Visible Light Measurements on the COMPASS Tokamak

Visible light measurements on the COMPASS tokamak

by Olivier Van Hoey Faculty of Engineering Department of Applied Physics Head of the department: Prof. Dr. Ir. C. Leys

Visible light measurements on the COMPASS tokamak

by Olivier Van Hoey

Promoter: Prof. Dr. Ir. G. Van Oost Copromoter: D. Naydenkova

The research reported in this thesis was performed at the Institute of Plasma Physics AS CR, Za Slovankou 1782/3, 182 00 Prague 8, Czech Republic

Thesis submitted in order to obtain the degree of Master of Physics and Astronomy, option: Research

Academic year 2009-2010 The most exciting phrase to hear in science, the one that heralds new discoveries, is not ’Eureka!’, but ’That’s funny...’ - Isaac Asimov.

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world - Archimedes

Nothing in life is to be feared. It is only to be understood - Marie Curie

No amount of experimentation can ever prove me right; a single experiment can prove me wrong - Albert Einstein

The science of today is the technology of tomorrow - Edward Teller Allowance to loan The author gives permission to make this thesis available for consultation and to copy parts of the thesis for personal use. Any other use is limited by the restrictions of copy- right, in particular with regard to the obligation to mention the source explicitly when citing results from this thesis.

Olivier Van Hoey May 20, 2010

i Acknowledgment The achievement of this thesis was not possible without the help and support of a lot of people. I would like to thank everyone who contributed to the realization of this thesis. The time I spent working on the project was very instructive and most of it even pleasant. I learned a lot about plasma physics, spectroscopy, tokamaks and fusion research. Furthermore, I met nice people from different places in the world and I learned a lot about Czech culture and habits. First of all, many thanks go to Prof. Guido Van Oost. He gave me the idea for the subject of my thesis and made it possible for me to go to Prague for performing this work. I could always go to him if I had any questions or problems concerning the project. I would also like to thank Diana Naydenkova. She was my mentor during the two months I stayed at the Institute of Plasma Physics in Prague. Due to her help I acquired a lot of knowledge. She guided me through the project and was always there if I had questions or problems. She was a very nice person to work with. Further, I also pay tribute to a lot of other people at the Institute of Plasma Physics. The institute provided me a comfortable office and a very nice flat. Many thanks go to Dr. Jan Stöckel. He gave me some very good ideas for my project and his comments concerning my work were very helpful. Also Dr. Vladimir Weinzettl deserves special thanks. He solved a lot of problems, especially concerning the access to the data server. Of course I also want to thank the rest of the tokamak team of the Institute of Plasma Physics. In a project like this, good results can only be obtained by the cooperation of all team members. The tokamak department at the Institute of Plasma Physics was a very pleasant environment to work in. Last but certainly not least, I would like to thank family and friends. They always supported me and showed a lot of interest in my work. Special thanks goes to my parents and my girlfriend Lisanne. My parents always encouraged me in my studies and made it possible for me to go to university. My girlfriend was there for me if things did not go as I desired or when I was stressed. She always succeeded to keep me motivated.

ii Metingen van het zichtbare licht aan de COMPASS tokamak

door Olivier Van Hoey

Afstudeerwerk ingediend tot het behalen van de graad van Master in de Fysica en Sterrenkunde, optie: onderzoek

Academiejaar 2009-2010

Universiteit Gent Faculteit Ingenieurswetenschappen

Promotor: Prof. Dr. Ir. G. Van Oost Copromotor: D. Naydenkova

Samenvatting

De komende decennia zal de vraag naar energie onvermijdelijk alleen maar toenemen. Vandaag de dag wordt het merendeel van onze energie gewonnen uit fossiele brandstoffen. De voorraad van deze waardevolle grondstoffen slinkt echter zienderogen. Bovendien gaat het verbranden van fossiele brandstoffen steeds gepaard met de uitstoot van CO2. Fossiele verbranding moet dus zo snel mogelijk vervangen worden door een alternatieve vorm van energieproductie. Kernfusie is een veelbelovende kandidaat-opvolger. Er is geen uitstoot van broeikasgassen, de fusiebrandstoffen zijn vrijwel onuitputbaar, ongevallen zoals in Tsjernobyl zijn uitgesloten en er is enkel kortlevend nucleair afval. Jammer genoeg is men er echter nog altijd niet in geslaagd om netto energie te winnen uit het fusieproces. Er zijn nog een aantal moeilijke hindernissen die moeten overwonnen worden. De meeste vooruitgang werd reeds geboekt in het tokamakonderzoek. In een tokamak wordt het hete fusieplasma opgesloten met behulp van sterke magneetvelden. Met het International Thermonuclear Experimental Reactor (ITER) project wil men aantonen dat het in een tokamak uiteindelijk toch mogelijk zal zijn op een commerciëlemanier energie te produceren met kernfusie. Eénvan de belangrijkste problemen waar men nog mee te kampen heeft, is de interactie tussen de hete fusiebrandstof en de binnenste reactormaterialen. Daarom wordt er tegenwoordig over heel de wereld veel onderzoek verricht in deze context. In 2007 werd de COMPASS tokamak van het UKAEA Culham Science Center (GB) opnieuw ge¨ınstalleerdin het Institute of Plasma Physics van de Academy of Science in Praag (Tsjechië). COMPASS is de kleinste divertormachine met een duidelijke H-mode en parameters die uiterst relevant zijn voor ITER. De tokamak is zeer flexibel en kosten- efficiënt. Daarom heeft COMPASS heel wat onderzoekspotentiaal. Het project in het

iii Institute of Plasma Physics is echter nog jong. Er zijn nog maar een beperkt aantal diag- nostieken beschikbaar. Bovendien werken het data acquisition system, het shape control system en het plasma position control system nog niet zoals het hoort. Daarom is men nu vooral bezig met het op punt stellen van die systemen en het optimaliseren van de ontladingen. Het geplande wetenschappelijk programma van het tokamakdepartement in Praag is o.a. gefocust op plasma-wandinteractie. De studie van het zichtbare licht uitge- zonden door het waterstofplasma in de COMPASS tokamak is zeer nuttig in deze context. Tijdens dit project werden gedurende 2 maanden de eigenschappen van de ontladingen in COMPASS bestudeerd. De nadruk lag op de studie van het zichtbare licht. Hiertoe werden de Ocean Optics HR 2000+ spectrometer en verschillende photomultiplier tubes (eventueel met interferentiefilters) gebruikt. Mijn eerste verblijf aan het Institute of Plasma Physics was van 06/07/2009 tot 06/08/2009. Eerst werden de HR 2000+ spectra bestudeerd. Vrijwel alle spectra werden ge¨ıntegreerd over de volledige duur van de ontladingen. Het merendeel van de ontladingen is momenteel namelijk te kort en de spectrometer is niet gevoelig genoeg om meerdere spectra op te nemen tijdens éénontlading. Spectra in COMPASS worden duidelijk gedomineerd door lijnstraling. De Hα en Hβ lijnen van waterstof zijn meestal de helderste lijnen. Men observeert ook vaak lijnen van koolstof en helium. De koolstof is afkomstig van de binnenste reactormaterialen en kan via allerlei plasma-wandinteracties in het plasma terecht komen. De helium is een overblijfsel van het kuisen van de reactor met een helium glow discharge. In ontladingen met heel sterke plasma-wandinteractie of disrupties duiken veel meer lijnen op. Naast waterstof-, helium- en koolstoflijnen zijn er dan ook andere lijnen zichtbaar. Wolfraam kan bijvoorbeeld in het plasma terechtkomen door het sput- teren van de wolfraamprobes in de divertorplaten. In COMPASS worden de breedtes van de lijnen gedomineerd door instrumentele- en Dopplerverbreding. Door het bepalen van de instrumentele breedte met behulp van een calibratiebron is het dan theoretisch gezien mogelijk om de ionentemperatuur te berekenen op basis van de experimenteel gemeten breedte. Het werd echter aangetoond dat de resolutie van de HR 2000+ niet volstaat om de vrij lage ionentemperaturen in COMPASS met een aanvaardbare precisie te bepalen. Door de beperkte resolutie was het ook niet mogelijk om het profiel van de Hα-lijn grondig te bestuderen. Het belangrijkste werk tijdens mijn eerste verblijf in Praag was de studie van de ontladingsparameters in navolging van [1]. De parameters die bestudeerd werden zijn de stroom door de centrale winding, de kringspanning, de plasmastroom, de intensiteit van de harde X-straling, de intensiteit van de zichtbare straling, de intensiteit van de Hα-lijn, de druk, de duur van de ontlading en het zichtbare spectrum. Het doel van de studie was te bekijken onder welke condities de ontladingen in COMPASS optimaal zijn. De belangrijkste conclusie was dat lange ontladingen en hoge plasmastromen op dit moment in COMPASS enkel mogelijk zijn als de druk in het interval 43 - 93 · 10−6 mbar ligt. In dit gebied konden 3 types ontladingen worden onderscheiden met significant verschillende eigenschappen. Voor hogere drukken waren alle ontladingen zeer gelijkaardig. Enkel korte ontladingen werden geobserveerd. Voor lagere drukken kon niet onmiddellijk een conclusie getrokken worden vanwege te weinig data. Jammer genoeg zijn zelfs de lange ontladingen in het intermediaire drukgebied nog niet lang genoeg. Bovendien treden er ook vaak disrupties en sterke plasma-wandinteracties op. De ontladingen in COMPASS zijn nog niet helemaal geoptimaliseerd. Een aantal ideeënom te eigenschappen van de ontladingen in de toekomst te verbeteren zijn

iv • toro¨ıdaalmagneetveld opdrijven tot zijn maximale waarde • het feedback systeem voor de controle van de positie van het plasma in orde brengen • optimaliseren van de stroomproﬁelen voor de verschillende spoelen • betere conditionering van de vacu¨umkamer • langere baking en glow discharge cleaning • sterkere pre¨ıonisatie

Mijn tweede verblijf aan het Insitute of Plasma Physics was van 24/02/2010 tot 24/03/2010. Een eerste studie die toen gemaakt werd behandelt de thermal ionization phase. Er werd getracht de experimenteel waargenomen tijdsevolutie van de elektronendichtheid en van de Hβ-intensiteit tijdens deze fase analytisch te beschrijven met het eenvoudige model voorgesteld in [2]. Er werden echter een aantal signiﬁcante afwijkin- gen gevonden tussen het model en de metingen. Er bestaat nog geen zekerheid over de oorzaak. Enkele mogelijke verklaringen zijn

• mogelijk bestaat het plasma initieel vooral uit koolstof • de interferometer en de photomultiplier tube hebben een verschillende observatiehoek • mogelijk zijn de A/D convertoren van het data acquistion system niet perfect gesyn- chroniseerd

Verder onderzoek is nodig om met zekerheid te kunnen zeggen wat de oorzaak van de afwijking is. Op basis van hetzelfde model werd nog een ruwe schatting gemaakt voor de elektronentemperatuur tijdens de thermal ionization phase. De berekende tempera- turen lagen voor alle ontladingen rond de 8 eV. Een tweede deel van het werk betreft de simulatie van de Hα- en Hβ-intensiteit met de simulatiecode FLYCHK [3]. Als input werd de tijdsevolutie van de elektronendichtheid en -temperatuur gevraagd. De evolu- tie van de dichtheid werd gemeten met de 2 mm microgolf interferometer. De elektronentemperatuur wordt momenteel niet gemeten in COMPASS. De tijdsevolutie van de elektronentemperatuur kon daarom enkel geschat worden. De tijdsevolutie van de Hα- en Hβ-intensiteit werd gemeten met twee photomultiplier tubes. Er werd een vrij goede kwalitatieve overeenkomst bekomen tussen de experimentele data en de FLYCHK simulatie. De twee pieken die typisch opduiken in de tijdsevolutie van de Hα- en Hβ-intensiteit konden worden gereproduceerd. De eerste piek is gerelateerd aan de volledige ionisatie van het waterstofgas. De tweede piek is waarschijnlijk gerelateerd aan de introductie van koude waterstof en onzuiverheden door plasma-wandinteractie. Ten slotte werd ook nog een ruwe schatting gemaakt voor de waterstofflux op basis van de tijdsevolutie van de Hβ-intensiteit. Door calibratie van de photomultiplier tube kon het Hβ-signaal worden S omgezet in de fotonenflux. Uit de ADAS database [4] werden de XB -factoren voor Hβ gehaald als functie van elektronendichtheid en -temperatuur. Daarmee kon dan tenslotte de fotonenflux worden omgezet in de flux van waterstofatomen. Er werd echter geen reken- ing gehouden met de contributie van waterstofmoleculen waardoor de berekening slechts een ruwe schatting is.

Trefwoorden: spectroscopie, kernfusie, energie, plasma, tokamak, COMPASS

v Contents

1 Introduction: The world energy problem 1

2 Thermonuclear fusion 6 2.1 Energy release in fusion reactions ...... 6 2.2 Coulomb barrier ...... 8 2.2.1 Coulomb barrier ...... 8 2.2.2 Conquering the Coulomb barrier in a hot fusion plasma ...... 10 2.3 Fusion fuels ...... 11 2.3.1 Possible fusion reactions ...... 11 2.3.2 Deuterium ...... 12 2.3.3 Tritium ...... 13 2.3.4 Lithium ...... 14 2.4 Energy balance of a fusion power plant ...... 15

3 Tokamaks and the ITER project 18 3.1 Conﬁnement in a tokamak ...... 18 3.2 Tokamak research ...... 21 3.2.1 Historical sketch of the fusion research ...... 21 3.2.2 ITER tokamak ...... 24 3.3 Pros and cons of tokamaks for future energy production ...... 27

4 Plasma-wall interaction and the plasma edge 29 4.1 Plasma-wall interaction ...... 29 4.2 Plasma edge ...... 31 4.3 Importance of PWI for ITER and future fusion machines ...... 35 4.3.1 Impurities ...... 35 4.3.2 Recycling ...... 36 4.3.3 Material degradation and dust formation ...... 36 4.3.4 Major concerns for ITER ...... 37 4.4 Possible plasma facing materials ...... 38

5 Radiation measurements and spectroscopy in tokamak research 41 5.1 Radiation measurements and spectroscopy ...... 42 5.1.1 Radiation quantities ...... 42 5.1.2 Spectroscopic instruments ...... 42 5.1.3 Radiation detectors ...... 46 5.1.4 Calibration ...... 50

vi 5.2 Radiation from a plasma ...... 51 5.2.1 Radiative processes in a plasma ...... 52 5.2.2 Collisional processes in a plasma ...... 54 5.2.3 Population kinetics of atomic levels in a plasma ...... 55 5.2.4 Line broadening mechanisms in a plasma ...... 60 5.3 Importance for tokamak research ...... 65 5.3.1 Hydrogen atoms ...... 66 5.3.2 Hydrogen molecules ...... 69

6 Experimental setup 71 6.1 COMPASS tokamak ...... 71 6.2 Ocean Optics HR 2000+ spectrometer ...... 77 6.3 Photomultiplier tubes ...... 79

7 Visible light measurements on COMPASS 82 7.1 First stay at the IPP ...... 82 7.1.1 Study of the visible spectra ...... 82 7.1.2 Study of the discharge parameters ...... 88 7.2 Second stay at the IPP ...... 99 7.2.1 Analysis of the start-up phase ...... 99 7.2.2 Modeling of measured Hα and Hβ intensities with FLYCHK . . . . . 105 7.2.3 Determination of hydrogen and carbon ﬂuxes ...... 110

8 Conclusions and suggestions for future experiments 115

vii List of Figures

1.1 Evolution of the CO2 concentration in the atmosphere ...... 4 1.2 Diﬀerent energy sources ...... 5

2.1 Average binding energy per nucleon for the diﬀerent isotopes ...... 7 2.2 Schematic representation of the coulomb barrier ...... 10 2.3 Energy dependence of the cross sections for the diﬀerent fusion reactions . . 12 2.4 The most important fusion reactions with their corresponding Q values . . 12 2.5 First commercial heavy water plant in Vemork (Norway) ...... 13 2.6 Brine in the Chilean Atacama desert used for the production of lithium . . 15 2.7 Evolution of the achieved fusion triple product ...... 16

3.1 Stepwise introduction of the tokamak concept ...... 20 3.2 The Russian T1 at the Kurchatov Institute in Moscow was the ﬁrst tokamak 22 3.3 JET at Culham (UK), the current world’s biggest tokamak ...... 22 3.4 The ITER site as it looks like for the moment ...... 23 3.5 The ITER site how it should look like in 2018 ...... 23 3.6 Model of ITER with its main components ...... 25

4.1 Poloidal diagram of the ﬂux surfaces for limiter or divertor conﬁguration . . 33 4.2 Most important atomic and molecular reactions in the plasma edge . . . . . 35 4.3 Predicted number of discharges in ITER for the 4 proposed material choices 40

5.1 Profile of a ruled diffraction grating with blaze angle θ ...... 45 5.2 The Czerny-Turner arrangement ...... 45 5.3 Schematic layout of a photomultiplier tube ...... 48 5.4 Radiative recombination emission coefficient for a hydrogen plasma . . . . . 54 5.5 Gaussian, Lorentzian and Voigt profiles with equal FWHM ...... 61 5.6 The hydrogen spectrum and the Bohr model ...... 67

6.1 Schematic representation of the COMPASS tokamak ...... 72 6.2 Comparison of the poloidal cross sections of several ITER relevant tokamaks 72 6.3 Inside view of the COMPASS tokamak vacuum vessel ...... 72 6.4 Close-up on part of the COMPASS inner vacuum vessel ...... 72 6.5 Transport of the COMPASS tokamak from Culham to Prague ...... 73 6.6 COMPASS tokamak installed at the IPP ASCR, Prague ...... 73 6.7 Poloidal ﬁeld coils in the COMPASS tokamak on a poloidal cross section . . 75 6.8 Schematic representation of the poloidal ﬁeld coils in COMPASS ...... 75 6.9 Outside view of the Ocean Optics HR2000+ portable spectrometer . . . . . 77

viii 6.10 Schematic interior view of the Ocean Optics HR2000+ portable spectrometer 77 6.11 Relative eﬃciency curve for the Ocean Optics H9 1200 grooves/mm grating 78 6.12 HR 2000+ spectral range and resolution as function of starting wavelength 78 6.13 Localization of the ports for the radiation measurements ...... 79 6.14 Absolute sensitivity curves for diﬀerent photocathodes ...... 80

