V − VfTe

)) +dI

dV(V − Vf ) (2.2)

Then, electron density and perpendicular heat flux can be calculated as follows:

ne = Jsat

√mi

2eTe(2.3)

q⊥ = γeneTe

√2eTemi

sin(θ) (2.4)

14

2. Divertor, Edge Plasma and Diagnostics

Figure 2.3.: Langmuir probe schema (left) [9] / Langmuir Probe current-voltage charac-teristic (right) [10]

Thus, LP are very useful divertor diagnostics since the main target plasma parametersJsat, Te, ne and q⊥ can be extracted from measurements. It should be noted that theion flux is measured every 10µs, but the voltage sweep needs a minimum of 2ms toestimate Te with the 4-parameter fit method. That is why only the fast ion flux mea-surements (Jsaf ) can be used in order to observe phenomena with a time scale between10−4s and 10−3s like Edge Localized Modes (ELMs, see Chapter 4).

Infrared cameras measure local temperature time profiles on the JET divertor tiles(see figure 2.2 above) assuming black-body radiation. Then, local perpendicular heatflux Q⊥ can be estimated every 200µs using the reversed heat equation.

Dα, Be(II), and W (I) spectroscopy are also useful for studying incoming/outcomingparticle fluxes on divertor, plasma impurities and sputtering. Dα emission correspondsto the transition between the third and the second deuterium’s lowest energy level.Be(II) and W (I) signals correspond respectively to Be+ and W 0 radiation.

15

2. Divertor, Edge Plasma and Diagnostics

Edge Plasma Diagnostics: Electron CyclotronEmission and Thomson ScatteringSome very useful diagnostics for studying edge plasma are electron cyclotron emission(ECE) radiometers and high resolution Thomson scattering (HRTS), they have beenused in H-mode in order to determine pedestal electron temperatures (see section 8.3).Thomson scattering is the elastic scattering of electromagnetic radiation by a free chargedparticle. In tokamaks and other experimental fusion devices, the electron temperaturesand densities can be measured with high accuracy by detecting the effect of Thomsonscattering on a laser beam.

Figure 2.4.: Some edge plasma diagnostics

16

3. Simple Understanding of SOLPhysics

The scrape-off layer (SOL) is the plasma region characterized by open magnetic fieldlines, between the last closed magnetic surface (separatrix) and the wall. The two-pointmodel can give us a simple understanding of physics at stake between the midplaneand the divertor. It is the most basic physical model of the divertor SOL to correlate theplasma temperature and density upstream with those on the target. It allows a more qual-itative than quantitative analysis of SOL phenomena, and it is only valid for relativelylow upstream densities in attached regime - a detachment is observed experimentallyfor high upstream densities, with a drop of temperature and density at the divertor. Themain physics assumptions needed to write the two-point model are the particle balance,the pressure balance and the power balance.

Figure 3.1.: scrape-off layer (SOL) simplified model

The 3 conservation laws (particles, momentum, energy) in the plasma are as follows:

3. Simple Understanding of SOL Physics

∂n

∂t+ ~∇.n < ~v >= Siz − Srec = Sp (3.1)

∂

∂tnm < ~v > +~∇(nm < ~v >2 +p.δ + Π) = n < ~F > +Smom (3.2)

∂

∂t(1

2nm < ~v >2 +

3

2neT )+~∇[(

1

2nm < ~v >2 ++

5

2neT+Π) < ~v > −~q] = nq < ~E.~v > +SE

(3.3)With ~q = −nχ~∇T

Assuming the steady-state ∂∂t

= 0, the two-point model (in 1 Dimension //) implies:

• Pressure balance (3.2): no friction in the ionization region and no viscosity

~∇//P = ~∇//(nmv2 + p) = 0 (3.4)

Assuming v = 0 upstream and v = cs (the sound speed) at the target, we derive alinear relation between upstream and target pressure:

nuTu = 2ntTt (3.5)

This equation corresponds to the attached regime, when plasma pressure at themidplane is proportionally correlated with the one at the target.

• Power balance (3.3): the total plasma pressure remains constant along theparallel direction in the SOL.

~∇[(1

2nm < ~v >2 + +

5

2neT + Π) < ~v >= 0 (3.6)

Thus, ~∇.~q = SE = 0 in the SOL and χ = κ0T52 such that q// = κ0T

52∂T∂s

⇒∫ L

0q//ds = −κ0

∫ TuTtT

52dT

⇒ q//L// = −27κ0(T

72u − T

72t )

⇒ T72u = T

72t − 7

2

q//L//

κ0

By assuming T72ref = −7

2

q//L//

κ0, we obtain:

T72u

T72ref

− T72t

T72ref

= 1 (3.8)

18

3. Simple Understanding of SOL Physics

- When Tu ∼ Tref , equation (3.8) implies Tt << Tref- If Tu >> Tref , then we have Tt ∼ Tu >> Tref

Finally, the Bohm condition on the wall implies (with cst =√

2eTtmt∼ T

12t ) :

q// = qt = γntcstTt (3.9)