7.1 Time integrated HR 2000+ visible spectrum (COMPASS shot 505) . . . . . 83 7.2 Time resolved HR 2000+ visible spectrum (COMPASS shot 862) ...... 84 7.3 Time evolution of Ip and visible radiation (COMPASS shot 862) ...... 85 7.4 Gaussian fitting of the Hα line (COMPASS shot 496) ...... 88 7.5 The four different IMFPS profiles used during the experiments ...... 89

7.6 Typical waveforms for IBT , IMFPS and IEFPS at COMPASS ...... 91 7.7 Table with the most important discharge parameters for the studied shots . 92 7.8 Scatter plots with ∆t, Ip and Vloop as function of p ...... 93 7.9 Typical spectra at COMPASS ...... 96 7.10 Typical Vloop, Ip, allV IS, Hα and HXR profiles at COMPASS ...... 97 7.11 Data plots for a typical shot (COMPASS shot 1132) ...... 102 7.12 Transmittance of the Hα interference filter as function of wavelength . . . . 106 7.13 Ideal time evolution of electron temperature and density during a shot . . . 108 7.14 Experimental time profiles of ne,Hα and Hβ (COMPASS shot 1132) . . . . 109 7.15 Simulation of Hα and Hβ radiation with FLYCHK ...... 109 S 7.16 XB ratio in the case of Hα for hydrogen atoms and molecules ...... 112 7.17 Hydrogen flux deduced from the Hβ signal (COMPASS shot 1132) . . . . . 114

ix List of Tables

1.1 Primary power consumption in the world ...... 2 1.2 Contribution of diﬀerent energy sources to the primary power consumption 3 1.3 Years of use of diﬀerent fuels at the current rate of power consumption . . . 3

2.1 Fuel consumption for diﬀerent energy production methods ...... 8

5.1 The four visible hydrogen Balmer lines and their corresponding wavelengths 68

6.1 Basic parameters of the COMPASS tokamak ...... 71 6.2 Basic parameters of the Ocean Optics HR2000+ portable spectrometer . . . 77

7.1 Instrumental broadening of the HR 2000+ spectrometer ...... 87 7.2 Doppler temperature determination for the CII line at 657.8 nm ...... 87 7.3 Parameters of the shots studied during my second stay at the IPP . . . . . 103 S 7.4 XB ratio for Hβ as function of ne and Te ...... 113

x Chapter 1

Introduction: The world energy problem

The Kyoto Protocol, global warming, CO2 emission reduction, the ecological footprint, greenhouse gases, renewable energy sources, nuclear non-proliferation,... Anyone who claims to have never heard about these things, must be living on a different planet. Newspapers, the internet, magazines and television shows bulge with these trendy terms. Googling for ’global warming’ results in no fewer than 30 900 000 hits! Al Gore’s effort for spreading his ’Inconvenient Truth’ delivered him the Noble Peace Prize. Nowadays the public support for environmental protection and wise energy management is getting wider and wider. Unfortunately it is not just a hype. There really is a problem. It is not easy to gain objective information about such a complex issue. Most publications are highly colored by the interests of the author. The best thing to do, is looking up the numbers and based on these draw your own conclusions. But even numbers appear to be very dependent on the source in this case. A lot of political and economical interests are intertwined with the energy problem. Though it is very important that people form an opinion about the issue. The future of mother earth is something that involves everyone. A very good book in this context is [5]. In this work MacKay tries to cover the issue as objective as possible with a lot of facts and figures. In this introductory chapter I will try to convince you that there is indeed a problem. The used numbers and graphs are based on [6]. Of course this is not the place to elaborate the whole issue. The only point I want to make, is that something has to be done. We have to stop the talking and start the acting. How much energy do we use now and how much energy will we use in the future? Let us take a look at table 1.1. It shows the per capita energy consumption in 2004 for some selected countries. Most striking is the large spread. A Qatari consumes 28 000 W, while a Chadian must be satisfied with 12 W. An average earthling consumes 2 340 W, which is still low compared to the European energy need of 4 900 W. Based on this information it is not difficult to predict that during the next decades the average energy need per person will increase drastically because of economical growth in the less developed countries. Especially densely populated giants in full development such as China and India will give and enormous boost to the world energy demand. An amplifying factor is the increase of the world population. The most realistic model of a study made by the World Energy Council and the International Institute for Applied System Analysis at the end of last

1 Table 1.1: Per capita total primary power consumption for selected countries [6] Country Per capita consumption (2004) Qatar 28 000 W United Arab Emirates 31 000 W Iceland 16 800 W Norway 14 200 W Canada 14 000 W Kuwait 15 700 W USA 11 400 W Australia 8 800 W Belgium 9 000 W The Netherlands 8 400 W Russia 7 000 W Japan 6 000 W Germany 6 000 W Europe (West and East) 4 900 W South Africa 3 900 W Brazil 1 660 W Cuba 1 400 W China 1 500 W Zimbabwe 570 W India 490 W Vietnam 380 W Mozambique 240 W Congo (Kinshasa) 51 W Chad 12 W World 2 340 W

2 Table 1.2: Contribution of diﬀerent energy sources to the primary energy production in the world [6] Energy source Contribution to primary energy production (2001) Oil 38% Coal 24% Gas 24% Fission 6.3% Hydro-electricity 6.4% Solar, wind, wood, waste 1.3%

Table 1.3: Years of use of different fuels at the current rate of consumption [6] Fuel Proved recoverable Years of use at the current reserves (2003) rate of consumption Coal 0.9 · 1012 tons 210 Crude oil 1.2 · 1012 barrels 30-40 Natural gas 170 · 1012 m3 60-70 Uranium 2.0 · 106 tons 2400-3000 century predicts a doubling of the world energy demand from 15 TWyr to 30 TWyr by 2050. Where does our energy come from? Table 1.2 shows the contribution of different energy sources to the primary world energy production. Table 1.3 shows how long it will take us to consume all known reserves of fossil fuels and uranium ore at the current rate of consumption. More than 92 % of our energy originates from these raw materials. Fossil fuels on their own are responsible for 86 %. It is clear that these materials are not inexhaustible at all. At the current pace we will run out of fossil fuels very soon. This would not only lead to political instabilities and price increases. The exhaustion of the valuable fossil materials would be a disaster for the chemical and pharmaceutical industry as well. And what about ’global warming’? This is a very controversial topic. Fact is that the earth is a very complex ecosystem in which everything is related with everything. Even specialists disagree on the issue. I will thus not venture to make a statement about the different theories. I will only focus on the observations considering the evolution of the CO2 content in the earth’s atmosphere. The contribution in ppm during the last 1000 years is given in figure 1.1. What we see here cannot be misunderstood. Apparently the CO2 concentration has been leveled at a value of about 280 ppm for a long time. There is even evidence that the concentration has remained at this level for the last 160 000 years. But around the Industrial Revolution the concentration suddenly started increasing steeper and steeper. Today we are already at a level of more than 360 ppm. When you see this graph it is very difficult to carry on saying it is probably just a fluctuation of nature. There is little doubt the CO2 emission by our intensive use of fossil fuels is the cause of this clear change. The next step in the reasoning is much more difficult. What is the effect of this change? A lot of scientists claim that it causes a steadily increase of the average earth temperature. ’Nice!’, you could say, ’No thick coats anymore!’. Unfortunately it is not

3 Figure 1.1: Evolution of the CO2 concentration in the atmosphere (in ppm) during the last 1000 years [6] that simple. Even a small temperature increase could imply a complex sequence of events very difficult to predict. Ocean currents, winds, the sea level and a lot of other things are all very dependent on the earth’s temperature. And at this very moment there are indeed clear proofs that temperature is increasing. The most famous example is the melting of the glaciers. Although one cannot yet prove with 100 % certainty a causal link between the CO2 level and the temperature increase, the fact remains that we are performing a very dangerous experiment with ourselves as guinea pigs. If this change in CO2 level indeed appears to have adverse effects to our ecosystem in a few decades, then we can not just stop these effects. First of all, we cannot simply end the emission immediately. Secondly, the CO2 cycle is very slow. It would take at least 100 years for the earth to restore the situation. And last but not least, nobody knows if this playing with our ecosystem is a reversible process. There is a chance that hysteresis will prevent us from restoring the ecosystem’s original state. I think my message is clear. Let me summarize. Today fossil fuels form the bulk of our energy production. There are two big problems with these kind of fuels. Firstly, they are exhaustible. Even at the current pace of consumption we will run out of fossil fuels very soon. Furthermore, it will be impossible not to exceed this pace greatly because the energy demand per person and the world population are both increasing. For political stability, energy prizes and the chemical and pharmaceutical industry it would be much better not to use up all the fossil fuels. Secondly, the CO2 emission, inevitably coupled to fossil fuels, causes a clear change in the composition of the earth’s atmosphere. This could be very dangerous. So there are no excuses. We have to change our current way of energy production and consumption drastically. Everybody has to increase the efficiency of their energy use. Scientists and engineers have to develop alternative ways of energy production. World leaders have to stimulate the process. It is in the context of this very important issue that I have chosen the topic for my

4 Figure 1.2: There are a lot of possible energy sources. All have their pros and cons thesis. Finding a decent substitution for the fossil fuels is not an easy task. A lot of environmental and economical criteria need to be fulfilled. A lot of research is necessary. Possible successors of the fossil fuels are fission, renewables, fusion or a combination of these. All three production methods have a lot of potential. For me fusion seemed the most interesting topic to work on as a physicist. Like all other candidates fusion has its pros and cons. The idea behind thermonuclear fusion is treated briefly in chapter 2. At the moment scientists have thought out different ways to realize fusion: tokamaks, stellarators, inertial fusion,... All concepts are still in an experimental phase. This thesis deals with the tokamak concept. The principal of this approach is explained in chapter 3. The experiments concerning tokamaks are well organized. A lot of countries all around the world work together on the ITER project. More details about this project can be found in the same chapter. In the context of my thesis I worked on the COMPASS tokamak in Prague. The tokamak research is very broad. Therefore, I concentrated on one topic, namely the measurement and spectroscopy of visible light. Visible light from the fusion fuel can learn us a lot about the interaction processes going on between the fusion fuel and the inner materials of the tokamak. Some general concepts concerning this interaction are given in chapter 4. Light measurements and spectroscopy in the tokamak research is discussed in chapter 5. More information about the COMPASS tokamak and its diagnostics can be found in chapter 6. In chapter 7 the results of my research at COMPASS are discussed. In the last chapter I make some conclusions and give some ideas for future experiments.

5 Chapter 2

Thermonuclear fusion

I could easily write my thesis without even talking about fusion. Actually the fusion process does not occur in the COMPASS tokamak. It is a small experimental reactor. But I think it is important to place a study in its broader context. In this way both the reader and the researcher himself are able to fully grasp the aim of the project. What are scientists doing and why are they doing it? Therefore, I will start with answering some basic questions about nuclear fusion. Where does the fusion energy come from (section 2.1)? What makes the realization of fusion so hard (section 2.2)? What kind of fuels does a fusion reactor need (section 2.3)? Under which conditions does a fusion reactor really produces energy (section 2.4)?

2.1 Energy release in fusion reactions

How does the fusion process work? The production of fusion energy is in a way similar to the burning of fossil fuels. During combustion of traditional raw materials - like oil, gas and coal - the chemical bonds of the hydrocarbons are broken in order to form stronger bound molecules with oxygen, like H2O and CO2. The bonds are thus rearranged such that the total mass of the reaction products is smaller than that of the reagentia. The famous Einsteinian relation E = mc2 then implies the release of energy. Chemical bonds are realized by the electromagnetic interaction. Typical binding energies are in the electronvolt range. Hence, one can expect an energy release of the same order of magnitude. During fusion it are the nuclear bonds of the fusion raw materials that are rearranged to get stronger bound nuclei. The equivalence of mass and energy again implies an exothermic reaction. Fusion, therefore, is analogue to the common burning process. The fusion analogs of electronic rearrangement, the electromagnetic interaction and fossil fuels are nuclear rearrangement, the nuclear interaction and light nuclei. However, altering the nuclear bounds is not as easy as altering the chemical bounds, as explained later on. The nuclear interaction is much stronger than the electromagnetic interaction. Typical nuclear binding energies are in the MeV range, about 6 orders of magnitude higher than chemical binding energies. Furthermore, in contrast to the electromagnetic interaction, the range of the nuclear interaction is ﬁnite. Beyond several femtometers the attractive force between protons and neutrons can be neglected. As will be explained in the next subsection this is the main source of diﬃculties appearing in the practical realization of fusion.

6 Figure 2.1: Average binding energy per nucleon as function of the mass number A

The average binding energy per nucleon as function of the isotope mass number A is depicted in figure 2.1. The shape of this curve can be understood by taking into account coulombic proton-proton repulsion, attraction caused by the strong and short ranged nuclear force and some less intuitive quantum mechanical effects. In [7] this model is described into more detail. Apparently Fe56 is the strongest bound nucleus. The graph also shows that there are two possibilities to produce energy by rearranging the nuclear bonds. One can go to the Fe56 peak from the right or from the left. The first approach is very well known. Heavy nuclei like U235 and Pu239 can be split into typically two lighter and stronger bound nuclei. A lot of energy, around 200 MeV per reaction, is released in the process. The fission process is realized for instance in common nuclear power plants. The second approach is fusion. Light nuclei like hydrogen (H1), deuterium (H2 or D) and tritium (H2 or T) can be fused to form a heavier nucleus together with a few tens of MeV’s energy. This energy is released in the form of kinetic energy of the reaction products and sometimes also by photon emission. The underlying reason for the high energy release during the fusion process is the high binding energy between nucleons. Only the bonds between quarks are stronger. The burning of light nuclei to heavy nuclei, therefore, must be very efficient. Much more efficient than fossil fuel burning. Actually all energy produced by burning fossil fuels ultimately comes from fusion. Plants convert CO2 and H2O into hydrocarbons. This photosynthetic reaction is endothermic. The necessary energy is supplied by the sun. And of course our indispensable star is only able to radiate because of fusion processes taking place in its core. Some of the so produced hydrocarbons become buried deep into the ground. After millions of years under influence of high heat and pressure levels these

7 Table 2.1: Fuel consumption for different energy production methods [6] Method Annual fuel consumption for a 1 GW power plant Coal 2 700 000 tons Oil 1 900 000 tons Fission 28 tons of U02 Fusion 100 kg D and 150 kg T hydrocarbons are chemically altered to form our fossil fuels. So the energy stored in gas, oil and coal actually comes from the fusion processes in the solar core. Therefore, it is not really surprising that fusion itself is much more efficient than the burning of fossil fuels, which is only the recovering of part of the fusion energy of the sun. Every conversion from one form of energy into another form of energy unavoidably implies partial transformation to useless heat, as predicted by the second law of thermodynamics. In the same way, one can say that fusion must be more efficient than fission. Heavy nuclei are formed by fusion in the stars. Hence, the energy stored in heavy nuclei comes from fusion as well. Indeed, from the fact that the left slope in figure 2.1 is much steeper than the right slope, one can conclude that fusion is even more efficient than fission. That fusion requires only small amounts of fuel is clearly visible in table 2.1, where the estimated annual fuel consumption of a hypothetical 1 GW power plant for different energy production methods is given. This is a first advantage of fusion. The ratio of energy release to raw material mass is very high.

2.2 Coulomb barrier

2.2.1 Coulomb barrier But no roses without thorns. Unfortunately fusion is not only much more efficient than fission or burning fossil fuels, it is also much more difficult to realize. What makes the realization of fusion so hard? The main issue is depicted in figure 2.2. Suppose one wants to fuse a deuterium nucleus with a tritium nucleus. Starting at an internuclear distance r = +∞, the two nuclei are brought together with a certain center of mass energy Ecm. At first the repulsive electromagnetic interaction predominates. The nuclear force can simply be neglected because of its finite range. In this repulsive regime the potential energy function U(r) can be approximated by the coulomb potential for point like particles. If the center of mass energy is large enough, the nuclei can be brought so close to each other that the internuclear distance r becomes comparable with the sum of the nuclear radii. The attractive interaction between the two nuclei then comes into play. The range of the nuclear force rnf is approximately equal to the sum of the nuclear radii. The enormous strength of the attraction between the nuclei now allows us to neglect the coulombic repulsion. On the potential energy diagram this attractive regime is approximated by a steep potential well between r = 0 and r = rnf . The potential energy at the bottom of this well is equal to minus the binding energy liberated by the fusion process. The edge of the well at r = rnf goes from this bottom level to the maximum potential energy Ub.

8 In result, the potential energy function U(r) can be approximated by the simple piece- wise function ( − r ≤ rnf U(r) = 2 . 1 Z1Z2e r ≥ r 4π0 r nf Going from r = +∞ to r = 0, the potential energy curve initially increases hyperboli- cally up to the maximal value Ub for r = rnf . In the case of deuterium-tritium fusion rnf ≈ r1 + r2 ≈ 4 fm and Z1 = Z2 = 1. The height of the barrier Ub at r = 4 fm is then 1.44 Ub = U(rnf ) ≈ MeV ≈ 0.36 MeV. (2.1) rnf [fm] If the particles have enough energy to overcome this coulomb barrier, they are able to fall into the potential well and fusion is possible. The fusion reaction in the case of deuterium and tritium is given by

D + T → α + n. (2.2) The energy released in this process can then easily be calculated by Einstein’s formula:

2 = ∆mc = mα + mn − mD − mT = 17.59 MeV. (2.3) Because this energy is usually much higher than the incoming energy of the D and T nuclei, conservation of momentum implies that the released energy is divided between the two particles inversely proportional with their mass. Therefore, the α-particle will have an energy of approximately 3.52 MeV, while the remaining 14.08 MeV will be given to the neutron. The difficulty of fusion is surmounting the repulsive barrier. Classically this is only possible when the center of mass energy is higher than the barrier. Particles with lower energies are reflected. According to quantum mechanics, however, such particles are not always reflected. There is a non zero chance to tunnel through the finite coulomb barrier. This probability is given by the Gamow factor G. For deuterium-tritium fusion this factor can be approximated by

− √ 34.4 G = e Ecm[keV ] . (2.4) Now one can understand that using fusion for energy production cannot be easy. Be- sides the energy release, also the fusion activation energy is much higher than that of the common burning process. Tunneling indeed permits particles to fuse even if their center of mass energy is lower than the barrier height, but the Gamow factor G decreases exponentially with decreasing energy. When Ecm = 10 keV, only 2 interactions out of 100 000 will result in an approach close enough for fusion. A positive energy balance does not only require fuel particles with suﬃciently high energy. The density also has to be high enough, such that they can react before losing their energy. Therefore, one needs highly energetic particles, a long energy conﬁnement time and a high fuel density. As will be explained in subsection 2.4, particle energies of the order of 10 keV are required. For the scientists working at the famous LHC experiment in Geneva this is of course peanuts. The problem is that accelerators simply do not work for our problem. Neither a beam-beam collision nor a beam-target collision would result in an energy producing fusion reactor because of

9 Figure 2.2: Schematic representation of the coulomb barrier the other two conditions. In the beam-beam collision the fuel density is to low, in the beam-target collision the particle energy is lost to soon.

2.2.2 Conquering the Coulomb barrier in a hot fusion plasma The only solution left to provide the reacting particles with enough energy is heating the fusion fuels to very high temperatures. This form of fusion is called thermonuclear fusion. The temperature of a system in equilibrium is a measure of the amount of random thermal motion of the particles inside the system. If the temperature is high enough, the thermal energy of the fuel particles allows to surmount the Coulomb barrier. Of course not all particles have the same thermal energy. There is a certain energy distribution. Assuming the simple Boltzmann distribution one has

√ − E f(E) ∝ Ee kt (2.5) df (E ) = 0 ⇔ E = kT. (2.6) dE p p The most probable thermal energy here is thus equal to the temperature times the Boltz- mann constant k. Using this equality it is possible to talk about temperature in units of energy. In the context of fusion it is common to specify temperatures in terms of electronvolt. What temperature do we need for fusion? Using equation (2.6) one can calculate that needed thermal energies of more than 10 keV correspond to temperature levels of about 100 000 000 Kelvin! This is about 7 times higher than the temperature in the solar core! At these temperatures every single atom is fully ionized. This ionized state of matter was identiﬁed for the ﬁrst time in a Crookes tube by Sir William Crookes in 1879. Later,

10 around 1920, Irving Langmuir invented the name plasma for these ionized gases. In fusion plasmas the electron and ion temperatures are equal (thermal plasma). A Plasma is sometimes called the fourth state of matter because of its typical characteristics which are completely different from the solid, liquid or gas state. Strictly speaking the ionization process of a gas is not really a phase transition because it does not occur at one specific temperature. Ionization of atoms or molecules requires energies of tens of electronvolts. These energies correspond with temperatures of some tens of thousands Kelvin. That is the reason why we are not really familiar with plasmas here on earth. We only know them from some rare events like flames, lightning and aurorae. However, in the universe, most matter occurs in the plasma state. A plasma is a gaseous medium consisting of electrons, positive and negative ions, charged dust particles, atoms, molecules and radicals. This composition is responsible for the extraordinary properties of plasmas. Charge separation and currents in a plasma cause electric and magnetic fields superimposed on the external electromagnetic fields. Therefore, a plasma behaves completely different from an ordinary gas. The presence of radicals and ions in plasmas also make them very reactive. Constant excitation and desexcitation processes in plasmas which are not fully ionized, cause the emission of light with frequencies characteristic for the composition of the gas. The exceptional properties of plasmas allows us the use them in a wide variety of applications like plasma display panels, fluorescent lamps, ozone generators, all kind of surface treatments, air purification,... However, the inevitability of a very hot fully ionized plasma in thermonuclear fusion makes the realization of a commercial fusion power plant very hard. First, one has to heat the fuels up to a temperature higher than the solar core. Second, a mixture of charged particles is very difficult to control and to model. Third, no single constructive material is able to withstand the extremely high temperatures. The last problem can in principle be solved by using a tokamak in which the charged particles are confined by electromagnetic fields (see chapter 3). However, even in a tokamak the inner reactor materials are bombarded by highly energetic particles and need to fulfill an enormous list of conditions which can never be fulfilled by one single material. In this way the Coulomb barrier may well have been surmounted, but a lot of other problems remain to be solved by scientists and engineers. Despite the huge progress made during the last decades, there are still some important issues to work on before fusion can be commercialized.

2.3 Fusion fuels

2.3.1 Possible fusion reactions There are a lot of fusion reactions possible. In ﬁgure 2.4 the most important reactions are shown. Which of these reactions will be used in a fusion power plant? For the isotopes used as fusion fuel one should have that

• their fusion process is exothermic

• the released energy is large

• the product of their electric charge is small in order to have a low Coulomb barrier

11 • the fusion probability (cross section) is high in the energy range of interest

• their resources are suﬃcient for at least hundreds of years

Figure 2.3: Energy dependence of the Figure 2.4: The most important fusion cross sections for the diﬀerent fusion re- reactions with their corresponding Q val- actions ues [8]

Based on these requirements and looking at ﬁgure 2.3, which shows the energy dependence of the total fusion cross sections, one can chose the most promising reactions. The processes of the p-p cycle occurring in our sun can be eliminated immediately. Their very small cross sections require an enormous pressure for sustainable fusion, which is not feasible here on earth. The reactions of the CNO cycle and the carbon burn can be forgotten as well, because the Coulomb barrier is way to high. The same can be said about the advanced fusion fuels. However, scientists have already been thinking about using these fuels later on, when the fusion technology is on a higher level. The ﬁrst three reactions are the only reactions feasible for the moment. Because of its very high cross section, especially the D-T reaction is very promising. The characteristics and resources of deuterium and tritium are discussed in the next subsections.

2.3.2 Deuterium Deuterium does not need that much discussion. It is an isotope of hydrogen with one neutron and one proton. The isotope is not radioactive and does not impose any health or environmental risks. Deuterium can be extracted from seawater in which it occurs with a concentration of about 154 ppm. Therefore, this part of the fuel is as good as inexhaustible. The technology for extracting deuterium by destillation or electrolysis is

12 Figure 2.5: First commercial heavy water plant in Vemork (Norway)

also well developed. In ﬁgure 2.5 one can see the ﬁrst commercial heavy water (D2O) plant which was built in Vemork (Norway) already in 1934. The plant had a capacity of 12 tons per year and was destroyed during World War 2 by the Allies because the Germans wanted to use the heavy water for making an atomic bomb. Deuterium in the form of D2O is still used nowadays in great amounts as moderator and coolant in heavy water reactors. In Canada one produces each year around 700 tons of heavy water for their CANDU reactors. The only drawback of using deuterium is the fact that heavy water in the wrong hands could be used for making nuclear weapons.

2.3.3 Tritium The second part of the fuel in a fusion reactor is tritium and is a more critical issue. This element is an isotope of hydrogen consisting out of two neutrons and one proton. Its chemical characteristics are thus equal to those of common hydrogen. The element is a β-radiator with a lifetime of about 12.3 years. The decay reaction is given by

3 − T → He2 + e +ν ¯e. (2.7) One has to be extremely careful with this radioactive isotope. The β emitted during the decay has an average energy of about 5.7 keV. Such a particle can only travel about 6 mm in air and is not able to cross the dead layer of our skin. So external tritium does not really pose a problem. But the danger is that tritium is inhaled or ingested. Tritium in our body will cause damage and an increased chance for developing cancer. Tritium is also able to replace one or more ordinary hydrogen isotopes in water or organic molecules. Without the necessary precautions the tritiated water (HTO) or organically bound tritium (OBT) can come in our water or food cycle, which is very dangerous. A detailed safety study of tritium in fusion reactors was made in [9]. Fortunately there is already some experience with tritium because it is a common product in present nuclear power plants (especially heavy water reactors). Tritium is also a useful isotope for some applications, like nuclear weapons, self-powering lights and oceanic transient tracers. Because of the quite short lifetime, the natural abundance of tritium is limited. It occurs only as small traces in water. Therefore, tritium must be produced somehow. A

13 very attractive approach is the bombardment of a lithium blanket with fusion neutrons. The following two reactions can take place

6 Li3 + n → T + α + 4.8 MeV (2.8) 7 Li3 + n → T + α + n − 2.87 MeV. (2.9) In the case of a lithium blanket one can consider deuterium and lithium as the actual fusion fuels.

2.3.4 Lithium Considering the discussion at the end of the previous subsection, it is also useful to take a look at lithium. This element is a soft and very reactive silver-white alkali metal. The name comes from the Greek word ’lithos’, which means ’stone’. J. J. Berzelius proposed this name because the element was observed for the first time in stone. Lithium is represented by the symbol Li and has atomic number 3. The only naturally occurring isotopes are Li6 (7.42 %) and Li7 (92.58 %). Under standard conditions lithium is the lightest metal and the least dense solid element. Because of its reactivity lithium only appears naturally in the form of minerals and salts. Although lithium is not extremely dangerous, one has to treat it in the right way for safety. When exposed to water, acids or oxidizing agents, there is always the risk of fire and explosion. Lithium also reacts exothermally with nitrogen in moist air at high temperatures. In solution lithium is toxic and targets the central nervous system. Breathing lithium dust or lithium compounds initially irritates the nose and throat, while higher exposure can cause a buildup of fluid in the lungs, leading to pulmonary edema. The softness and reactivity of lithium prohibits the use as constructive material. How- ever, lithium occurs in numerous applications: lithium-ion batteries, ceramics, glass, lu- bricants, alloy hardeners, pharmaceuticals (treatment of manic depression), hydrogenat- ing agents, heat transfer liquids, rocket propellants, vitamin A synthesis, nuclear reactor coolant, underwater buoyancy devices,... With an average concentration of about 60 ppm, lithium is a quite common element in the earth’s crust. For the moment there is no lack of the element. Most lithium is found in minerals like amblygonite, spodumene, petalite and lepidolite (e.g. in Australia) and brines (e.g. in the Atacama desert, see figure 2.6). Lithium is present in seawater as well with a concentration of about 0.17 ppm. But this extraction process is still very expensive. There exists no accurate information about the world lithium resources. One can only make crude estimations about the total amount of lithium. In [10] it is predicted that one could use lithium for fusion applications and the other present applications for a period of about 250-600 years. However this paper is already 5 years old. The last years the lithium-ion battery industry is booming at an incredible speed. If the electric or hybrid cars become a real success, the demand for lithium will be enormous. In that case it could well be that the current lithium resources will not suffice. Furthermore the extraction of lithium from the numerous brines in South America evokes protest from the people living there. During the extraction process one uses chemicals which strongly pollute the ground water. So the limited amount of lithium could be a problem in the not so far future. This could be solved for example by making the process of lithium extraction from seawater

14 Figure 2.6: Brine in the Chilean Atacama desert used for the production of lithium more eﬃcient and cheaper. The extractable lithium reserves would then be as good as inexhaustible.

2.4 Energy balance of a fusion power plant

To conclude this general chapter about thermonuclear fusion it is useful to take a look at the energy balance of a D-T fusion reactor. Needless to say, the produced energy comes from the fusion processes taking place in the hot plasma core. The fusion power density in the core can be expressed as

PF = nDnT < σF v > QF . (2.10)

In this equation nD is the density of deuterium nuclei or deuterons, nT the density of tritium nuclei or tritons, < σF v > the product of the D-T fusion cross section and the center of mass velocity averaged over the deuteron and triton velocity distributions and n QF the energy released during one fusion reaction. By choosing nD = nT = 2 this power density is maximized. With n as average fuel density, the fusion power density can then be written as

n2 P = < σ v > Q . (2.11) F 4 F F One of the most important sources of energy loss is Bremsstrahlung. Every acceler- ating charged particle emits a continuum of radiation. The emission is only signiﬁcant for charged particles with very low mass and strong centripetal acceleration. Free electrons in a plasma, accelerated by the positive nuclei, lose part of their energy by so called Bremsstrahlung. This radiation is emitted in the X-ray region for which a plasma is trans- parent. This unavoidably implies loss of useful energy. Quantum mechanical calculations for the Bremsstrahlung power density (see e.g. [11]) result in the proportionality relation

2 2 1 PBr ∝ n Z T 2 . (2.12)

15 Figure 2.7: The fusion triple product achieved in diﬀerent tokamaks as function of the ion temperature. The break even Q = 1 and the ignition regions are shown. In the inaccessible region the Bremsstrahlung radiated power is too large. In the reactor relevant region we have Ti ≈ Te [12]

Here n is again the average fuel density, Z the effective atomic number of the plasma and T the electron temperature. The occurrence of Z in equation (2.12) is easy to understand because nuclei with higher electric charge cause stronger electron accelerations. Therefore, it is very important to prevent the introduction of high Z impurities into the plasma. In order to have a positive energy balance, PF must at least be higher than PBr. Increasing the average fuel density n does not change the balance because both PF and 2 PBr are proportional to n . The effective atomic number Z in equation (2.12) cannot be made infinitely small. Fortunately the factor < σF v > in equation (2.11) increases with 1 the electron temperature on a pace faster than T 2 . One can calculate that for electron temperatures above 4 keV the fusion power density in a pure D-T plasma is higher than the Bremsstrahlung power density. The invasion of impurities in the plasma will increase the critical temperature very fast because the effective atomic number of the plasma appears as a square in equation (2.12). Besides the high temperatures inside the fusion plasma, this is another reason why the choice of the inner reactor material or plasma facing material (PFM) is so critical. In a finite fusion reactor there is of course also energy loss caused by conduction and convection. One usually expresses the entire energy loss per time as

E 3nkT V PL = = , (2.13) τE τE where E is the total energy in the fusion plasma and τE the empirical energy conﬁnement 3 time. Taking into account that the average energy of a plasma particle is 2 kt and that the number of electrons and ions is equal, one can obtain the last expression in equation

16 (2.13). In equation (2.2) one can see that the fusion of a deuteron with a triton results in a neutron and an approximately 4 times heavier α. Therefore, the kinetic energies of the neutron and the α are respectively En = 14.08 MeV and Eα = 3.52 MeV as explained in subsection 2.2.1. In a tokamak (see chapter 3) the charged particles are confined by electromagnetic fields. Therefore, the neutrons will be able to escape from the reactor, but the α particles are trapped and will contribute to the heating of the fusion plasma. If the number of fusion reactions per second is sufficiently high, the heating caused by the α particles will make the use of external heating systems redundant. In analogy with the burning of fossil fuels this situation is called ignition. The ignition criterion can be written as ! n2 3nkT < σF v > Eα − V > 0. (2.14) 4 τE In this equation both terms should be averaged over the reactor volume. Making use of the approximately quadratic temperature dependence of < σF v > in the range between 10 and 20 keV this can be rewritten as

−3 nT τE > 3 − 5 m · keV · s. (2.15) The exact value depends on the profiles of n and T and on the use of average or peak values. The product of fuel density, temperature and energy confinement time is sometimes called the fusion triple product. This product is a good indication of the progress towards the first commercial fusion power plant. In figure 2.7 one can see the evolution of the triple product during the last decades. Typical desired values for a tokamak are n = 1020 m−3, T = 10 keV and τ = 3 s. The density n may not be much higher in order to keep the fusion reactions under control. Of course ignition is not a necessary condition for a positive energy balance. A fusion reactor can also produce energy without being ignited. A good measure for the efficiency of a fusion reactor is given by the so called Q value

P V Q = F . (2.16) PH

Here PF is again the fusion power density and PH is the continuous heating power needed to keep the plasma temperature high enough for sustaining the fusion reactions. So, in a non-ignited fusion plasma, part of the produced energy must be recycled to heat the fuel. This decreases the eﬃciency. More details about the energy balance of fusion reactors can be found in [13], [14] and [15].

17 Chapter 3

Tokamaks and the ITER project

In chapter 2 the origin of fusion energy, the conditions under which fusion reactions can occur on earth and the suitability of different light isotopes as fusion fuel were discussed. Knowing what fusion is, under which conditions it can take place and what the preferred fuels are, however, is only the beginning. Much more important is knowing how to convert this scientific theory into a well working power plant. Actually this is the most difficult part. As explained in chapter 2, fusion on earth requires a D-T plasma at temperatures of more than 120 000 000 K. It is clear that such a hot plasma simply cannot be confined by material walls. If matter is not able to confine the fusion fuels, one has to resort to one of the 4 fundamental forces. Based on their very short ranges, the weak and the strong forces can immediately be eliminated. Only the gravitational and the electromagnetic forces remain. Gravity is used in an approach called inertial fusion. In this case one strongly compresses a tiny D-T pellet with extremely powerful lasers or particle bundles. Much more progress has been made in magnetic confinement fusion and more specific in the tokamak approach. Tokamaks are the subject of this chapter. In section 3.1 the way in which magnetic fields in a tokamak confine charged plasma particles is explained qualitatively. Scientists are working on fusion since many decades. For the moment a very important step is being made on the road towards the first commercial fusion power plant, the famous ITER project. The history of the fusion research, the international ITER cooperation and some aspects of the huge ITER tokamak are discussed in section 3.2. Finally in section 3.3 the main advantages and disadvantages of a tokamak power plant are evaluated. More information on tokamaks can be found in a lot of publications. The standard work on tokamaks is [14]. A good introduction to tokamaks is given in [15] and [16]. A good source of information about ITER is the site of the project [17]. The history of magnetic confinement fusion is treated e.g. in [18].

3.1 Conﬁnement in a tokamak

As explained in the introduction of this chapter, the hot fusion plasma must be confined by means of force fields. In a tokamak one uses magnetic fields to imprison the charged particles. In this section it will be explained how the confinement in a tokamak is established.