The three equations (3.5), (3.8) and (3.9) enable us to predict the evolution of nt andTt on the target during a ramp density in the plasma core, as performed during the pulse#82342. Assuming total pressure remains constant along the parallel direction in theSOL, if nu is low Tu must be high such that Tt ∼ Tu according to (3.8) and nt ∼ nuaccording to (3.5). If nu is high, Tu must be low and (3.8) implies Tt << Tu suchthat we can determine nt ∼ n3

u using (3.9). nt increases and Tt decreases during the

ramp density such that the particle flux Γt = ntcst ∼ ntT12t increases and the heat flux

qt ∼ ntT32t remains constant on the target, since there is no power losses in the SOL

with this model.JET experiments show that it is only true for low upstream densities. Divertor detach-ment happens for high nu, leading to a drop of particle and heat fluxes. Then, thetwo-point model is no longer valid and other physical processes like radiative powerlosses, neutral-ions collisions or volume recombination have to be studied. Combiningthe previous formula nt ∼ n3

u and Jsat = ntcst ∼ ntT1/2t ∼ n

2/3t (using equation (3.9)

with constant SOL power), the degree of detachment (DeD) can be experimentally esti-mated as follows:

DeD =n2u

Jsat∗ (Jsatn2u

)attached (3.10)

In attached regime (and relatively high nu), the degree of detachment is expectedto be equal to 1 if PSOL remains constant, and then DeD > 1 in detached regimes.Actually, 4 divertor regimes are identified: attached, high-recycling, partially detached(DeD ∼ 3) and fully detached (DeD ∼ 8) regimes. These regimes can be observedthanks to the ion saturation current of Langmuir probes, as displayed in figure 5.3 andfigure 5.4 on the outer target. Detached regimes imply a low heat and particle flux on thedivertor, but impurities and cold particles going back to the plasma core can destabilizeit and lead to disruption. Attached and high-recycling regimes imply a good particlesrecycling on the divertor - preventing them from degrading the plasma core, but a highheat and particle flux on the divertor.

19

4. Introduction to H-mode andELMs

The efficiency of the fusion reaction is determined by the amplification factor Q, i.e.the ratio between produced fusion power and heating power. ITER is aimed to reachQ = 10 (JET holds the current world record of 0.64) with 50MW of heating power and500MW of fusion power. Plasma performances depend on three parameters : the iontemperature Ti, the ion density ni and the energy confinement time τE . According tothe Lawson criterion, niTiτE > 1021(keV.m−3.s) is required for ignition.In the eighties, it was discovered on the ASDEX tokamak [11] that confinement can beimproved by a factor 2 above a certain power threshold. This improved confinementmode (see figure 4.1) was called H-mode for High confinement, in opposition with thenormal L-mode (for Low confinement mode). The H-mode is a stabilization of theturbulence in the edge of the plasma core with the creation of a pressure pedestal actingas a heat and particle transport barrier.

Figure 4.1.: Modes of plasma confinement [3]

L-mode leads to core instabilites called sawteeth (periodic abrupt relaxation of thecore temperature). Sawteeth can now be avoided by working in determined operatingdomains in current, magnetic field and heating power. H-mode will be the baseline forfuture "advanced tokamaks" like ITER. Unfortunately, H-mode comes with edge insta-bilities called Edge Localized Modes (ELMs) in which regular pedestal collapses (see

4. Introduction to H-mode and ELMs

figure 4.2) lead to few percent loss of total plasma energy. The ejected hot particlesreach the divertor’s plasma facing components and lead to a significant energy deposi-tion (up to several MJ) over a very short time (few ms), causing the erosion of divertormaterials by physical sputtering (see appendix K).

Figure 4.2.: Time development of an ELM crash [1]

W sputtering on targets due to high energy particles from ELMs - for the most partBeryllium impurities, but also W self-sputtering, other impurities and D-T (see [12]) -are a major source of concern since even small concentration of W in the plasma corelead to significant radiative losses and thus degradation of performances. An experimen-tal estimate of the energy of the particles during ELMs would be a useful informationto evaluate the W impurity production on the divertor targets.

21

Part II.

Technical Part of the Project

5. A New Tool for LP ProfileAnalysis on Divertor Targets

On JET, LP data are stored separatly and Jsat, Te, ne and Qp target profiles are notproduced automatically. A post-treatment is needed in order to gather all LP data andcorrelate them with their positions. The sweeping of the strike point position has alsoto be taken into account. That is why a user interface designed to automatically processLP data has enabled us to standardise the post-treatment, display and analyse (shape andpeak) quickly target profiles. Other post-treatment have been added to the interface, likea widget fitting the power decay length on both targets and an ELM detection algorithmfor intra-ELM and inter-ELM analysis.

5.1. Data processing from JET experimentsData directly obtained from JET experiments are stored in servers as JPF (Jet PulseFile). The data processed from the JPF are stored as PPF (Processed Pulse File). Forinstance, current and voltage associated with each LP are stored as JPFs, while Jsat andTe calculated by processing JPFs are stored as PPFs.

Figure 5.1.: Data storage for JET experiments

To facilitate LP data analysis, we have built a tool capable of displaying target profilesusing PPFs, for further post-treatments such as fitting routines or ELM analysis.

5. A New Tool for LP Profile Analysis on Divertor Targets

5.2. Divertor Profiles ReconstructionTarget profiles can be obtained by correlating LP data at a given time with their positionson the target. The position of the two strike points are given by magnetic reconstruction,such that the strike point can be chosen as the origin of the spatial axis. In order to avoidany issue with the orientation of the tile, the curvilinear abscissa s along the surface ofthe tile has be chosen as the spatial variable.

Figure 5.2.: Inner and Outer targets at t = 53.32s for pulse #82342

In order to study the time evolution of the divertor spatial profiles, data can be puttogether to get a time and space 2D matrix. The main challenge is the sweeping ofthe strike point position during experiments - the probes relative positions vary during apulse - such that the data grid is not regular in space. At each measurement time, a linearinterpolation in space is applied in order to get a regular grid, resulting in the figure 5.3below with a classical "contourf" function:

Figure 5.3.: Jsat [MA/m2], Pulse #82342 - Inner (down), Outer (up) Targets

24

5. A New Tool for LP Profile Analysis on Divertor Targets

5.3. Implementation in a Python GUI Interface

The "Langmuir Probes TARGET-PROFILE" interface is designed to be a helpful toolfor experimental analysis, by accessing quickly and easily divertor profiles processedfrom Langmuir probes data. This GUI allows the user:

• to select data he wants to process

• to remove faulty probes

• to display a time slice of target profiles

• to rescale the figures

• to display general data on the first figure: heat power Ptot or PNBI , upstreamdensity ne,LA, etc.

• to save the results in his own private PPFs.

Figure 5.4.: Python GUI Interface "Langmuir Probes TARGET-PROFILE"

The figure 5.4 above displays the Jsat profiles for the Inner (IT) and Outer (OT) tar-gets in the pulse #82342 as an example. In this particular case, we can see in the firstplot starting from the top that the line averaged density is ramped and it appears clearlythat the ion flux on the target first saturates and then decrease (second and third plots

25

5. A New Tool for LP Profile Analysis on Divertor Targets

from the top for the OT and IT respectively). This process is called divertor detachment.In the lower plots we can see a time slice of the IT and OT Jsat profiles.

Two functions have recently been implemented in the interface, as described below:

• Profile fit function. The first function allows the user to estimate the power (andion flux, density, temperature) decay length λq,n,T,J on the JET divertor targets,using the time slice previously desbribed and the "FIT" menu (see section 6.2 andappendix D). This will be detailed in Chapter 6.

• ELM-removal function. The second one removes the ELMs such that inter-ELManalysis and H-mode power load scaling can be performed easier. It comes froman ELM detection algorithm written by S. Devaux and A. Autricque (see [13] andappendix B), fitting heat flux or Be(II) radiation peaks at divertor.

Figure 5.5.: Python GUI Interface - inter-ELM analysis

The figure 5.5 above presents an inter-shot Jsat analysis realized for a recent pulse#87103. Its purpose was to study power load scaling in H-mode, in JET-ILW verticalOT. Green lines corresponds to beginning and end of identified ELMs. The time slice onouter target shows the cleaned inter-ELM Jsat profile (the zero value is a faulty probe),with data cumulated over 0.6s.

26

6. LP Profiles fitting forDetermining the SOL PowerDecay Length

6.1. Power decay length challenges and fittingmodels for IR data

Power exhausted from the plasma core reaches the divertor in a thin layer in which thepower density profile decreases with a characteristic decay length λq. Since present ac-tively cooled plasma facing components can not sustain heat flux densities higher than10MW/m2 in steady state, it is crucial to determine λq on present experiments and topredict what it will be for ITER.Fitting divertor profiles is needed for calculating λq with accuracy. The larger the powerdecay length is, the lower the target heat flux density is, since the power spreads outonto the divertor.

In attached regimes, the power density profiles on the divertor targets can be fitted bythe following formula (6.1), proposed by T. Eich and B. Sieglin (see [14]), in which thewidth extent of the power deposition area on the divertor targets is characterized by twovalues:

• λq which represents the power decay length at the outer midplane separatrix re-gion.

• S which is due to the competition between parallel and perpendicular transport inthe divertor volume.

q(s̄) =q0

2exp

((S

2λq

)2

− s̄

λqfx

)erfc

(S

2λq− s̄

Sfx

)+ qBG (6.1)

With s̄ = s− s0

This fit function is a convolution of the following exponential fit function q(s̄) =q0 exp(− s̄

λqfx) with a Gaussian with a width S. q(s̄) represents the heat flux density,

s is the spatial variable, s0 the strike point position, λq the power decay length, S theGaussian width, and fx the magnetic flux expansion parameter. fx > 1 is used toestimate λq at the midplane.

6. LP Profiles fitting for Determining the SOL Power Decay Length

Such fits have been processed for JET and ASDEX-Upgrade during inter-ELM inH-mode, with IR cameras data, as shown in the figure 6.1 below.