The movement of a particle with charge q and mass m in a magnetic ﬁeld B~ can be

18 calculated using Newton’s equation of motion

d~v F~ = m (3.1) dt and the expression for the Lorentz force F~L

F~L = q~v × B.~ (3.2) The diﬀerential equation for the velocity vector ~v of the particle in a homogeneous magnetic ﬁeld can easily be calculated using equations (3.1) and (3.2)

d~v = ~ω × ~v. (3.3) dt Equation (3.3) describes the cyclotron motion of a charged particle around the magnetic ﬁeld lines with cyclotron frequency

qB~ ~ω = − (3.4) m and radius of curvature mv ρ = . (3.5) qB Looking in the direction of the magnetic field lines a negatively charged particle gyrates clockwise, while a positively charged particle gyrates counterclockwise. Particle trajectories in more complex magnetic fields or in the presence of an additional force can often be seen as the superposition of this gyration motion and a drift of the gyration center. Figure 3.1 clearly shows how a tokamak makes use of magnetic fields to confine charged particles. The most simple magnetic confinement configuration one can think of is the one shown in figure 3.1 (a). Current carrying coils centered around a cylindrical configuration generate a quasi-homogeneous magnetic field directed along the axis of the cylinder. If the field is chosen strong enough, the radius of curvature given by equation (3.5) will be small compared to the dimensions of the cylinder. The charged particles are then confined in the radial direction. The problem with this cylindrical configuration is the fact that particles are not confined in the axial direction. A logic solution for the end losses is joining the two ends in a torus as indicated in figure 3.1 (b). By closing the configuration, however, an outwards force is introduced. It is not difficult to understand the origin of this instability. Using Ampère’slaw and taking into account the symmetry of the system, one can see that the magnetic field of the torus is toroidal and given by

µ I B = 0 tot , (3.6) t 2πR with µ0 the magnetic permeability of the vacuum, Itot = NI the total current in the poloidal direction through the N toroidal magnetic field coils and R the distance from the center of the system. The field Bt decreases with increasing radius R. Using equation (3.5) one can see that the radius of curvature ρ of the particle trajectories then must be decreasing with increasing radius R. The magnetic field gradient generates opposite vertical drifts of positively and negatively charged particles as represented schematically in

19 Figure 3.1: Stepwise introduction of the tokamak concept

~ ~ the right part of figure 3.1 (c). The vector ∇ B is pointing towards the center of the torus. The center in figure 3.1 (c) must lie then at the right side. The separation of positive and negative particles in turn results in a vertical electric field, pointing downwards in figure 3.1 (c). An electric fields accelerates the gyrating charged particles in one half of their motion and decelerates them in the other half. The situation is opposite for positive and negative particles. In this way finally a horizontal drift is generated. As can be seen in figure 3.1 (c), the drift is outwards both for positive and negative particles. The radial expansion of the fusion plasma can be avoided by the introduction of an additional poloidal magnetic field. This field can be generated either by a current through external coils or by a current in the plasma itself. The first approach is used in a stellarator. A tokamak relies on the second principle. The idea is depicted schematically in figure 3.1 (d). A variable current is sent through the transformer winding. The resulting variable magnetic flux in the iron transformer core then causes a toroidal current in the plasma, which can be seen as the secondary winding of a transformer. This toroidal plasma current generates the desired poloidal magnetic field. The combination of the poloidal and toroidal magnetic field results in helical magnetic field lines. Following a certain field line, one will always stay at a certain toroidal surface. The nested toroidally shaped surfaces are known as magnetic surfaces. The radial expansion does not occur anymore in this configuration. In tokamak experiments it is very useful to control the shape and the position of the

20 fusion plasma very precisely. Therefore, it is common to add additional poloidal magnetic field coils circulating the tokamak in toroidal direction. This configuration is shown in figure 3.1 (e). Even with these additional coils the tokamak still looks pretty simple. However, besides particle confinement, a tokamak has a lot of other functions to fulfill. Therefore, a real tokamak looks much more complex. The main components of a real tokamak are given in subsection 3.2.2 for the example of the ITER tokamak. It may also seem here that the only remaining task is building the fusion power plant. However, there are still some major problems to cope with. Especially plasma-wall interaction, plasma heating, current drive and confinement remain very critical topics.

3.2 Tokamak research

3.2.1 Historical sketch of the fusion research Fusion research already has a long history. The discovery of the fusion process fits in the mid 19th century’s solar energy riddle. People were wondering were the sun’s energy comes from. The general idea was a simple combustion similar to the burning of a fire. Geologists stated that the earth’s shaping processes must have been active during at least a few hundred thousand of years. Simple combustion then requires inconceivable amounts of matter. Scientists concluded thus that the solar energy must be generated in a completely different way. In the same century Hermann von Helmholtz and Lord Kelvin proved that even a steadily gravitational collapse of the sun could not account for all the produced energy. A first clue on the real origin of the energy was given in 1905 by Einstein’s most famous equation E = mc2. It dictates that even a small amount of solar mass can be converted into an enormous amount of energy. In 1920 Francis William Aston observed that the mass of a helium atom was somewhat smaller than the summed mass of 4 hydrogen atoms. Based on Aston’s measurement, astronomer Sir Arthur Eddington suggested that maybe the sun produces energy by converting hydrogen atoms into helium atoms. In 1939 Hans Bethe wrote the article ’Energy production in stars’, treating the fusion processes occurring in the stars more profoundly. This paper delivered Bethe the Nobel Prize for Physics in 1968 and once and for all solved the solar energy riddle. After the theoretical successes of the first half of the 20th century, most experimental progress on fusion was made during the second half of last century. After World War II and the ’successful’ Manhattan project, there was an increased interest in fusion and nuclear physics in general. Scientists started thinking about possible ways in which the fusion process could be used for producing energy here on earth. During the next two decades, research groups in the UK, the USA, the USSR, Japan, France and Germany developed different kinds of fusion reactors like stellarators, magnetic pinch devices and inertial fusion. Important names occurring in this period are Sir George Thomson (Impe- rial College), Peter Thonemann (Oxford), Lyman Spitzer (Princeton), James Tuck (Los Alamos) and Edward Teller (Lawrence Livingmore Laboratory). In the beginning, because of the Cold War, fusion research was classified as ’Top Secret’. It is only after the famous ’Atoms for Peace’ conference (1958) in Geneva that the first steps towards international cooperation were made. On the third IAEA ’International Conference on Plasma Physics and Controlled Nu- clear Fusion Research’(1968) in Novosibirsk, fusion research was completely reorientated by the announcement of the very successful experiments on the Russian tokamaks. A

21 Figure 3.2: The Russian T1 at the Kurchatov Institute in Moscow was the ﬁrst tokamak

Figure 3.3: JET at Culham (UK), the current world’s biggest tokamak

22 photograph of the world’s first tokamak can be seen in figure 3.2. The name ’tokamak’ is an acronym for the Russian words ’toroidalnaya kamera’ (toroidal chamber) and ’mag- nitnaya katushka’ (magnetic coil). The concept was developed by Igor Tamm and Andrei Sakharov in the 1950’s. Lev Artsimovich leaded the experimental program in Moscow at the Kurchatov Institute and the theoretical studies were directed by Mikhail Leon- tovich. The generated temperatures were about 10 times higher than in any other fusion device at that moment. Furthermore the confinement times were much better. There- fore, most fusion research groups started concentrating at tokamak research. It is then no surprise that today’s focus is still on the tokamak approach, which is much more developed than the other approaches. Tokamaks can be found all over the world. Every single tokamak is unique. Different research groups deal with different aspects of the tokamak research. For the moment, the Joint European Torus (JET) at Culham in the UK is the biggest tokamak in the world (see figure 3.3). Other tokamaks are TEXTOR (Jülich, Ger- many), JT-60 (Naka, Japan), Tore Supra (Cadarache, France), DIII-D (San Diego, USA), COMPASS (Prague, Czech Republic), ASDEX Upgrade (Garching, Germany), KSTAR (Daejon, South Korea), HT-7 (Hefei, China), TCV (Lausanne, Switzerland),... During the last decades, world leaders became more and more aware of the threatening energy crisis. Fusion in tokamaks appears to be very promising in this context. The laws of nature, however, dictate that a tokamak power plant has to be very large. Some aspects can be extrapolated from the existing small experimental tokamaks. But eventually a full scale experimental reactor has to be built in order to prove the feasibility of energy production by means of fusion. This can of course only be realized by a huge international cooperation. The idea for such a project was born at the ’Geneva Superpower Summit’ (1985). The child was named ’ITER’, International Thermonuclear Experimental Reactor or ’the way’ in Latin. Today the project is supported by 7 parties (Russia, the USA, the EU, Japan, China, South Korea and India) representing over half of the world’s population. In 2005 it was decided that the huge ITER tokamak will be built at Cadarache, near Aix- en-Provence in Southern France. For the moment the ITER site looks quite empty, as can be seen in figure 3.4. The 180 hectares of the site have already been prepared. This year the first buildings will appear. Scientists and engineers all over the world are working on the different parts for the ITER tokamak and the surrounding systems. The first plasma is planned for 2018. The ITER site should then look like the model in figure 3.5. A lot of additional information and pictures can be found on the internet site of the project [17].

Figure 3.4: The ITER site as it looks like Figure 3.5: The ITER site how it should for the moment look like in 2018

23 And what after ITER? Hopefully ITER will show that it is indeed possible to use fusion for commercial energy production. The next step is then the building of DEMO or Demonstration Power Plant. Scientists and engineers are already thinking about the conceptual design of this machine. According to the current time schedule, DEMO should put its ﬁrst fusion power into the grid as early as 2040. But that is for the far future. Now it is important that research groups all over the world make dedicated experiments on their experimental tokamaks. Results from these smaller tokamaks will be indispensable during the construction and design of the components for ITER and DEMO. There are still some important problems to tackle.

3.2.2 ITER tokamak In section 3.1 the basic structure of a tokamak was described based on particle conﬁne- ment. A real tokamak has a lot of additional components for heating, creating vacuum, maintaining vacuum, shielding from high thermal loads and high-energy neutrons, diagnostics, extracting heat and impurities, cooling of superconducting magnets, remote handling, power supply, fuel supply, cooling, treating activated materials,... The ITER tokamak will be the largest and most sophisticated tokamak built up to now. It is instructive to take a closer look at the major components foreseen in the current design. In ﬁgure 3.6 one can see a model of ITER and some of its components.

• Magnets: The magnet system of ITER comprises 18 superconducting toroidal field coils, 6 poloidal field coils, a set of correction coils and a central solenoid. The extremely high magnetic fields up to 13 Tesla, required for confining the fusion plasma, make the use of superconducting magnets necessary. The superconductors will be cooled by supercritical helium. The main function of the toroidal field magnets is to confine the plasma particles. The 18 coils are composed out of strands with a total length of 150 000 km and a weight of 6540 tons. The poloidal field coils, placed outside the toroidal field coils, pinch the plasma away from the wall and contribute to the shaping and stability of the plasma. Both the poloidal and toroidal field coils lie between the vacuum vessel and the cryostat. At this position they are cooled and shielded from the high-energy neutrons at the same time. The central solenoid functions as large transformer, inducing the main toroidal plasma current up to 17 MA, and ’backbone’ of the magnet system.

• Vacuum vessel: The ITER vacuum vessel is a hermetically sealed, doughnut- shaped, stainless steel container inside the cryostat providing an enclosed vacuum environment for the fusion reactions. With its height of 11 m and internal diameter of 6 m, the vessel will be twice as large and sixteen times as heavy as any previous tokamak. The double steel walls will allow cooling water to circulate between them. The inner surfaces of the vessel will be covered by blanket modules for shielding from the hot fusion plasma and the high-energy neutrons. Together with its 44 ports (for remote handling, diagnostic systems, heating systems and vacuum systems), the vacuum vessel will weigh about 8000 tons, slightly more than the Eiﬀel Tower.

• Blanket: The blanket is one of the most critical and technically challenging components in the ITER tokamak. It provides shielding of the outer components from the high heat load and the fast neutrons inside. The neutrons lose their kinetic energy in

24 Figure 3.6: Model of ITER with its main components

25 the blanket, converting it into heat. This heat is then collected by the coolants and will, in DEMO and the later commercial reactors, be used for electrical energy production as in an ordinary power plant. For purposes of maintenance of the vacuum vessel, the blanket wall will be modular. Each of the 440 individual segments will measure 1m x 1.5m and weigh up to 4.6 tons. A segment will consist in turn out of two parts. First part is a detachable plasma facing ﬁrst wall consisting out of beryllium for removal of the plasma heat load. Second part is a semi-permanent shield out of high-strength copper and stainless steel dedicated to the neutron shielding. Later in the ITER project, sophisticated modules will be inserted for testing the concept of tritium breeding out of lithium.

• Divertor: The divertor is also a plasma facing component and thus critical. It is located at the bottom inside the vacuum vessel and its function is to extract heat, helium ash and impurities from the plasma. With magnetic coils the field lines are shaped such that the divertor region is removed from the plasma core with its closed flux surfaces (see figure 4.1). The plasma layer between the last closed flux surface and the plasma facing material is called the scrape-off layer (SOL). In this layer the plasma particles are directed towards the divertor target plates where they can be extracted. The divertor supporting structure in ITER will be made primarily from stainless steel. The plasma facing parts will be made in the first experiments from carbon fiber-reinforced composite (CFC) and eventually from tungsten, a high- refractory material which will be able to withstand the harsh environment.

• Neutral Beam Injector (NBI): A tokamak power plant requires temperatures around 150 000 000 K. With only the ohmic heating resulting from the induced plasma current, such temperatures will never be reached. Therefore, additional heating methods will be used in ITER. One of these is neutral beam injection (NBI). One starts with negative deuterium ions. These are accelerated up to 1 MeV and neutralized. Neutral particles can enter the plasma without any problem. Once in the plasma, they transfer their energy by means of collisions with the plasma particles.

• RF heating system: The ITER fusion plasma will also be heated by radio waves at certain frequencies. In Ion Cyclotron Resonance Heating (ICRH) the ions are heated, while in Electron Cyclotron Resonance Heating (ECRH) the energy is transferred to the electrons. This requires a wave generator, a transmission line and an antenna coupling the waves into the plasma. It is very diﬃcult to tune the system such that the waves heat the plasma eﬃciently.

• Cryostat: The ITER cryostat is a very large, stainless steel structure surrounding the vacuum vessel and the superconducting magnets. It provides a super-cool, vacuum environment. The gap between the two concentric walls is ﬁlled with helium gas slightly above one atmosphere, acting as thermal barrier. The cryostat is 31 m high and 36.5 m wide. There are many openings in it for the cooling system, auxiliary heating, magnet feeders, diagnostics, removal of blanket and divertor parts,...

With all these technologically very advanced systems the story is not yet ﬁnished. ITER will also have diﬀerent diagnostic systems, a sophisticated vacuum system, a remote

26 handling system and hot cells for the treatment of contaminated materials, a power supply system providing up to 620 MW energy in peak periods, a fuel system and a cooling circuit. For more details I refer to the ITER site [17].

3.3 Pros and cons of tokamaks for future energy production

Throughout the last two chapters some general aspects of fusion and tokamak power plants were discussed. Fusion in a tokamak appears to have many advantages compared to fossil fuel burning, ﬁssion and renewable energy production. Unfortunately there are some drawbacks as well. In this section the major pros and cons of commercial energy production in tokamaks are presented.

Advantages

• Deuterium is one of the two fuel isotopes required for the most attractive fusion reaction here on earth. The isotope is present signiﬁcantly in ordinary water and can be extracted without any problem. Therefore, it is virtually inexhaustible. (in contrast with fossil fuel burning and ﬁssion)

• The by-product of the deuterium-tritium fusion reaction is the harmless helium gas. No toxic- or greenhouse gases are emitted. (in contrast with fossil fuel burning)

• Fusion can only occur under very strict conditions, such that an uncontrolled chain reaction is excluded. Any deviation from normal operation will result in shutting down the reactor. (in contrast with ﬁssion)

• A fusion power plant will produce only short-lived nuclear waste by a careful selection of materials. After about 100 years already the materials could be reused. (in contrast with ﬁssion)

• The raw materials needed for fusion and the by-products of fusion cannot be used for the production of nuclear weapons. The radioactive tritium isotope is produced and consumed inside the reactor. Furthermore, at any time only a limited amount of tritium will be present in the reactor. (in contrast with ﬁssion)

• The needed amount of fusion fuels is very small. (in contrast with fossil fuel burning and ﬁssion)

• At present both deuterium and lithium occur all over the world quite abundantly. The energy of fusion power plants therefore, will be available in every country at any time of the day. (in contrast with renewable energy production)

• Fusion allows quite compact large scale power plants of 1 GW and more. (in contrast with renewable energy production)

Disadvantages

• Tritium is the second needed isotope. Due to its short lifetime, it occurs only as traces in nature. Therefore, tritium will be produced by neutron bombardment of lithium. The limited lithium reserves could pose a problem in the not so far future,

27 especially when the lithium battery market keeps booming. The mining of lithium from seawater could solve this problem if the extraction process can made more eﬃcient.

• The fusion research is very time and money consuming. After decades of research still no net energy is produced. The ITER project will show us if fusion is really worth all that patience and money.

• Nuclear waste is unavoidable. Highly energetic neutrons produced in the D-T reaction will induce radioactivity and the inner reactor materials will be contaminated with tritium. Careful material selection and design can however limit the amount and lifetime of the nuclear waste.

• The laws of nature prohibit small scale fusion power plants. Net production of energy unavoidably implies a minimum reactor size. This could be a problem in desolated areas, where small scale power plants are more desired.

Clearly even a tokamak will never be without disadvantages. But I think the perfect energy source does not exist. Renewables, fission and fusion, according to me, all three have their task. Renewables are the so called ’green’ energy sources. They directly use what mother nature produces. Their efficiency is quite low, but will for sure be improved significantly during the next decades. Renewables will probably never be able to provide energy worldwide and uninterrupted. They would, however, be very useful as minor component on the future energy market. That implies of course the need for another, more stable and large scale energy source. Today fission and fossil fuel burning play this role. As explained in chapter 1, fossil fuel burning is just no option. So of the present energy sources only fission remains. Nuclear power plants produce a large amount of long lived radioactive waste. Unfortunately there is no alternative for the moment. Hence, it is very important to support the research on fission as well. In this way nuclear power plants can be made more efficient and the long lived radioactive waste can be reduced as much as possible. In the mean time, scientists and engineers have to think about an alternative for fission. This is where fusion comes into play. Considering all good things it has to offer us, it would be a shame losing courage because fusion is so hard to realize. As long as there is hope, it must be the duty of mankind to do everything they can in order to get control over the power plant of the stars. Hopefully ITER will shows us that we are on the good way...