Figure 6.1.: Fits of IR Power Width on Target in H-mode, JET and ASDEX-U [14]

6.2. Power Width Fitting with LP Measurements

The "T. Eich" fit function previously described in equation (6.1) has been chosen forfitting divertor profiles with LP measurements, in both H-mode [14] and L-mode [15],assuming fx = 1. The same equation is used for all LP data: Jsat, Te, and processedQp,ne. The following figure 6.2 shows that the fit function is consistent with experimentalLP target profiles:

Figure 6.2.: Fit tests with Jsat, Te and resulting Qp outer target profiles, data cumulatedover ∼ 1s, JET, pulse #86843

28

6. LP Profiles fitting for Determining the SOL Power Decay Length

A least square algorithm has been implemented to estimate the best fit parameters,with data cumulated over a chosen time window when the strike point sweeps over thedivertor tiles. Unfortunately, the least square algorithm can easily crash if the first guessis not close enough to the solution. A "pre-fit" function - combination of two hyperbolictangents with a linear flat top - easily convergent has been introduced (see appendix C).This pre-fit function is used to extract a good first guess for the physical fit function andprevent the algorithm from diverging.The results show that a good approximation of the strike point position can be calculatedin this way and compared to the magnetic reconstruction (usually ∼ 1-2cm). Compar-ing Langmuir probes and IR cameras results will also enable us to cross-check the valueof λq, which is a crucial parameter for the feasibility of future tokamaks like ITER.

The figure 6.3 below shows 2 examples of fits performed during recent power loadscaling experiments on the vertical OT, in both L-mode (#87097 on the left) and H-mode (#87103 on the right). The discontinuity on the right side is due to calibrationissues probably induced by a partially melted LP.

Figure 6.3.: Fit of Qp OT profiles in L-mode (left) and H-mode (right)

If clean profiles are obtained in L-mode, work remains to be done in H-mode. Thislarge data dispersion in H-mode can be due to Te fitting issues and ineffective ELMdetection for relatively small ELMs, and will be investigated further.fx = 1 has been chosen, such that λ represents the decay length on the target and notestimated at the midplane. A function processing fx is being created by J. Horacek inorder to be implemented in the interface, estimate the decay length at the midplace andcompare the results with other tokamaks, since λq on the target depends on the divertorconfiguration.

29

7. Divertor and Pedestal DynamicsDuring type I ELMy on JET-ILW

ELMs are very intense and fast (∼ 1ms) phenomena, leading to pedestal collapse andhigh power and particle flux peaks at the divertor targets. Yet, some diagnostics have atime resolution high enough to observe and describe ELM dynamics, as ECE radiome-ters, Langmuir probes, or IR cameras.This chapter presents different experimental observations on ELM dynamics in type IELMy H-mode at both pedestal and outer divertor target. Here in particular, the secondunexpected pulse observed after each ELM is discussed.

7.1. Intra-ELM DynamicsThis work can be compared to a 2008 study on pedestal dynamics in ELMy H-modeplasmas in JET (see [16]). Time signature of divertor and edge plasma diagnosticsduring ELMs are shown below:

Figure 7.1.: ELM time traces at both pedestal and divertor

7. Divertor and Pedestal Dynamics During type I ELMy on JET-ILW

The pedestal temperature (Te,PED) and density (ne,PED) are respectively estimatedfrom ECE radiometers and line integrated interferometers. The ion current (Jsat) andheat flux (Q⊥) on outer target are respectively measured by LP and IR, and are integratedover the tile 5 as Dα and Be(II) spectrometer signals. ELMs are characterized by acrash in Te,PED and ne,PED, and Jsat, Q⊥, Dα and Be(II) radiation peaks as observedin the figure 7.1 above. Since Be impurities seem to be the main responsible for Wsputtering on the divertor targets (see [12]) during inter-ELM and intra-ELM, the signalfor the intensity ofBe(II) line radiation gives information on the W sputtering associatedwith an ELM (see appendix G). Dα signal is consistent with Jsat, and both show anunexpected second cold peak on the outer target few milliseconds after each ELM. Thisphenomenon is described in detail in the next section 7.2.A coherent ELM averaged signal of diagnostics time traces over the pulse #84778 (∼ 30ELMs) has been useful in order to get one typical intra-ELM profile averaged overa discharge as presented in the figure 7.2 below. An ELM detection algorithm (seeappendix B) has been used on heat flux (IR) measurements. Cumulated ELM data areaveraged using IR peaks maxima as temporal origin.

Figure 7.2.: ELM coherent averaging over the pulse #84778

Te,PED is decreasing and recovering faster than ne,PED as observed in [16], with 3msdelay between the two minima. Here, it can also be noticed that The Q⊥ peak comes

31

7. Divertor and Pedestal Dynamics During type I ELMy on JET-ILW

first on the outer target, followed by Jsat after ∼ 1ms.

7.2. Cold Pulse Regime after Type-I ELMs

As seen in the previous section 7.1, a second peak is observed in both Jsat and Dα aftereach ELM without its counterpart heat flux peak in IR signal, indicating a cold pulse. NoBe(II) nor W (I) radiation peaks (see appendix G) are measured during this regime. Itmeans that this cold pulse is not responsible for significant sputtering. This phenomenahas already been observed in ASDEX-U (divertor IIb) experiments, and one possibleexplanation was given in 2007 (see [17]). The cold pulses have also been observed ayear ago at JET, and are still being investigated. Absorption/desorption of deuterium inthe divertor are evocated, and an outgassing theory has been recently presented by S.Brezinsek in order to explain the cold pulse origin. The cold pulse interpretation will bediscussed further in the next section 7.3.