28 Chapter 4

Plasma-wall interaction and the plasma edge

Visible light measurements and spectroscopy in tokamaks are very useful tools for studying the interaction between the edge of the plasma and the plasma facing materials (PFMs), as explained in section 5.3. Therefore, it will always remain an important diagnostic method in fusion research. All the interaction processes between the plasma edge and the PFMs are known under the common name of plasma-wall interaction (PWI) and play a decisive role in tokamaks. PWI is a very complex interplay between different phenomena and is not yet fully understood. An outline of the most important PWI processes is given in section 4.1. The influence of the plasma edge is discussed in the next section. Section 4.3 explains why the study of PWI is so important for ITER and future fusion machines and what the major points of concern are. Based on all this information the different possible PFMs for ITER are discussed in the last section of this chapter. More information about the topics discussed here and related topics can be found in the book of Wesson [14], the proceedings of the Carolus Magnus Summer school 2009 and in a lot of articles. For instance [19] and [20] are good and up-to-date articles concerning PWI for ITER and future fusion machines.

4.1 Plasma-wall interaction

The inner reactor materials of a tokamak are continuously bombarded by energetic particles (ions, atoms, neutrons) and subjected to an enormous heat flux. Both particles and heat have a large impact on the properties of the materials. Especially the divertor target plates have to endure very severe conditions. The rest of the divertor and the wall are subjected to particle and heat fluxes as well. The fluxes hitting these areas are however much lower. Neutral and charged particles have a completely different behavior. Neutral particles can move freely across the magnetic field lines, while charged particles in first approximation follow the magnetic field lines. But both neutral and charged particles can come into contact with solid objects (limiter, divertor, wall). They can then release particles from the solid material, return to the plasma in the same form, neutralized or as molecular compounds, stick to the surface or migrate into the solid. Species released from the surfaces are ionized and transported in the vessel along the magnetic field lines. Some fraction

29 of the transported material is pumped out through the divertor, the rest is re-deposited, possibly together with fuel species. Furthermore also collisions between particles are very important. The major processes related to impinging particles are:

• adsorption: Impinging particles with not to much energy can be adsorbed to the surface. Physical bonds with a relatively small binding energy of about 0.3 eV are possible for all species. Some particles can also form a chemical bond with a higher binding energy of about 3 eV. In a tokamak typically CO and H2O are abundantly present at the PFM surfaces. These adsorbed molecules form an important source of impurities. Therefore, diﬀerent techniques for reduction of the adsorption were developed (baking, glow discharges, boronization, carbonization). During the baking process the ﬁrst wall is heated, while glow discharge cleaning is based on particle bombardment. Carbonization leads to strong hydrogen adsorption. More information about these processes is written e.g. in [14] section 9.6.

• implantation: Hydrogen and impurities with high enough velocity can penetrate into the PFMs and come to rest in the bulk of the material at an interstitial site or a vacancy after a number of elastic and inelastic collisions. Small particles can then diﬀuse through the PFM and eventually reach the surface again.

• backscattering: Some of the bombarding particles will not stick to or penetrate in the PFMs, but are scattered back immediately to the plasma. These particles ﬁrst undergo thermalization by collisions in the solid material and most of the time they also pick up one or more electrons such that they are neutralized. Sometimes the particles are released back to the plasma as molecules. Hence the PFMs’ surfaces function as source of neutral rather cold atoms and molecules.

• physical sputtering or erosion: Each combination of a projectile (ion or neutral) and a target can result in the release of a target atom by momentum transfer. This physical sputtering is only possible beyond a certain energy threshold characteristic for the combination of a projectile and a target and related to the potential energy barrier at the surface. If the energy is high enough such that chemical interaction can be neglected, sputtering can be seen as a cascade of binary collisions leading to a target particle with high enough energy to leave the solid surface. The physical sputter yield decreases with sublimation energy of the target and increases with energy transfer. The average energy transfer depends strongly on the mass ratio. Therefore, the sputter yield for hydrogen projectiles and/or high Z target is very small (the yield of hydrogen impinging on carbon is 1-2%, while for tungsten it is around 0.001-0.01%). Knowing this it is easy to understand that impurity self- sputtering can result in a runaway process. When going to higher projectile energies, the yield ﬁrst increases approximately linearly, but then decreases again because the collision cascade is taking place always deeper and deeper in the solid. The yield also depends on the angle at which the projectile hits the target.

• desorption: Analogous to physical sputtering, particle impact can also result in the release of atoms and molecules which were previously adsorbed to the PFMs.

• chemical sputtering or erosion: In contrast to physical erosion, chemical erosion is only possible for special combinations of projectile and target materials (e.g. the

30 combination of hydrogen and carbon results in the formation of hydrocarbons). The particles are now not released by momentum transfer, but due to chemical reactions. In this case there is no threshold. Diﬀerent experiments proved that the chemical erosion yield decreases with increasing particle ﬂux or surface temperature.

• deposition and codeposition: Especially the divertor target plates are eroded by impinging particles. However, also the rest of the divertor and the inner wall are eroded by ions due to turbulent radial transport and by charge exchange neutrals. The result is that all kind of impurities (most tokamaks operate with diﬀerent wall materials) enter into the plasma. This impurities can then in turn cause erosion, but they can as well be adsorbed or implanted onto the PFMs. Therefore, layers of mixed materials are deposited on the PFMs. Because carbon chemically interacts with hydrogen isotopes it is possible that the deposited layers also contain hydrogen. This process in which fuel isotopes are trapped inside deposited layers is called codeposition and is very important.

• re-erosion: Of course the deposited layers can be eroded as well.

• neutron impact In ITER and future fusion reactors strong neutron fluxes are expected. Unhampered by the magnetic field the neutrons will bombard all PFMs. This results in significant altering of the material properties (brittleness, thermal conductivity,...)

Besides all these effects due to impinging particles also arcing appears and the high heat flux can cause sublimation, melting or melt layer ejection, thermal fatigue and crack formation. In [21] and [22] the processes related to particle and heat fluxes are treated into more detail. The interaction with the PFMs is influenced by the properties of the PFMs, but also by the plasma edge parameters (temperature, density, radiation), the transport processes in the plasma, the magnetic topology, the species represented in the plasma,... PWI is very difficult to understand because it involves different domains from plasma physics and atomic and molecular physics to chemistry, surface physics and material science. Furthermore the eroded impurities have strong influence on the plasma characteristics which makes that the choice of the PFMs and the characteristics of the plasma edge are coupled in a nonlinear way. It is very difficult to grasp all the physics of PWI. A lot of dedicated experiments and modeling is necessary to understand things at a fundamental level and to be able to predict what will happen in ITER. The problems related to PWI are probably the most difficult problems on the road to the first commercial fusion power plant one has to tackle.

4.2 Plasma edge

PWI is determined both by the design and composition of the PFMs and the properties of the plasma edge. Hence, the plasma edge is a very important region of the fusion plasma. Plasma scenarios should be chosen which result in optimal characteristics for the edge region with respect to PWI. The transport processes in the edge can be very complex and depend on the mode of operation. Simpliﬁed one can say that there is both diﬀusion from the plasma core to the

31 boundary region and penetration of particles released from the wall which are immediately excited and ionized by collisions with highly energetic electrons. Of course in reality the situation is much more complex than that. Transport is also something which is not fully understood. But that is another story. More information about transport processes in the plasma edge can be found in [23],[24]. As explained in chapter 3 the plasma particles are confined by a strong magnetic field. Of course the field cannot extend to infinity. At a certain radius the magnetic flux surfaces are not closed anymore. Beyond the so called last closed flux surface (LCFS) the particle trajectories intersect the PFMs. The shape of the LCFS is mainly determined by the magnetic field configuration. For the moment there are two kind of configurations as shown in figure 4.1:

• limiter conﬁguration: The closed magnetic surfaces are interrupted by one or more solid surfaces which determine the position of the LCFS. The limiter surfaces are usually ring shaped. This conﬁguration alone will not work for a fusion power plant because the particles released from the limiter can too easily penetrate the plasma core.

• divertor configuration: The LCFS is completely determined by magnetic fields. Outside the LCFS the plasma flows towards the divertor target plates. Therefore, these plates must be able to withstand strong PWI. In this way most of the PWI is removed some distance from the LCFS and the plasma core. The impurities released from the target plates are ionized and may be swept back to the target by the plasma flow before they can reach the LCFS and enter the confined plasma. There are several possible magnetic configurations for a divertor. The most successful has been the toroidally symmetric or poloidal field divertor. Toroidal conductors create a null in the poloidal field and a separation of open and closed magnetic surfaces. This results in a mode of operation with improved energy confinement (the so called H-mode).

The narrow layer between the LCFS and the wall is called the scrape-off layer (SOL). In this region the plasma flows to the divertor target plates. More information on the physics of the SOL can be found in [14] section 9.4. The particles flowing in the SOL are neutralized at the target plates. The resulting gas pressure is high enough to achieve efficient pumping through the channels below the divertor chamber. Half of the total heating power is convected towards the divertor target plates (for ITER estimated up to 10 MW/m2). The main functions of the introduction of the divertor concept are:

• Minimizing the impurity content in the core plasma by removing the PWI region from the conﬁned plasma

• Removing alpha particle power for energy production

• Removing helium ash from the fusion reaction and other impurities

Another important concept related to the plasma edge is the plasma sheath. This is the drop of the electric potential near the wall, which is essentially caused by diﬀerence in thermal velocities of electrons and ions. The origin of the plasma sheath is discussed more profoundly in [14] section 9.2. The consequence of the plasma sheath is that the positive ions are accelerated towards the wall, while electrons are slowed down. High Z

32 Figure 4.1: Schematic diagram of poloidal ﬂux surfaces in a tokamak (a) with a limiter and (b) with a divertor. The toroidal ﬁeld is normal to the page. [14]

33 impurities were already very efficient in sputtering the PFMs because of their high mass. The acceleration of high Z impurities by the sheath potential increases this efficiency even more. Cold neutral species released from the PFMs undergo many atomic and molecular processes when entering the plasma edge. Most processes are due to impact of highly energetic ions. In lesser amount also collisions with ions play a role. Some important reactions are given in figure 4.2. In order to be able to model the plasma edge and PWI correctly, the cross sections σ and the corresponding reaction rates < σve > of all significant processes should be known very precisely. The most recent data source is the Atomic Data Analysis Structure (ADAS) [4]. The reaction rates are function of plasma temperature and plasma density. In the edge the plasma temperature is not necessarily equal to the impurity temperature. When the plasma temperature is high, the collision rate is to low to allow the impurities to be thermalized before they are ionized. Different species thus can have different temperatures. In the plasma edge it occurs also frequently that the plasma is not thermal, the ion and electron temperature are different. It was not until the end of last century that the important role that hydrogen molecules play in the plasma edge was starting to be recognized. Before it was assumed that most hydrogen was recycled from the PFMs in atomic form and that the molecular contribution could simply be neglected. The last two decades, however, molecular spectroscopy in tokamaks all over the world has shown clearly that the contribution of hydrogen molecules in front of divertors and limiters can be very significant [25],[26],[27],[28]). The fraction of hydrogen coming from molecules influences the properties of the plasma edge in an important way. A good PWI model thus cannot work without taking into account the effect of the presence of hydrogen molecules. During measurements in TEXTOR it was even shown that the molecular hydrogen flux from a carbon limiter was comparable to the atomic flux at low carbon surface temperature. By heating of the test limiter surface the molecular contribution could be reduced. Up to 1100 K hydrogen was predominantly released as molecules. Above 1100 K a clear reduction of the H2-flux (50% of the original flux at 1370 K) was observed [27]. In some cases not taking into account the presence of molecules can result in large errors. A first example is the underestimation of hydrogen fluxes when derived from Balmer line radiation measurements (see section 7.2.3). Sometimes this underestimation can be as large as a factor of 2 [26]. Another example where the presence of molecules is clearly visible is in the velocity distribution of hydrogen atoms recycled from the PFMs. In the presence of molecules there are three different populations of hydrogen atoms. Each population is characterized by its own temperature and velocity distribution. This is observable in the shape of the hydrogen spectral lines by Doppler broadening or Doppler shift [29]:

• around 0.3 eV (cold): Dissociation of strongly vibrationally excited molecules is responsible for these cold hydrogen atoms with energies even lower than the Frank- Condon energy. Molecules in vibrationally excited states can dissociate with small energies because excitation now can take place into lower energies of the repulsive 3 state 2p Σu [27]. It was indeed shown in [30] that the vibrational temperature of hydrogen molecules reemitted from tungsten surfaces continuously exposed to a ﬂow of hydrogen atoms and molecules is high. The exact mechanism for generation of

34 Figure 4.2: Most important atomic and molecular reactions in the plasma edge [14]

these highly excited molecules is not yet clear, but it is probably due to mechanisms in the solid materials.

• around 4 eV (warm): Cold atoms can be heated by interactions between the cold neutrals and the hot ions.

• around 100 eV (hot): By charge exchange hot ions can become hot neutrals.

4.3 Importance of PWI for ITER and future fusion machines

PWI is a key issue in thermonuclear fusion research. Contact between the plasma edge and the PFMs has a lot of adverse eﬀects. But a tokamak without any PWI is of course not possible. Helium ash, other impurities and last but not least heat for power production need to be exhausted. The trick is to optimize the PFM choice, the magnetic conﬁguration and the plasma edge parameters such that the advantages of PWI are maximized, while the disadvantages are minimized. The most important topics are impurity radiation, fuel recycling, material degradation and dust formation.

4.3.1 Impurities There are two sources of impurities in a tokamak. Fusion of a deuteron and a triton results in the formation of neutron and a helium nucleus. The neutron is free, while the charged helium nucleus is confined by the magnetic field. α-particles are the first type of impurities. However, they are only present in tokamaks where fusion actually happens. In most experimental tokamaks the working gas is ordinary hydrogen and the conditions do not allow fusion. In these tokamaks there are however other impurities coming from the PFMs, as explained in section 4.1, by erosion, melting, evaporation or desorption. Below the most important effects of the introduction of these impurities are given:

• line radiation: All atoms and partially stripped ions can emit line radiation (see section 5.2.1). If the plasma is optically thin, as is mostly the case, the result is loss of energy and thus reduction of the fusion energy gain. But impurity line radiation does not have to be disadvantageous. If it is well controlled and only appears in the plasma edge it reduces the heat ﬂux towards the wall. Deliberate seeding of impurities (mostly noble gases) can be beneﬁcial for tokamak operation. However,

35 if the impurity content is not well controlled and impurities start radiation also in the plasma core, the line radiation prohibits good functioning. This is especially a problem during the start-up phase because impurities radiate most strongly at low temperatures. When the impurity content is too high it can even happen that only very short discharges are possible [31]. High Z impurities are most dangerous. They require higher temperatures to stop radiation because of the high ionization energies. Furthermore high Z impurities are more eﬃcient in eroding the PFMs. In this way they can create even more impurities resulting in a runaway process.

• disruptions: Edge cooling and the consequent current proﬁle modiﬁcation can lead to disruptions in some cases.

• fuel dilution: The presence of impurities implies dilution of the fuel and hence decrease of the fusion power density.

• bremsstrahlung: As explained in section 2.4 especially high Z impurities cause bremsstrahlung, which also results in fusion energy loss.

4.3.2 Recycling Each plasma ion, on average, goes to the divertor target plate or limiter and returns tot the plasma many times during the discharge (adsorption or implantation followed by desorption or sputtering, backscattering). For the light and small hydrogen isotopes this recycling process is very important because they have high velocities already for moderate energies leading to high penetration depths and they readily diffuse through most PFMs. The ratio of the particle flux returning to the plasma to the incident flux is called the recycling coefficient. In some cases this coefficient may be even greater than 1 because of previously adsorbed gas atoms or molecules. The recycling flux density is highest at the limiter or divertor target plates. However, recycling also occurs at the walls due to charge exchange. Recycling makes it very hard to control the fuel density. The situation is difficult to model. The equilibrium concentration of hydrogen in the PFMs depends on the fueling pressure, the wall temperature and the shot history. Furthermore hydrogen forms molecules, not only with itself but also with carbon for instance. More information on recycling can be found in [14] section 9.4 and in [32]

4.3.3 Material degradation and dust formation The PFMs in a tokamak have to endure very severe conditions. First of all impinging ions and atoms erode the surface by physical and for some materials also by chemical sputtering. These impurities can then again be deposited or codeposited with fuel particles on the PFMs’ surfaces. The result is that there are regions with net erosion and regions with net deposition. It is clear that net erosion regions puts severe restrictions on the PFM lifetime. But also net deposition regions can be a problem. The characteristics of such mixed material layers may be completely diﬀerent from the original material. Furthermore future fusion power plants will work with the radioactive tritium. Tritium implantation in the PFM saturates, but codeposition of tritium will increase the vessels tritium content unlimited. This is a major problem both from economical and safety point of view. The erosion and deposition processes can also result in the formation of dust which is a safety issue as well.

36 Another aspect is the impact of neutrons. In each fusion reaction a 14 MeV neutron is produced. These fast uncharged particles are not hampered by the magnetic field and bombard all PFMs. They can create microstructural defects in the solid material and alter its properties. The two most important issues in this context are the reduction of the thermal conductivity and embrittlement. Further materials should be chosen which are not activated by impinging neutrons to reduce the amount and lifetime of radioactive waste. Other material degradations are caused by the high heat fluxes from the fusion plasma. They can result in melting, melt layer ejection or sublimation when the material does not melt. Periodic temperature changes also induce thermal fatigue. Very short extremely high fluxes increase the temperature very fast and can result in crack formation due to thermal shock. All this has strong influence on the structural strength of the material and hence also on its lifetime.