The measured delay between the ELM and the cold pulse is typically 7-8ms, for aduration of 2-4ms. According to the abrupt Dalpha radiation peaks (few 100µs) on thefigure 7.1, the cold pulse seems to be a faster phenomena than the ELM. These peaksare smoothed by the averaging on the figure 7.2At the beginning of the cold pulse regime, the pedestal electron temperature is alreadypartially recovered but the electron density is just starting to recover from the ELMcrash. At the ion flux peak, the pedestal density is also partially recovered and beginsto saturate while the temperature is temporarily slightly depleted. Then, both pedestaldensity and temperature slowly recover (∼ 10ms) their pre-ELM values.

Concerning MHD, Mirnov coils signals have been observed by E. Solano. It appearedthat very small oscillations can be observed just before the cold pulse, but they are notsimilar to an ELM collapse (see appendix I).

7.3. Discussion

Intra-ELM. It is shown that Te,PED collapses and recovers faster than ne,PED. A pos-sible explanation could be different time scale of ejection of plasma particles throughthe separatrix and recovering from the plasma core. Particles with high velocities areejected faster from pedestal than slow particles, such that measured Te,PED would de-crease faster than ne,PED. Then, Te,PED recovers since pedestal is refueled by the hotplasma core, but ne,PED would keep decreasing because of the slow ejected particles.

Cold Pulse. The cold pulse does not seem to be a "cold ELM" since no collapse isobserved in Mirnov coils signals, but it remains unclear since smalls oscillations areobserved before cold pulses and could be linked to MHD. These small oscillations, sat-uration of ne,PED, small depletion in Te,PED synchronized with the bump in Jsat andDα seem to show that it is not only a local phenomena in divertor or edge plasma andboth should be studied together.

32

7. Divertor and Pedestal Dynamics During type I ELMy on JET-ILW

The interpretation described in ASDEX-U, 2007 (see [17]) assumes that the coldpulse may be due to a cold high recycling divertor regime which occurs only at highdensities. It argues that ions originating from the ELM and reaching targets may berecycled as neutral in the SOL after a small delay of penetration into material surfaces.Applying the two-point model, since it is valid between targets and upstream plasmawith time scale of the cold peak slow enough compared to the parallel ion sonic trans-port time, they come to the relation (7.1) below:

Γtq//∼ n

4/7u

T10/7u T

5/7t

(7.1)

As Tt remains low during the second cold pulse, they infer that a Tu should increaseslower than nu during the recovery phase, such that the ratio Γt

q//increases in agreement

with experiments. This assumption seems to be qualitatively plausible since Te,PED sat-urates and ne,PED increases during the cold pulse in JET-ILW experiments.

Another possible interpretation of the cold pulse proposed by S. Brezinsek is that ab-sorbed deuterium particles in the divertor plates are massively released when the targetis abruptly heated up to 300K during the ELM. This outgassing would create a neutralcloud in front front of the divertor targets and the quick ionization of this cloud wouldproduce the Dα peak and the flux of cold ions measured by the LP.Looking at both pedestal and divertor, the neutral cloud would explain why ne,PED startsrecovering faster before the cold pulse and recovers slower after it is vanished. AbruptDα radiation peaks seem to indicate a fast ionization process in the SOL. At some point,the neutral cloud would be quickly ionizes and cold ions would follow magnetic fieldlines, one part reaching targets, the other part recovering the pedestal. These incomingcold ions would explain the slight depletion of Te,PED and the Jsat and Dα peaks. Thisinterpretation seems plausible but will require further work to conclude.

33

8. Estimation of Target ImpactEnergy per Particule duringELMs

The ITER baseline scenario, with 500MW of fusion power and Q = 10 will relyon a Type I ELMy H-mode, with 200-300kJ mitigated ELMs. In this context, tung-sten (W) particles sputtered from divertor targets during ELMs are a source of con-cern since small W impurity concentration in the plasma core would dramatically de-grade its performances. It is usually assumed that the peak target electron temperature(Te,DIV ) during an ELM is equal to the pedestal Te,PED, and that the ion impact energyE0 ∼ 3kTe + 2kTi ∼ 5kTe. An experimental confirmation of this assumption would beimportant since the Te,DIV during ELMs is a crucial parameter for the W sputtering inthe divertor. The purpose of this chapter is to study if Te,DIV can be estimated duringELMs under some physics assumptions, by coupling infrared (IR) and Langmuir probes(LP) measurements, to verify its coupling to Te,PED.

8.1. LP measurements validity

It could be argued that Jsat measured by LP cannot be used during ELMs, since thetypical ELM time scale ∼ 1ms is faster than the LP’s voltage sweep and the electronscoming from ELMs have too much energy to be repelled by the probes biasing.