4.3.4 Major concerns for ITER The long pulse lengths and high power and particle ﬂuxes ensure that the biggest step towards the next-step fusion devices will be the understanding and control of the PWI region. Because PWI is a critical issue for ITER and future fusion power plants, a special European task force was founded which is charged with the design and development of the PFMs for ITER. The most persistent problems related to PWI are assumed to be:

• tritium retention • PFM erosion • dust formation

These three processes are the most important factors determining the lifetime of the PFMs and the availability of the reactor. Lifetime and availability are very important, both for ITER and future fusion machines. Some parts of the ITER PFM are not easily replaceable or not replaceable at all. Therefore, the lifetime of these components should be high enough to ensure a lot of experiments. For future commercial fusion power plants which will need to operate continuously it is even more critical. So far it has been estimated that the steady state erosion in ITER will not be a problem for the lifetime of PFMs. Erosion of the wall may pose a problem in case of a concentration of the plasma fluxes to small wall areas. The major problems are coming from so called edge localized modes (ELMs) and disruptions. These events are accompanied with extremely high particle and heat fluxes. Disruptions should be completely avoided in a commercial fusion power plant. In ITER, where the operational limits will be explored, disruptions will of course occur but should be limited to a minimum. ELMs are even more difficult to tackle. They are intrinsic to the H-mode discharge regime which will probably be used in ITER and future fusion machines. So they will always be present. The only solution for this problem is mitigation to lower energies. Scientist are at the moment developing different techniques for this purpose, like pellet pace making and chaotic magnetic field in the edge lines created by edge ergodisation coils. ELMs are also linked with energy confinement. An optimum balance should be chosen between good energy confinenement and ELM energy. The energy confinement can be adjusted by changing the plasma edge parameters and the magnetic topology.

37 It is not easy to make clear predictions in the context of PWI for ITER and future fusion machines because there is a considerable gap from existing tokamaks. Some aspects can be extrapolated from experiments at these smaller tokamaks or simulated in the linear PWI devices (e.g. Magnum-PSI in the Netherlands [33]). Other aspects can only be modeled by computer simulations. However, there is still a lot of improvement needed in these complicated models. For the moment most models result only in qualitative agreement with experiments. So it is very important that a lot of experimental time on tokamaks and other relevant machines is reserved for PWI related experiments. This experimental work together with development of more accurate models should result in a deep understanding of the PWI processes that will occur in ITER and future fusion machines. The most urgent tasks to be performed in this context are:

• Development of high quality diagnostics which can be used under very harsh conditions

• Enhanced data on a range of fundamental physical properties (atomic, molecular, surface physics)

• Investigate the properties of mixed material layers

• Study of redeposition and erosion of redeposited layers

• In-situ and ex-situ measurements of layer thickness on PFMs

• Study of the properties of the ﬂuxes from the PFMs (ﬂux density, velocity distribution, molecular fraction,...)

• Development of fuel and dust removal techniques

• Investigation of hydrocarbon properties (dissociation rates, reﬂection probability,...)

• Evolution from the coupling of separate models for background plasma and solid material to a high conﬁdence predictive code combining all

• Modeling in 3 dimension to take into account the toroidal assymetry experimentally observed

4.4 Possible plasma facing materials

In a recent review article the diﬀerent possible PFM choices for ITER are evaluated [20]. The evaluation was made based on the estimated number of discharges possible without any problems. Due to safety reasons measures have to be taken when:

• for part of the PFM 2/3 of the initial thickness is eroded

• the total tritium inventory of the vessel is larger than 700 g

• the amount of dust surpasses 670 kg

38 The estimations where made for planned ITER conditions: discharges of about 400 s, a power ampliﬁcation factor Q = 10 and a fusion power Pfus = 500. Of course it are only estimations because extrapolations and modeling are accompanied by sometimes large errors. But it gives a good idea about which material choices will probably be the most suitable for ITER. Three materials have been choses as candidate materials for ITER:

• beryllium: Beryllium has two properties which are beneﬁcial for PFMs. It is the lightest metal. As discussed before the introduction of high Z impurities results in high sputter yields and strong radiation losses. Therefore, the low Z beryllium is a good PFM candidate. Furthermore it is a good oxygen getter which is advantageous for the vacuum characteristics of the tokamak. There are however disadvantages as well. Beryllium cannot be used at high heat ﬂux region like the divertor because it melts already at 1560 K. One must also be very careful with Be because it is a toxic element.

• carbon (graphite or CFC): In contrast to most other materials carbon does not melt. It only sublimates from 3825 K. Therefore, it is the preferred material for high heat ﬂux regions like the divertor target plates. Unfortunately carbon is also characterized by strong physical and chemical erosion. The chemical reactivity in a hydrogen environment results in the formation of hydrogenated species and codeposited layers. This of course gives rise to an important increase of the tritium inventory. Therefore, the use of carbon should be limited as much as possible.

• tungsten: In medium loaded areas (rest of the divertor) carbon is not necessary and beryllium is not yet possible. In these PFM regions tungsten is preferred. Only a small amount of physically sputtering occurs, while there is no chemical erosion. Furthermore W melts only at 3695 K. The disadvantage of W is the fact that it is a high Z element. Fortunately tungsten is too heavy and thus it does not drift to the conﬁned plasma volume.

For the moment it seems that one of these materials or a combination of the three will be used for ITER and future fusion machines. In the review article for possibilities where evaluated:

• CFC for the divertor target plates, W in the rest of the divertor and Be on the ﬁrst wall

• complete W divertor and a Be ﬁrst wall

• W for all PFMs

• CFC for all PFMs

The first option will very probably be chosen for the initial ITER PFMs. However the other options are still open. Especially in the later stage of ITER experiments. In figure 4.3 the estimated number of discharges possible from point of view of the different safety issues are summarized for the for material choices. From the standpoint of plasma wall interaction issues alone and providing plasma scenarios with strongly reduced ELMs, no significant fast ions production and mitigated disruptions an all-W device would solve best

39 the lifetime, dust generation and tritium issues. However, the compatibility of the plasma scenarios required to reach the performance foreseen for ITER with W walls remains to be demonstrated. An important task of the ITER task force for PWI is the improvement of the current wall concept and in parallel the development of new wall concepts.

Figure 4.3: Number of discharges required for reaching the safety limits due to erosion, dust generation and tritium inventory for the four material options for ITER [20]

40 Chapter 5

Radiation measurements and spectroscopy in tokamak research

A prominent characteristic of a plasma is the fact that it radiates. This radiation is spread out over a wide wavelength range and is caused by all kind of processes going on inside the plasma. Measurement of this radiation gives not only information about the species present, but also about the conditions of the plasma and the processes going on inside. Therefore, radiation measurements and spectroscopy are valuable tools for plasma diagnostics. In the ﬁrst section of this chapter the basics of radiation measurements are explained: radiation quantities, spectroscopic instruments, radiation detectors and calibration of a radiation measurement system. The origin of the radiation from a plasma is treated in section 5.2. In this section radiative processes, collisional processes, population kinetics and line broadening mechanisms pass the review. The knowledge of these concepts is essential in interpreting the radiation measurements correctly. In the last section it is explained why radiation measurements are so important for tokamak research. In the whole chapter the focus is on visible radiation measurements. Visible radiation is studied because for this work one was mostly interested in the behavior of the plasma edge and the PWI. In the PWI region the plasma is quite cold and almost all radiation is emitted in the visible region. Furthermore the instrumentation is easiest for measurements in the visible range. Visible light can pass through air, glass or quartz without any problem. There are two kind of radiation measurements: active and passive. In the passive measurements one simply looks at the emission of the plasma. Active measurements are based on the absorption of an incident bundle of light. Hence passive measurements are more easy to perform and they do not disturb the plasma. These are the kind of measurements used in this work. Plasma spectroscopy is already an old science and quite well established. The foun- dations of plasma spectroscopy were laid in the context of astrophysics. There are a lot of good books treating the topic. The standard work is the book of Griem [34]. Other interesting books are [11],[35]. A good book concerning optical measurements in general is [36]. More information about the structure of the atomic, ionic and molecular energy levels can be found in [37],[38]. An introduction to plasma spectroscopy for tokamak research is given for instance in the articles [39],[40].

41 5.1 Radiation measurements and spectroscopy

5.1.1 Radiation quantities In order to make quantitative analysis of radiation ﬁelds possible, a lot of diﬀerent quantities and units were introduced in the context of radiation. The most important quantities are summarized below:

• Radiant ﬂux Φ in W : total energy emitted per unit time

W • Radiant flux density φ in m2 : radiant flux emitted per unit area W • Irradiance E in m2 : radiant flux received per unit area W • Radiant intensity I in sr : radiant flux emitted per solid angle J • Fluence H in m2 : energy deposited per unit area during a given time W • Radiance L in m2sr : radiant flux emitted per unit projected area per solid angle W • Emission coefficient (r) in m3sr : radiant intensity emitted by a unit volume • Spectral quantities: derivated with respect to wavelength

In passive radiation measurements the radiation is collected from all places in the plasma along the line of sight. When light absorption can be neglected, as is mostly the case in typical tokamak conditions, one measures the local emission coeﬃcient (r) integrated over the complete line of sight as radiance L. This complicates the interpretation of the measurements.

5.1.2 Spectroscopic instruments In the simplest measurements radiation in all wavelengths for which the detector is sensitive is added together. Unfortunately a lot of information is lost in this way. It is much more interesting to spectrally resolve the radiation. The result of a spectrally resolved measurement can be a graph with the wavelength on the x-axis and the intensity on the y-axis. Therefore, it is of course necessary to split the radiation into the different wavelengths. This can be done in two ways. If one is only interested in all the radiation in a certain narrow wavelength region (e.g. one specific spectral line) one can make use of an interference filter. If one really wants to resolve the intensity as function of the wavelength one has to resort to dispersive elements as prisms, diffraction gratings or crystals. Also interferometers can be used for this purpose. The use of interference filters is not difficult. An interference filter or dichroic filter is an optical filter that only transmits light in a certain spectral band. Such a filter consists of multiple thin layers composed out of dielectric or metallic materials having different refractive indices. At the interfaces between two consecutive layers the light is partially reflected. This eventually results in multiple light bundles which have traveled different path lengths. The interference effects occurring by the superposition of these light bundles depend on the thicknesses and refractive indices of the layers. By carefully designing the filter it is possible to let only the light in a narrow spectral band interfere

42 constructively. Such a ﬁlter placed in front of the detector then makes sure only that light will be measured. For a spectrally resolved measurement one should chose the most appropriate dispersive component. This depends on the aims of the experiment. A spectroscopic instrument has four very important characteristic determining its usefulness:

• spectral resolution • throughput • spectral range • imaging quality

The spectral resolution is a measure for how well a the system is able to resolve peaks at different wavelengths. If one has two monochromatic bundles of light, there is a certain minimal difference in wavelength δλmin for which the spectroscopic system will still give two clear distinguishable peaks. This is the spectral resolution. If the wavelengths are closer to each other separation is not possible anymore. The resolving power is given by the ratio R = λ . The higher the resolving power, the better the resolution. Next one δλmin has the throughput. This is a quantity in optics which determines how much light of the source can pass through the system. Another important concept is the spectral range. It is not possible to look at all wavelengths with one single system. A spectroscopic system always has a certain sensitivity curve. It shows how sensitive the spectrometer is for each wavelength. This curve depends the characteristics of the different components of the system. The wavelength region available for study in a certain spectroscopic instrument is called the spectral range. One always has to pay attention that the spectral region one wants to observe indeed can be observed with the used spectrometer. Finally also the imaging quality is an important point of concern. The optical elements in the spectrometer form an image of the narrow entrance slit through which the radiation enters the spectrometer. Ideally the image is a replica of the entrance slit. It is impossible to optimize all these characteristics. In most cases the improvement of one property implies the deterioration of another. For most applications however diffraction gratings are the best choice. Prisms, Fabry-Pérotétalonsand Fourier transform spectrometers are used only for some special purposes. A diffraction grating is a linear array composed of a high number of equally spaced identical structures, called grooves. Characterizing a grating is done by its length l, N the groove number of grooves N or the groove density l (number of grooves per unit length) or the groove separation d, the groove width w and the shape of the grooves. There exist two techniques for developing a grating. A first technique uses a diamond tip to rule the grooves in the surface. The grooves are then coated by a thin reflective metallic layer (mostly aluminum, gold or platinum). This expensive parent grating is used for the manufacturing of cheaper replicas by a casting procedure with epoxy resin. The grooves made in this way are triangular. Holographic gratings are a more recent development. They are made by recording the interference fringes from two crossed laser beams on a photosensitive layer. The resulting grooves are sinusoidal and line densities lines up to 6000 mm are no problem. Illuminating such a grating with a monochromatic bundle of light of wavelength λ results in an infinite number of peaks emitted in certain well defined directions. The peaks

43 in these directions are caused by positive interference between light bundles reflected from the different grooves. Each peak corresponds with a certain order of diffraction p. With diffraction theory it can be shown that for a light bundle hitting the grating perpendicular the intensity under a certain angle v is given by

" #2 2π 2 sin Nπdv I(v) ∝ sinc wv · λ (5.1) λ πdv sin λ From this it can be calculated that the diffraction peaks are separated from each by N − 2 λ λ secondary maxima spread over an angle d and have an angular width ∆λpeak = Nd . The larger N, the smaller the secondary maxima and the narrower the major peaks. Further, the pattern of peaks is modulated by a broadth sinc function caused by the fact that the grooves have a finite width w. The minimal wavelength difference δλmin for a certain order p for which the angular separation of the peaks is greater than their width is then λ given by δλmin = Np . Hence, the resolving power for a grating is λ R = = Np (5.2) δλmin The resolving power can be increased by increasing the dimensions of the grating. The spectral range is determined by the wavelength difference ∆λmax for which consecutive diffraction peaks from the different wavelengths start to overlap each other

∆λmax = δλminN (5.3) From the relations (5.2) and (5.3) it is clear that one will need to find a compromise between large spectral range and good spectral resolution. This compromise depends of course on the aim of the research. In practice one almost always uses gratings in reflection and not in transmission. In this way the losses due to the untransparent regions are eliminated and the efficiency is increased enormously. An important technique related to gratings in reflection is the blazing process. The grooves are now not parallel to the grating surface anymore, but tilted over a blazing angle θ (see figure 5.1). The introduction of the blazing angle modifies the sinc function related to the shape of the grooves such that the reflectivity is increased for a certain diffraction order and wavelength range. One typically says that the grating is blazed to a certain wavelength for a certain order. Blazing is not possible for holographic gratings because of their sinusoidal groove pattern. The diffraction efficiency can however be controlled by adapting the modulation depth of the grooves. Nowadays also ion etching techniques are being employed to change the sinusoidal profiles into triangular profiles.

44 Figure 5.1: Proﬁle of a ruled diﬀraction grating with blaze angle θ

Figure 5.2: The Czerny-Turner arrangement

45 Diﬀraction gratings are mostly sold as part of a bigger spectroscopic system. The basic components of most systems are

• entrance slit (possibly with connection for optical ﬁber)

• collimating mirror or lens

• diﬀraction grating

• focusing mirror or lens

• exit slit

• detector

The light of the source enters the spectrometer via the entrance slit. The entrance slit influences both throughput and spectral resolution. A smaller slit enhances the spectral resolution but reduces the throughput. In some applications, as in tokamak research, the harsh environment makes it necessary to remove the spectrometer from the light source. Therefore, one has to resort to spectrometers which are equipped with a connection for an optical fiber. The incoming radiation is first collimated by a curved mirror or a lens, then diffracted by the grating and finally again focused by a curved mirror or a lens on the exit plane. Each wavelength is focused to a different position in this plane. Collimating and focusing is mostly done by means of mirrors, because lenses are subject to chromatic abberation and absorption. The only problem with mirrors is the fact that their reflectivity decreases at short wavelengths. Therefore, one sometimes uses curved gratings, which combine focusing and dispersing properties. When one would make use of a photodiode or photomultiplier tube (PMT) only a very narrow wavelength range at a time could be detected through the exit slit. The width of the exit slit also has an influence on the spectral resolution in this case. Scanning by rotating the diffraction grating allows measuring over a broader wavelength range. When properly designed, this arrangement allows canceling of coma and reducing astigmatism. This type of configuration is called a monochromator in stead of a spectrometer. By using a linear array of detectors like a charge-coupled device (CCD) this scanning is not necessary anymore and a complete spectrum can be recorded at once. An exit slit is then not used anymore and the spectral resolution is influenced by the pixel size of the detector array. One of the most frequently used configurations for such a spectrometer is the Czerny-Turner configuration shown schematically in figure 5.2. Besides all components discussed above, also the housing of the spectrometer is very important. A good housing reduces the stray light level. There will always fall some light on the detector which is not mend to fall on it. There are different sources of stray light: light can leak through the housing or light entering the entrance slit can be reflected or scattered by the walls and the surfaces of the optical components. Stray light should be limited as much as possible in order to reduce the noise level.

5.1.3 Radiation detectors Eventually the ﬂux of photons, spectrally dispersed or not, needs to be converted into an electric signal (a current or a voltage) such that it can be manipulated. This is the task of

46 a detector. There are a lot of possible radiation detectors, each with their pros and cons. The best detector does not exist. The most suitable detector for a certain experiment depends on the aim of the experiment. Some important concepts related to detectors are

• spectral sensitivity: response of a detector depends on the wavelength of the light

• eﬃciency: expresses how easy photons can be converted into an electric signal

• spectral range: only photons in a certain spectral range cause a detector response

• rise time: detector needs some time to built the complete signal

• delay: some detectors have an intrinsic time delay

• linearity: for good measurements a linear response is desired

• dynamic range: ratio maximum non-distorted signal to minimum detectable signal

• dark signal: even without illumination a detector will give a non-zero output value

In order to compare diﬀerent detectors special quantities have been introduced

• quantum eﬃciency: ratio photons creating a response to total number of photons

A V • sensitivity: electric response of the device created measured in W or W • dark counting rate: number of counts per second under no light illumination

• dark current: output current under no light illumination

It is impossible to discuss in this subsection all possible light detectors in detail. Only the photomultiplier tube (PMT), the photodiode, the charge-coupled device (CCD) and the bolometer will be treated brieﬂy because these are the detectors used in this work.

Photomultiplier tube (PMT) The main layout of a typical PMT is shown in figure 5.3. The arrangement of the different components can be somewhat different, but the general idea remains the same. The complete system is put in a vacuum enclosure. In the first step the light falls via a glass or quartz window onto a semitransparent photocathode coated on the vacuum side of the entrance window. If a photon has enough energy it can cause an electron to leave the thin layer at the other side by the photo-electric effect. But not all photons with enough energy will release a photoelectron. The fraction of photons effectively releasing an electron is called the quantum efficiency η and is typically in the range 10-25 %. The η-value is different for different wavelengths and depends also on the photocathode material. In the UV and visible spectral range it is no problem to find suitable photocathode materials. By using the suitable scintillators it is possible to detect VUV and X-ray radiation as well. Thallium-activated sodium iodide NaI(Tl) for instance absorbs hard X-ray photons and emits fluorescence radiation in the visible and UV spectral region. Furthermore also the thickness of the photocathode is essential. Too thin layers result in too much photons penetrating through the photocathode, while too

47 Figure 5.3: Schematic layout of a photomultiplier tube

48 thick layers make it more difficult for the photo-electrons to leave at the other side of the photocathode. The photo-electrons already form a small electric signal. However, for low photon fluxes this signal is to weak. Therefore, a photomultiplier tube makes use of an amplification system. The photo-electrons are focused and accelerated towards a series of dynodes. Each subsequent dynode is put at a somewhat higher voltage such that the electrons are accelerated from dynode to dynode. At each dynode the electron bombardment results in the liberation of secondary electrons with a multiplication factor δ which depends on the dynode material and the electron energy or voltage difference. For a voltage difference of 100-150 V between two subsequent dynodes one typically has δ = 4. A common PMT has 9-12 dynodes and thus requires a voltage source of about 900-1800 V. The voltage is mostly delivered by the combination of one single voltage source and a linear resistive voltage divider. To guarantee a constant current amplification, the voltage must be very stable and thus the anode current must be limited to ±1% of the current through the resistors of the voltage divider. The anode current is also limited because a too high current causes heating of the photomultiplier assembly. Typically the maximum value is something like 100 µA. It is also clear that any magnetic field in the neigbourhood of the PMT must be avoided because it influences the electron trajectories and thus also the current amplification. Eventually a much larger current reaches the anode. The current is typically multiplied by a factor of 106 − 107. One can then measure this current directly with a current meter or one can measure the voltage produced across a load resistor. The output current for a constant photon flux depends of course on the voltage difference applied between the cathode and the anode. For increasing voltage difference the current first increases but eventually reaches a plateau, which is the preferred region of operation. On this plateau the response is linear up to a certain photon flux from which space-charge effects cause the beginning of the non-linear response region. The signal is typically formed after a time delay of 20-100 ns due to the finite time required for the electron avalanche to propagate. A rise time of 1.5-15 ns is caused by the small differences in path length between the electron trajectories. As all other radiation detectors the PMT has a dark current. This current is caused by thermal electron emission, leakage currents and electrons released from the inside of the tube by radioactive radiation from the environment. It sets a lower limit on the detectable photon fluxes. The spectral range of a PMT is primarily determined by the photocathode material and the transmission of the window. The long wavelength end is determined by the work function of the photocathode material, while the short wavelength end is determined by the window transmission cut-off.

Photodiode Semiconductor detectors are also based on a photo-electric eﬀect, but in this case the eﬀect is internal. Photons absorbed in the semiconductor excite electrons from the valence band or donor levels into the conduction band or from the valence band into the acceptor levels. In this way free charge carriers are created and the conductivity is increased. This results eventually also in a measurable electric signal. In a photodiode the sensitive detector volume is the depleted region located around the junction of a p-type and an n-type semiconductor. The pn-junction is operated with a reversed bias voltage. When this voltage is chosen large enough, the current becomes

49 independent of the voltage and is given by

η(λ)Φ(λ) I = −e + I (5.4) hν d with η(λ) the quantum efficiency, Φ(λ) the impinging photon flux and Id the noise of the dark current, which can be reduced significantly by cooling. The quantum efficiency is a strong function of the wavelength and depends on the choice of the semiconductor. In the visible range one uses mostly silicon. The η-value can be quite high for photodiodes with typical values of 80 %

Charge-coupled device (CCD) For the measurement of a complete spectrum linear detector arrays are very useful because they can detect the whole spectrum in one time without the need for scanning. Nowadays one uses mostly the so called charge-coupled devices (CCD). The basic elements of a CCD are pixels made up of metal-oxide-semiconductor (MOS) capacitors integrated on a single chip. The pixel array can be one or two dimensional. When a pixel is bombarded by photons, free electron hole pairs are created, which charge the capacitor. A proper sequence of clock voltage pulses then transfers the charge packets through the array of capacitors till they reach the last capacitor of a row. There the respective voltage changes are read by an A/D converter and stored in a memory for further processing. The major disadvantage is that it takes quite some time (about 1 ms) to read everything out. Much higher time resolution is possible with photodiodes or PMTs.

Bolometer A bolometer is a completely diﬀerent kind of detector. It is not based on the liberation of charge carriers. Bolometers are based on the temperature increase of the detector material caused by impinging radiation. This change in temperature can be converted into an electric signal for instance by making use of the fact that the resistance of a material is a function of its temperature. In contrast to most other detectors the spectral response here is quite constant over a large wavelength region.

5.1.4 Calibration Very important for radiation measurements is the calibration. The output of a radiation detector is a certain current or voltage. When dealing with radiation these quantities are of course not very meaningful. Much more information can be deduced from the measurements when it is possible to convert the current or voltage in one of the quantities from subsection 5.1.1. This is called intensity calibration. Further, for spectrally resolved measurements also the wavelength needs to be calibrated.

Wavelength calibration The wavelength calibration is not that diﬃcult. One should measure the spectrum of a lamp with a well known pattern of lines in the spectral region of interest. The exact positions of these lines can be found in databases as that of the National Institute of Standards and Technology (NIST) [41]. The lines produced by the lamp should also

50 be as free as possible from broadening mechanisms such that the apparatus proﬁle can be measured (see subsection 5.2.4). The instrumental width of the apparatus proﬁle must always be subtracted from the measured with before interpreting the line width by mechanisms as Doppler broadening, Stark broadening,...

Intensity calibration The calibration of the intensity is somewhat more diﬃcult. It is best done for the complete measurement system as a whole. A standard source of known radiance must be placed such that the radiation of the source ﬁlls the full solid angle of the spectroscopic system just as in the real measurement. The best source for such calibrations is a black body radiator because it has a well known spectral radiance determined by Planck’s law that depends only on temperature and wavelength

2hc2 1 L(λ, T ) = 5 hν (5.5) λ e kT − 1 It is also possible to use other standard sources which then have to be calibrated regularly by black body radiators. The type of lamp one should use depends on the wavelength range of interest. In the visible range one frequently uses tungsten ribbon lamps. By dividing the known spectral radiance curve of the standard source by the measured spectrum one gets the conversion factor for each wavelength. This curve is also called the spectral sensitivity of the system.

5.2 Radiation from a plasma

A plasma emits and absorbs electromagnetic radiation. In the passive radiation measurements performed in this work one looks at the emission of the plasma. This emission is strongly related to the electronic, vibrational and rotational energy levels of atoms, ions and molecules present in the plasma. The energetic structure of the plasma species can be quite complex, but is well known since many decades. Details about this can be found in many books, e.g. [37] and [38]. Some basic information about atomic and molecular hydrogen energy levels is given in subsection 5.3.1 and 5.3.2. Radiation not only originates from electronic transitions between the energy shells. It can for instance also be caused by the Bremsstrahlung process. In the context of tokamak research, however, it is not the relation between the emission spectra and the energy levels that is of importance. The emitted radiation in a plasma is also influenced by the plasma conditions and the processes going on in the plasma. In plasma spectroscopy one wants to deduce information about the plasma from the measured radiation. Radiation measurements carry a lot of information. Unfortunately it is very difficult to read this information. Therefore, one has to understand all processes going on in the plasma very well. There are a lot of different processes which are all intertwined with each other. In typical tokamak conditions it is impossible to calculate things analytically. Hence modeling of the plasma is necessary. In this section the basics of such models are explained. In the first subsection radiative processes in the plasma are discussed. Subsection 5.2.2 treats the collisional processes going on in the plasma. The population

51 kinetics resulting from radiative and collisional processes are described in 5.2.3. Finally, the last subsection gives some information about line broadening mechanisms in a plasma.

5.2.1 Radiative processes in a plasma All radiation emitted by the tokamak plasma eventually comes from electrons making a transition from a higher to a lower lying energy level. Electrons can either be free or bound to a nucleus. Therefore, there are 3 kinds of electron transition possible resulting in diﬀerent types of emitted radiation.

• line radiation: discrete radiation lines due to bound-bound transitions corresponding with internal transitions in atoms, ions or molecules

• recombination radiation: continuum radiation with edges due to free-bound transitions when electrons recombine with ions

• bremsstrahlung: continuum radiation due to free-free transitions when electrons are deﬂected in the electric ﬁeld ions

Of course also the reverse processes can occur. This results then in the absorption of radiation. However, due to the low particle densities in a tokamak these processes can mostly be neglected.

Line radiation The most prominent aspect of a spectrum from a typical fusion plasma are the narrow peaks corresponding to line radiation. Due to collisional and radiative processes a sig- niﬁcant amount of atoms, ions, molecules and molecular ions will be in excited states. These species can then decay to the ground state or other lower lying excited states by spontaneous radiative decay. The photon energy for a transition from a level p into a level q is given by

E(p) − E(q) ν = (5.6) p→q h The probability that an electron in the energy level p will spontaneously jump into the lower lying level q can be calculated by using quantum mechanics. This probability can −1 be expressed as the Einstein coefficient of spontaneous emission Ap→q in units s or in the dimensionless line strength. The calculations require the knowledge of the electron wave function. However, these are only known exactly in the case of hydrogenic ions. In other cases approximations must be made. The transition probabilities can also be found by making dedicated experiments. A good up to date database in this context is that of NIST [41]. Making use of the Einstein coefficient A(p → q) one can write for the emission coefficient (see subsection 5.1.1) for the line radiation related to the transition p → q

hν = p→q A(p → q)n (p) (5.7) p→q 4π z From this expression it is clear that the line intensities can be related to the population of excited species. In fact the line radiation peaks or not really delta functions. Several

52 mechanism cause broadened in wavelength or frequency (see subsection 5.2.4). Therefore, the lines are characterized by a normalized line shape L(ν)

(ν)p→q = p→qL(ν) (5.8) Besides the spontaneous emission, there also exist two stimulated processes: stimulated emission and absorption. These processes are also have there respective Einstein coeﬃcients. All Einstein coeﬃcients can be related to each other by looking at the case of thermodynamic equilibrium. However, in typical tokamak conditions the stimulated processes can mostly be neglected. Therefore, these will further not be discussed.

Recombination radiation A less prominent feature in the spectrum of a tokamak plasma is the radiation due to recombination. Beside excitation also ionization takes place in the fusion fuel. Hence in a plasma there are a lot of free electrons and ions. These can recombine in diﬀerent ways. One possibility is radiative recombination in which the excessive energy is emitted as photons. The energy of such a photon is given by

Eγ = hν = Ekin + [E(∞) − E(q)] (5.9)

In this equation Ekin is the kinetic energy of the initial free electron. This energy can take any value and this is the reason why recombination radiation is continuum radiation without the narrow peaks characteristic for line radiation. The energy diﬀerence [E(∞) − E(q)] is the ionization energy for the bound energy level q. The radiation has several sharp edges related to the discrete nature of the energy shells of the ﬁnal electron state. Every process has its inverse process. For radiative recombination this process is photoionization. Both processes are connected with each other by the principle of detailed balance.

A(z+1)+(g) + e− )* Az+(q) + hν (5.10) This principle can be used to deduce the recombination cross sections from the photoionization cross sections. In this way the radiative recombination emission coeﬃcient can be calculated as well, which typically results in a spectrum as shown in ﬁgure 5.4

Bremsstrahlung Bremsstrahlung is the radiation caused by the slowing down of charged particles. In tokamaks Bremsstrahlung originates from the deflection of free electrons in the electric field of the ions. The process was already discussed before in section 2.4. Quantum mechanically this corresponds with an electronic transition between two free electron states. Because now both the initial and final state are free states the emitted radiation has no narrow lines or edges. Bremsstrahlung is characterized by a pure continuum spectrum with a maximum at the wavelength. 620 λmax [nm] = (5.11) kTe [eV]

53 Figure 5.4: Emission coeﬃcient of radiative recombination of a hydrogen plasma with kTe = 5 eV [11]

5.2.2 Collisional processes in a plasma Even important as the radiative processes are the collisional processes. These processes make sure that the plasma is populated by ions, electrons and excited species. Electrons are the most energetic particles in a plasma and thus the electron collision processes are almost always dominant. The probabilities of the different possible processes are usually described by so called cross sections σ(v), which depend on the relative velocity between projectile and target. Cross section are in units m2. Related to the cross sections are the rate coefficients X in units m3s−1. The relation between the two is given by Z 3 3 X =< σv >= σ(v)vf1(v1)f2(v2)d v1d v2 (5.12) v1,v2 The integration arises because of the fact that plasma species always have a certain energy distribution. Electrons have such high energies that for processes with electrons as projectiles the target species can be considered stationary. Calculation of these cross sections is sometimes very difficult and requires a lot of approximations. It is also possible to deduce the cross sections from dedicated experiments. A status of the database of the different cross section for the case of atomic and molecular hydrogen is given in [42]. The most important collisional processes are

• Collisional excitation and deexcitation: A free electron can collide with a bound electron. The result is an energy transfer between the two electrons. Depending on the direction of the transfer this process can cause either excitation or deexcition of the bound electron. Collisional excitation becomes less important for higher principal quantum numbers. The excitation process towards the next shell is important in the population kinetics of excited species.

A(p) + e− )* A(q) + e− (5.13)

54 • Collisional ionization and three body recombination: When a free electron collides with a bound electron, sometimes enough energy is transfered towards the bound electron in order to liberate it and cause ionization. Also the opposite process can happen if two electrons hit a certain ion. One of the two electrons can then become a bound electron, while the second electron runs away with the liberated energy. Three-body recombination is preferentially into excited states in contrast to radiative recombination where the ground state is preferred.

Az+(q) + e− )* A(z+1)+(g) + e− + e− (5.14)

• Autoionization and dielectronic recombination: Dielectronic recombination is a two-step process. A fast incoming electron is resonantly captured into a double excited state p∗ by simultaneously exciting one electron. This state will then either autoionize or it will decay to a lower singly excited level ﬁnalizing the capture.

A(z+1)+(q) + e− → Az+(p∗) → Az+(p) + hν (5.15)

Only electrons with kinetic energies in a certain narrow interval can participate because this capture process is resonant. Only at low electron temperatures radiative recombination dominates. Otherwise dielectronic recombination is by far the stronger channel. The inverse process is autoionization. Here a double excited particle can ionize itself by deexciting one electron and giving the released energy to the other electron such that it can become free. • charge exchange: The target ion captures an electron from the fast atom into a level p. Also this is a resonant process.

+ + Afast + B → Afast + B(p) (5.16) 5.2.3 Population kinetics of atomic levels in a plasma Knowledge of the atomic, ionic and molecular level population distributions in a plasma is a key step in the analysis of observed spectra. For each type of particle and for every charge stage of this particle all diﬀerent excited species have their own rate equation. Together all these equations form a set of coupled diﬀerential equations of the type

dn (p) z = −R (p →) + R (← p) + Γ (p) (5.17) dt z z z The right hand side of this equation represents the sum of the rates of all possible radiative and collisional transitions out and into the level p of a certain species in charge stage z possibly accompanied by an external flux due to diffusion and convection. It is practically impossible to calculate an analytic solution for this kind of problem. There is an enormous amount of possible transitions to be considered. Therefore, one always has to reduce the number of rate equations by taking into account only the most relevant processes and by considering the pertinent time scales. In this subsection several plasma models are discussed which describe the population kinetics under certain thermodynamic conditions. Another difficulty is the fact that not all cross sections or rate coefficients are known sufficiently accurate. The precision of a certain model depends strongly on the availability of accurate cross section data.

55 Thermodynamic equilibrium (TE) The simplest kind of model is that for which the plasma is in complete thermodynamic equilibrium (TE). In this case the rate of each process is exactly balanced by the rate of its inverse process. This equilibrium situation is also called the detailed balance. The complete physical state of the plasma can then be expressed by a ﬁnite number of thermodynamic variables such as density and temperature. For TE there is only one temperature for all species of the system. The particle level population distributions are determined by Boltzmann statistics or Fermi-Dirac statistics for very high density and the Saha ionization distribution. From Boltzmann statistics for a certain charge stage of a particle the population of a certain energy level can be related to the total population by the relation

n (p) g (p) E (p) − E (g) z = z exp − z z (5.18) nz Uz(T ) kT

In this equation nz(p) is density of the species in charge state z and excited state p, g is the ground state, nz is the total number of particles in charge state z, gz(p) is the statistical weight of the level p of the charge state z taking into account the degenerate sublevels and Uz is the partition function given by

∞ E (i) − E (g) U (T ) = X g (i) exp − z z (5.19) z z kT i=g This expression diverges mathematically for an isolated ion because the number of levels and the statistical weight go to infinity when approaching the ionization limit. However, in a plasma the coulomb field of the charged particles lowers the ionization energy reducing the infinite sum to a finite one. Hence the divergence is removed. The calculations to come to the Boltzmann formula (5.18) can be extended to continuum states by considering them as states of free electrons. This results in the Saha or Saha-Eggert equation, relating successive ionization stages of a certain particle

3 nz+1ne Uz+1(T ) 2πmekT 2 Ez(∞) − Ez(g) = 2 2 exp − (5.20) nz Uz(T ) h kT

In this equation the densities nz+1 and nz are the total densities of the species in respectively charge stage z +1 and z, Uz+1 and Uz are the corresponding partition functions and the energy difference Ez(∞) − Ez(g) is the ionization energy of the ground state. Increasing the plasma density influences the balance due to lowering ionization energies. At constant temperature the ionization equilibria shift towards lower ionization stages with increasing electron density. This is related to the fact that three-body recombination increases much faster with electron density than collisional ionization. In TE the radiation field is isotropic and homogeneous with an intensity given by the Planck function

2hν3 1 Bν(T ) = 2 hν (5.21) c e kT − 1 However, the detailed balance is often not valid for the radiation processes. There is almost always a non-zero energy transfer between photons of diﬀerent frequencies and

56 loss of radiation from a plasma with ﬁnite dimensions is almost unavoidable. Therefore, thermodynamic equilibrium is rarely realized in laboratory conditions.