- The first issue can be avoided using the fast ion saturation current of the probe(JSAF), removing data outside the saturation region and estimating the ion flux every10µs. Then, A complete profile can be obtained using coherent averaging over severalELMs, as seen in Chapter 7.

- If most of the electrons coming from ELMs are not repelled by LP, the measured ioncurrent is expected to be much lower than the real ion flux, since electrons cancel the ioncurrent in the probe. That is why LP measurements are expected to be inconsistent withother diagnostics during ELMs. Yet, coherent averaging signals in the figure 7.2 showsthat LP Jsat measurements seem to behave in agreement with Dα spectroscopy. Thisconsistency is unexpected since Te,PED is higher than −eVLP ∼ 150eV and electronsshould not be repelled by the probes. A possible explanation can be found in the free-streaming model (see [18]), which describes ELM parallel transport as a quasineutralplasma expansion into infinite vacuum. This model predicts that most of parallel elec-tron energy is transferred to ions in the SOL, as plasma from ELM remains quasineutral(so electrons remain attracted by ions). Thus, electrons only keep their perpendicular

8. Estimation of Target Impact Energy per Particule during ELMs

energy and could be slow enough to be repelled by LP. This assumption will have to beinvestigated further.

Our idea was to check consistency of LP measurements by calibrating Dα on Jsatduring the inter-ELM, and then to compare measured Jsat and the one expected fromDα calibration during ELMs. This calibration has been performed using the total ionflux from LP and the total photon flux from Dα radiation, both integrated over the tile5 surface, for several discharges. A typical calibration factor ∼ 20 was found duringinter-ELM, as shown in appendix H.

Figure 8.1.: Jsat/Dalpha calibration during ELM with coherent averaged signal

The comparison between measured and expected Jsat is shown in the figure 8.1 be-low, for the pulse #84782. It was found that both follow the same trend and the ratioJsat/Dα remains below 1.5 and above 0.5 during the ELM phase.It is observed that Jsat is not underestimated during ELMs, compared to calibrated Dα

signal, and that both signals have a similar amplitude with less than 50% discrepancyduring the ELM. This difference could be explained by different phenomena with lim-ited impact, like secondary electron emission, or high recycling regime and other plasmaconditions changing the ratio of emitted photon per incoming ion during ELMs.

Thus, it has been assumed that fast Jsat measurements can be used to study ELMdynamics on the JET divertor targets, even if work remains to be done in order to un-derstand atomic processes at stake on the target during ELMs.

35

8. Estimation of Target Impact Energy per Particule during ELMs

8.2. Target Electron Temperature Estimates byCoupling LP/IR

As previously seen, Te cannot be directly derived from LP’s voltage sweep (2ms >ELM time scale), and only the fast ion saturation current Jsat can be measured every10µs using the saturation region of the probe. Consequently, Jsat has to be coupledwith Q⊥ measured by IR cameras in order to estimate the energy of the particles reach-ing the targets. Therefore, target and pedestal temperatures can be compared in JETexperiments with various plasma currents, to test the usual assumption that the ELMpeak Te,DIV is equal to Te,PED. Jsat (LP) and Q⊥ (IR) can be locally coupled on theouter target. Assuming a sheath heat transmission coefficient γ ∼ 7-8 (as suggested in[9], [19] and [20]) and taking into account the oblic angle θ⊥ of magnetic field lines, thetarget plasma temperature T can be derived from the equation (3.9) as follows:

T =Q⊥

γ ∗ Jsat,// ∗ sin(θ⊥)(8.1)

T estimates are shown for the pulse #84778 in the figure 8.2 below. It should benoted that T corresponds to interpolated Jsat and Q⊥ values and should be interpretedcarefully, since Jsat can be underestimated when LP measurements are missing.

Figure 8.2.: Target Electron temperature estimates during ELMs, pulse #84778

36

8. Estimation of Target Impact Energy per Particule during ELMs

The main assumptions used for this model are:

• γ = 7 (sheath).

• Te = Ti = T .

• Toroidal symmetry.

• LPs measure the real Jsat.

First observations indicates that T has the expected order of magnitudes for bothinter-ELM (10-30eV as measured by LPs) and intra-ELM (0.5-1 keV) conditions, withpedestal temperatures ∼ 850eV . Then, a coherent averaging over several ELMs hasbeen used as shown in the figure 8.3 to recover complete Jsat and Qp temporal profiles,avoiding any interpolation issue, and to obtain a typical type I ELM T time trace signa-ture.

Figure 8.3.: T estimated on outer target during an averaged ELM

37

8. Estimation of Target Impact Energy per Particule during ELMs

8.3. Comparison with Pedestal Temperatures

In order to compare target temperatures to pedestal temperatures during ELMs andcheck the assumption TPED ∼ TDIV with different pedestal values (different plasmacurrents from 2MA to 3MA), an ELM database has been created over several pulses.Te,PED has been determined using JETPED (see Chapter 2), a tool specifically designedto analyze edge profiles. Both ECE and HRTS are used to estimate pedestal Te witha tangent hyperbolic fit function. Charge Exchange (CX) spectroscopy is displayed onthe figure 2.4 only to check the assumption Te = Ti at pedestal.Te,DIV has been estimated at the strike point position using the coherent averaged signalpreviously described in the section 8.2.

Figure 8.4.: Te at Pedestal VS Divertor (OT) during averaged ELMs, with 9 discharges

The figure 8.4 above presents the results for 9 pulses, with three different γ values:3, 7 and 20, since γ may depend on phenomena like secondary electron emission orenergy exchange (Ti > Te) in the SOL (see appendix J). A correlation between Te,PEDand Te,DIV is clearly identified. More pulses with higher and lower plasma currents

38

8. Estimation of Target Impact Energy per Particule during ELMs

have to be added to the database to confirm the linear dependance.

Thus, it has been found that the behaviour of LP signal remains consistent with Dα

radiation during ELMs. It may indicate that LP measurements remains valid and canbe used during ELMs, using fast ion saturation current. This consistency could be ex-plained by parallel energy transfert from electrons to ions in the SOL, as described bythe ELM parallel transport model in [18], and it will have to be investigated further.Assuming the LP measurements validity, a method to estimate TDIV during ELMs bycoupling LP and IR measurements has been described. Then, first results of the com-parison with TPED seem to show a linear dependance between TDIV and TPED.

Finally, It should be noticed that this work aimed to compare temperatures at pedestaland on the outer divertor target with a simple model; but the equivalent analysis shouldbe performed with energy, since the coupling LP/IR measures the target impact energyper particule and impact energy depends on both temperature and dynamic velocity ofthe plasma.

39

Conclusion

An accurate knowledge of divertor physics will be needed for future tokamaks likeITER, in order to prevent the divertor from being damaged by the plasma and theplasma core from being degraded by impurities. To that end, the new interface "LPTarget-Profile" is a useful standard tool to quickly process and display ion current, heatflux, temperature and density profiles on both inner and outer JET divertor targets. Ithas been used during inter-shot to study detachment and to determine strike points po-sitions, but for the most part to determine the power decay length on the outer target, inboth L-mode and H-mode. An ELM detection algorithm implemented in the interfacehas been useful to study specifically inter-ELM or intra-ELM.A cold pulse regime has been observed after each ELM in LP measurements and com-pared with other diagnostics. This cold pulse has already been observed in JET andASDEX-U; high recycling regime and outgassing are considered, but its origin remainsunclear and is still being investigated.Finally, comparison with Dα radiation shows that LP measurements may remain validduring ELMs. Therefore, IR data have been coupled with LP measurements in order tostudy the target impact energy per particule during ELMs, which would be a crucial in-formation to predict W sputtering for future tokamaks like ITER. Using a simple modelof sheath, first estimates of target electron temperature are found in expected order ofmagnitudes for both inter-ELM and intra-ELM, and they are consistent with pedestaltemperatures from ECE and HRTS. This work will require further analysis to demon-strate LP measurements validity; then impact energy estimates would allow to predictW sputtering and compare it with experiments.

Bibliography

[1] EFDA. website. http://www.efda.org/.

[2] CCFE. website. http://www.ccfe.ac.uk/.

[3] IRFM-CEA. website. http://www-fusion-magnetique.cea.fr.

[4] ITER. website. http://www.iter.org/.

[5] R. A. Pitts et al. Phys. World 19 (2006) 20.

[6] J. Wesson. Tokamaks. Oxf. Sc. Publication, 2004.

[7] G. Arnoux et al. Power handling of the jet iter-like wall. Phys. Scr. (2014) 014009.

[8] J.P.Gunn et al. The influence of magnetization strength on the sheath: Implicationsfor flush-mounted probes. Rev. Sci. Instrum. 66, 154 (1995).

[9] P.C. Stangeby. The Plasma Boundary of Magnetic Fusion Devices. Taylors andFrancis, 2000.

[10] C. Guillemaut. Modelling of the edge of a fusion plasma towards ITER and exper-imental validation on JET. PhD thesis, Aix-Marseille University: France, 2013.

[11] ASDEX-Upgrade. website. http://www.ipp.mpg.de/16195/asdex/.

[12] S. Brezinsek and JET-EFDA contributors. Plasma-surface interaction in the be/wenvironment: conclusions drawn from the jet-ilw for iter. 2014.

[13] A. Autricque. Dynamics of the divertor target heat loads in the JET tokamak.Internship Report, Plasma Boundary Group, 2014.

[14] T. Eich et al. Empirical scaling of inter-elm power width in asdex upgrade and jet.Journal of Nuclear Materials 438 (2013) S72-S77.

[15] A. Scarabosio et al. Outer target heat fluxes and power decay length scaling in l-mode plasmas at jet and aug. Journal of Nuclear Materials 438 (2013) S426-S430.

[16] M.N.A. Beurskens et al. Pedestal and scrape-off layer dynamics in elmy h-modeplasmas in jet. Nucl. Fusion 49 (2009) 125006.

[17] M. Wischmeier et al. High recycling outer divertor regimes after type-i elms athigh density in asdex upgrade. Journal of Nuclear Materials 363-365 (2007) 448-452.

Bibliography

[18] D. Moulton et al. Quasineutral plasma expansion into infinite vacuum as a modelfor parallel elm transport. Plasma Phys. Control. Fusion 55 (2013) 085003.

[19] R.A. Pitts et al. Elm transport in the jet scrape-off layer. Nucl. Fusion 47 (2007)1437-1448.

[20] D. Tskhakaya et al. Interpretation of divertor langmuir probe measurements duringthe elms at jet. Journal of Nuclear Materials 415 (2011) S860-S864.

42

Part III.

Appendix

A. Internship Description

B. ELM detection

This work comes from Adrien Autricque’s internship ("Dynamics of the divertor targetheat loads in the JET tokamak", 2014) and can be find in detail in his report (see [13]).

Figure B.1.: Peak detection by shifting IR temporal trace

The ELM detection algorithm compare the IR temporal power trace with itself in-creased by an offset, in order to detect every peak above a certain threshold. Then, atime window is determined using the power trace derivative. Each ELM can be fittedusing an hyperbolic tangent function (see appendix C).

Figure B.2.: ELM time window determination with power trace derivative

C. Hyperbolic Tangent Fit Function

A very flexible and adaptative hyperbolic tangent fit function has been developed by S.Deveaux and A. Autricque in order to fit peaks in experimental measurements (ELMtraces, divertor profiles). It uses two increasing and decreasing hyperbolic tangents witha linear flat top, as described below:

F (t) =p0 + p7

2+p4t+ p3 − p0

2tanh(p2(t−p1))− p4t+ p3 − p7

2tanh(p5(t−p1−p6))

(C.1)

Figure C.1.: Hyperbolic tangent fit function parameters

This fit function is not related to Physics, but the high number of parameters allowsthe function to fit several kinds of peak with a good accuracy and to obtain preciousinformation on the shape of the peak (maximum, growth and decay time, etc).

D. LP Target-Profile GUI

Figure D.1.: LP Target-Profile - JSAF (fast ion saturation current) profiles in H mode,pulse #84778

D. LP Target-Profile GUI

Figure D.2.: LP Target-Profile - Edit-Probes Menu

48

D. LP Target-Profile GUI

Figure D.3.: LP Target-Profile - Profile Fitting Menu

49

E. Pedestal dynamics with ECE

Figure E.1.: Radial and temporal temperature profile of edge plasma during a type IELM on JET-ILW

Figure E.2.: ECE radial profile before and after an ELM crash

F. Outer/Inner Target Comparisonduring ELMs

Figure F.1.: Outer and Inner Targets during Type I ELMs

G. Spectroscopy during ELMs

Figure G.1.: W(I), Be(II) and Dalpha spectroscopy during ELMs

H. Langmuir Probes Calibration

Figure H.1.: Calibration coefficient between ion saturation current (LP) and Dalpha ra-diation for the pulse #84778

I. Mirnov Coils collapse duringtype I ELM

Figure I.1.: Mirnov Coils collapse during type I ELM

J. Sheath Heat TransmissionCoefficient

Figure J.1.: Simple schema of sheath with oblic magnetic field lines [9]

The sheat heat transmission coefficient can be estimated with Te 6= Ti and secondaryelectron emission coefficient δe (see [9]) as follows:

γ ≈ 2.5TiTe

+2

1− δe− 0.5 ln[(2π

me

mi

)(1 +TeTi

)(1− δe)−2] (J.1)

Figure J.2.: Sheath heat transmission coefficient as a function of Ti / Te [9]

K. Physical Sputtering

Figure K.1.: Physical sputtering yield of D+ on W and Be surfaces

Yp(E0, α = 0) = Q ∗ Sn(ε) ∗ g(Eth/E0) (K.1)

Yp = Physical sputtering yield, Q = Yield Factor, Sn = Nuclear stopping power,ε = E0

ETFReduced energy, with Eth, ETF the Thomas-Fermi and threshold energy.

Sn(ε) =3.441

√ε ln(ε+ 2.718)

1 + 6.355√ε+ ε(6.882

√ε− 1.708)

(K.2)

g(δ) = (1− δ2/3)(1− δ)2 (K.3)

L. Free Streaming Model

Please, see [18] for the complete theory of "quasineutral plasma expansion into infinitevacuum as a model for parallel ELM transport".

A parallel energy transfert from electrons to ions is expected in the SOL, as shown inthe figure below. The free-streaming model (without sheath effect) predicts the targetheat and particle flux during ELMs, assuming Ti0 = Te0, ni0 = ne0, and cs/vTe ∼ 0(derived from equations (31) and (34) for x = L in [18]):

Jsat(t) = ne ∗ σ0 ∗τLt2∗ exp(− 1

2(t/τL)2) (L.1)

Qtot(t) = Jsat(t) ∗ T0 ∗ [(cs/vT i)

2

2(t/τL)2+ 2] (L.2)

With σ0 the initial extent of the ELM filament, cs the sound speed, τL = Lcs

the char-acteristic parallel transport time.

Figure L.1.: Thermal, dynamic and total energies for electrons and ions as a function oftime for a hydrogen plasma with Te0 = Ti0 [18]