Local thermodynamic equilibrium (LTE) Complete thermodynamic equilibrium is rarely achieved. An example where TE is valid is in interior of stars. In most other situations radiation escapes readily from the plasma leading to radiation fields below Planck’s law and deviations from TE. Local thermodynamic equilibrium (LTE) is similar to TE except that radiation processes are not described by a detailed balance. The population distributions can still be calculated by the Boltzmann (5.18) and Saha equations (5.20) and free electrons still have a Maxwellian energy distribution. But the radiation field is now no longer determined by the Planck function (5.21) and depends not only on local plasma conditions but also on population distributions and atomic transition probabilities. LTE is valid for relatively high density and low temperature when collisional processes are far more important than radiative processes. In this case the radiative processes have no significant influence on the population distributions. Electrons are much faster than ions because of their low mass. They will establish the equilibrium. Hence it is the electron temperature that is of importance. LTE will be a good model for all population levels of a certain ion if the collisional rate across the largest energy gap in the term system is approximately ten times higher than the corresponding radiative rate.

nz(p)neXz(p → q) ≥ 10nz(p)Az(p → q) (5.22)

The minimal value for the electron density ne can then be calculated as function of the energy gap and the electron temperature Te.

−3 20 3 1 ne[m ] ≥ 1.4 × 10 (Ez(p)[eV ] − Ez(q)[eV ]) (kTe[eV ]) 2 (5.23)

For a hydrogen plasma with electron temperature kTe = 5 eV this requires an electron density higher than 3.3 × 1017 cm−3. This is much higher than typical tokamak conditions. Even when LTE is not valid for a certain plasma, it will always be possible to find levels for which collisional transitions are highly favored over radiative transitions. The model in which LTE is only valid for certain levels is called partial local thermal equilibrium (PLTE). With decreasing electron density deviations from LTE will first occur for the largest energy gaps. In case of hydrogen-like and helium-like ions this is between ground state and first excited state. More precise conditions than the relation (5.23) for the validity of the LTE or PLTE model follow from more exact collisional radiative models (see further in this subsection).

Corona equilibrium (CE) The coronal equilibrium (CE) is valid low electron densities. It got its name because it was first used to model the radiation from the corona region of the sun. For coronal conditions the electron density and radiation field are so low that collisional deexcitations and three body recombinations are insignificant and can be neglected. In steady state collisional excitation is thus balanced by spontaneous decay

57 X nz(p)Az(p →) = ne nz(q)Xz(q → p) (5.24) q

In the above equation Az(p →) is the rate of spontaneous radiative decay away from the level p and Xz(q → p) is the rate coeﬃcient for collisional excitation from the level q to the level p. Further the excited level populations are assumed to be negligible compared to the ground state populations (except for metastable levels) due to the low collisional excitation rates compared with spontaneous decay rates. The population density of a level p in steady state is then given by

n (p) n X (g → p) z = e z << 1 (5.25) nz(g) Az(p →) The emission coeﬃcient of the line corresponding with the transition p → q can for this case be written as

hν (p → q) = p→q Γ n X (g → p)n (g) (5.26) z 4π p→q e z z Here Γ = Az(p→q) is the branching ratio for the radiative transition from the level p p→q Az(p→) to the level q. In steady state another balance is that between collisional ionization and radiative recombination

rr neSznz = neαz+1nz+1 (5.27) with Sz the rate coefficient for collisional ionization of the particles in charge state z and rr αz+1 the rate coefficient for radiative recombination for particles in charge state z + 1. This relation is the equivalent of the Saha equation (5.20). The equation is however not universal but depends on the specific ions involved. Later it was found that one gets better results by including also the dielectronic recombination. For the CE free electrons usually are assumed to have a Maxwellian velocity distribution. An approximate validity condition for CE for hydrogen-like ions is given by

0.1(z+1)2 h −3i 16 6 ne m ≤ 6 · 10 (z + 1) kTe [eV ] e kTe[eV ] (5.28)

For a pure hydrogen plasma with kTe = 5 eV the electron density should then be lower than 3 · 1011 cm−3. This is much lower than typical tokamak conditions. However, the CE can be used for some levels and is especially valid for highly diluted impurities in a tokamak plasma.

Collisional radiative model (CRM) Unfortunately for most tokamak conditions neither LTE nor CE is valid. In this case a more general and more complicated approach is necessary. For tokamak research one makes mostly use of a so called collisional radiative model (CRM). In such a model one starts from a set of coupled diﬀerential equations. This set consist of rate equations for the diﬀerent states which take into account the most important processes. It is impossible to include all physics in a CRM. One has to make reasonable approximations in order to get to a solution. Otherwise it is impossible to solve the problem. In contrast to LTE

58 or CE the local population distributions are now not only determined by local collisional processes, but also by radiative processes of non-local nature. Typically one starts from rate equations of the type

    dnz(p) X de−exc X exc X = −nz(p) ne  X (p → k) + X (p → k) + Sz(p → g) + Az(p → k) dt z z k

p k

p k>p cr rr dr +nenz+1(g) neαz+1(g → p) + αz+1(g → p) + αz+1(g → p) (5.29)

The terms is this diﬀerential equation respectively represent

• collisional deexcitation from the level p to all lower lying levels

• collisional excitation from the level p to all higher lying levels

• collisional ionization from the level p to the ground state of the next ionization stage

• spontaneous emission from the level p to all lower lying levels

• collisional excitation from all lower lying levels to the level p

• collisional deexcitation from all higher lying levels to the level p

• spontaneous emission from all higher lying levels to the level p

• three body recombination from the ground state of the next ionization stage into the level p

• radiative recombination from the ground state of the next ionization stage into the level p

• dielectronic recombination from the ground state of the next ionization stage into the level p

Such a rate equation takes into account most processes. Photoionization and photoexcitation are excluded. However, opacity can almost always be neglected because of the typical low densities in a tokamak. When it has to be taken into account it is mostly done by making use of the so called population escape factors. One has to solve the multi-level atomic rate equations in a self-consistent way together with the radiation ﬁeld computed from a radiation transport equation. The escape factors formally reduce the spontaneous transition probabilities. Excited states reach quasi-steady state on very short time scales compared to the changes of the densities of the ground states and metastable states and of the plasma parameters. For the relatively cold and undense edge plasma the population density of excited states is mainly determined by collisions with electrons or heavy particles and radiation, while the ground state populations mainly depend on transport processes. The population density of excited states is established on a time scale of a few nanoseconds,

59 while the ground state densities change much more slowly on a typical time scale between microseconds and milliseconds. Therefore, it is common to include only time variation for ground states and perhaps some metastable states. This implicates that the excited levels follow the variation of the ground state instantaneously. The ground state densities can be considered as quasi-constant input values for the CRMs. The set of coupled differential equations can transformed into a simple equation for the evolution of the ground state density nz(g) dn (g) z = −n n (g)Seff (T , n ) + n n (g)αeff (T , n ) (5.30) dt e z z e e e z+1 z+1 e e eff Here Sz is the collisional-radiative ionization coefficient, which takes into account multi- step excitation and deexcitation followed finally by ionization and discounts electrons eff which return to the ground state. αz+1 is the collisional-radiative recombination coefficient, which accounts for all recombination processes ending in the ground state. Bot coefficients depend on the electron temperature and density. In an analogous way the excited level population density nz(p) can be written as function of the ground state densities nz(g) and nz+1(g)

nz(p) = C0(p, ne,Te)nz+1(g) + C1(p, ne,Te)nz(g) (5.31) It is customary to normalize the population densities in the above equation to their Saha- Boltzmann population density. The equation is then transformed to the form

nz(p) nz(g) SB = r0(p) + r1(p) SB (5.32) nz (p) nz (g) where the population coefficients r0(p) and r1(p) can be determined by the CRM for all electron densities and temperatures. A lot of models were developed. The model for hydrogen is the most simple because of the less complicated atomic structure (see subsection 5.3.1). One of the first CRMs for hydrogen was developed by Johnson and Hinnov [43]. More recent data can be found in the ADAS package [4]. A very interesting tool is the FLYCHK code [3] (see also section 7.2.2). With this code steady-state and time-dependent calculations of population and charge- state distributions from low to high-Z elements can be performed. Also photoexcitation and photoionization are included in the FLYCHK model. The code is maintained at NIST [41] and can be used interactively through the internet. It is continuously improved and extended. CRMs for molecules is more complex than for atoms, but increasingly needed for understanding plasmas near the wall and the divertors in fusion devices. Sawada and Fujimoto [44] developed a CRM for a mix of hydrogen in atomic and molecular form. Unfortunately for molecules still a lot of information is lacking, especially for vibrationally excited species. The quality of the results from CRMs depends strongly on the existence and quality of the cross sections or rate coefficients. Therefore, a lot of work is still needed in this context. An overview of the status of the cross section data is given in [42].

5.2.4 Line broadening mechanisms in a plasma At first sight one would expect the line radiation of atomic and ionic species to be composed out of a number of infinitely narrow monochromatic peaks. However, several processes spread the lines out in wavelength as was stated already in subsection 5.2.1. The effect of

60 Figure 5.5: Gaussian, Lorentzian and Voigt profiles with equal FWHM the different broadening mechanisms is described by the normalized line shape function L(ν) or L(λ). An important quantity of such a line profile is the full width at half maximum (FWHM), symbolically written as ∆λ1/2. There exist three line shapes which are very common in plasma spectroscopy. • Gauss profile √ 2 v 2 ln 2(λ−λ0) G u 4 ln 2 ∆λG LG(λ; ∆λ , λ0) = u e 1/2 (5.33) 1/2 t G 2 π∆λ1/2 • Lorentz profile ∆λL 1 1/2 L (λ; ∆λL , λ ) = 2 (5.34) L 1/2 0 ∆λL π 2 1/2 2 (λ − λ0) + ( 2 ) • Voigt profile G L G L LV (λ; ∆λ1/2, ∆λ1/2, λ0) = LG(λ; ∆λ1/2, λ0) ∗ LL(λ; ∆λ1/2, λ0) (5.35) v u 4 ln 2 = u V (x, a) t G 2 π∆1/2 (5.36) a Z +∞ e−t2 V (x, a) = 2 2 dt (5.37) π −∞ a + (x − t)

√ λ − λ0 x = 2 ln 2 G (5.38) ∆λ1/2 L √ ∆λ1/2 a = ln 2 G (5.39) ∆λ1/2

61 When two effects act at the same time one has to make the convolution of both line shapes. As stated above the convolution of a Gaussian and Lorentzian gives Voigt profile. This special profile is well known and can be found tabulated in literature. When two Gaussians are convoluted one gets again a Gaussian with FWHM

2 2 G 2 G1 G2 ∆λ1/2 = ∆λ1/2 + ∆λ1/2 (5.40) The convolution of two Lorentzians gives a new Lorentzian with

L L1 L2 ∆λ1/2 = ∆λ1/2 + ∆λ1/2 (5.41) Also the convolution of two Voigt profiles results in a Voigt profile with the FWHM of the Gaussian and Lorentzian components given by (5.40) and (5.41). The three discussed profiles are depicted also in figure 5.5. In this graph the FWHM of the three profiles were choses equal. For the Voigt line shape the Gaussian and Lorentzian components each contribute 50% to the total line shape. Below the most important broadening mechanisms will be discussed.

Natural broadening Every line has some natural width. This is caused by the fact that every excited state has a finite lifetime. Classically, when radiation is damped exponentially, Fourier analysis shows that the resulting spectrum has a Lorentzian profile. Quantum mechanically the Heisenberg uncertainty principle also predicts a finite spread in photon energy

¯h ∆E∆t ≥ (5.42) 2

N ∆λ1/2τ =h ¯ (5.43) N In the last expression ∆λ1/2 is the FWHM of the Lorentzian proﬁle related to natural broadening and τ the lifetime of the level considered. In practically all cases, however, this natural broadening can be neglected because of other more important broadening mechanisms. Typical natural line widths are less than 10−5 nm, unless spontaneous emission rates or autoionization rates are high.

Instrumental broadening Another mechanism which always influences the measured spectra is instrumental broadening. Every spectrometer has a certain resolution. This is caused by the intrinsic resolution of the grating, scattering, imperfections,... Therefore, even a perfectly monochromatic line would result in the measurement of a line with a certain width. This line profile is typically Gaussian and is called the instrumental profile. It is important that this profile is measured before experiment. In this way one can take the effect into account without any problems. The width of the instrumental profile depends on the spectroscopic system that was used. It is best to calibrate the complete spectroscopic system at once such that all effect that can cause errors are taken into account.

62 Doppler broadening When a particle emits line radiation and is in the mean time moving towards or away from the observer along the line of sight with velocity v, the spectral line is shifted in wavelength. In the non-relativistic approximation this shift is given by

∆λ |v| shift = (5.44) λ c In practice radiation is mostly coming from an ensemble of particles. When they are drifting together in the same direction this shift can be observed. Another effect is the so called Doppler broadening. This broadening mechanism is the result of the averaging of the Doppler shift produced by the thermal motion of the particles. In case of a Maxwellian velocity distribution the results is a Gaussian line profile with full with at half maximum given by s s ∆λDoppler 8kTi ln 2 −5 kTi [eV] = 2 = 7.715 · 10 (5.45) λ mic mi [u] In section 4.2 it was explained that hydrogen in a fusion tokamak can be produced in different ways. Most experiments show the presence of three hydrogen populations with different temperature. Therefore, a typical line shape is the result of the superposition of multiple Doppler profiles. This complicates the line shape analysis a lot. In plasmas where broadening is dominated by Doppler broadening the ion temperature can be determined from the FWHM of the Doppler profile according to equation 5.45. Doppler broadening prevails at high temperatures, low electron densities and low ion masses.

Broadening due to magnetic fields Magnetic fields split the energy levels of atomic systems and hence also the spectral lines. According to the strength of the magnetic fields one can distinguish two effects. If the field is not to high such that the magnetic interaction is much less important than the spin-orbit interaction the Zeeman effect occurs. In this case each level with a certain total angular momentum quantum number J splits into (2J + 1) states characterized by the magnetic quantum number M. Transitions with ∆M = 0 (π-components) are allowed by the selection rules. The corresponding radiation is linearly polarized when observed perpendicular to the magnetic field. Also transitions with ∆M = ±1 (σ-components) are allowed. This radiation is circularly polarized in the direction of the field and linearly polarized in the direction perpendicular to it with the plane of polarization perpendicular to the magnetic field. Quantum mechanics dictates that the Zeeman energy splittings are given by

∆E = MgµBB (5.46) with µB the Bohr magneton and g the Land´efactor expressed in the case of LS-coupling by

J(J + 1) − L(L + 1) + S(S + 1) g(J, L, S) = 1 + (5.47) 2J(J + 1) Expressed in wavelengths one then has

63 2 ∆λp→q [nm] = [Mpg(Jp,Lp,Sp) − Mqg(Jq,Lq,Sq)] λ [nm] B [T ] (5.48)

For singlet systems (S = 0) one has g(Jp,Lp,Sp) = g(Jq,Lq,Sq) = 1. The result is one unshifted π-component and two shifted σ-components which together form a Lorentz- triplet. This is called the normal Zeeman effect. For S 6= 0 more complex patterns are observed. This so called anomalous Zeeman effect was one of the first hints for the existence of spin. For much higher magnetic fields the magnetic interaction overwhelms the spin-orbit interaction (Paschen-Back effect). In this case each electric dipole multiplet splits into three components, an undisplaced central component and two symmetrically shifted components. The selection rules now are

∆MS = 0 (5.49)

∆ML = 0, ±1 (5.50) The energy shift is given by

∆Ep→q = ∆MLµBB (5.51) For typical tokamak conditions both the Zeeman and the Paschen-Back effect can only be seen when the spectrometer has a very high resolution. In [45] it can be seen that wavelength intervals of 0.01 nm should be spectrally resolved to perform Zeeman studies. The effects caused by magnetic fields are enhanced for longer wavelengths and higher ion masses when compared to Doppler broadening. Therefore, Zeeman studies are typically performed for heavy ions and long wavelengths.

Stark broadening At low temperatures and high electron densities Stark broadening is the dominant effect. It is a type of pressure broadening caused by charged particles. Pressure broadening caused by uncharged particles can be neglected in tokamak plasmas which are highly ionized. A uniform electric field shifts the central wavelength of a spectral line. Stark broadening is caused by the time-varying microfields related to the charged particles in a plasma. The calculations for this effect are very complex because the long-range coulomb interactions influence many charged particles. An exact solution of the corresponding time-dependent Schrödingerequation is impossible. There exist two extreme approximation

• impact theory: The perturbing field fluctuations are assumed to be very fast compared to the radiation emission time. The emitted wave train is then perturbed by instantaneous impacts of charged particles. The fast random collisions result in a Lorentz profile. This approximation is typically made for the fast electrons in the plasma. • quasi-static theory: In this case the perturbing particles are assumed to move so slowly during an emission such that the perturbing field can be approximated as quasi-static. This approximation is typically made for slowly moving plasma ions.

However for typical conditions in the tokamak edge the eﬀects due to Stark broadening can simply be neglected [46].

64 Opacity broadening A last broadening effect is opacity broadening. Also this effect can be neglected for most lines in typical tokamak conditions. For some rare cases a certain spectral line can be optically thick. The line is then broadened because during transport towards the observer the photons near the line center are more readily absorbed than the photons more away from the center. The broadening effects can be calculated by solving the radiation transfer equations.

5.3 Importance for tokamak research

Radiation measurements and spectroscopy are extremely valuable tools in tokamak research. The inside of the tokamak vacuum vessel is a very harsh environment. Fur- thermore the diagnostics should not disturb the conditions to much. Therefore, a lot of instruments simply cannot be used inside a tokamak. But passive radiation measurements are well suited for increasing our knowledge of the processes inside. These measurements give information about the species present in the fusion fuel and about the conditions and processes going on in the plasma. The list of things one can deduce from radiation measurements is very long. A few examples are

• ion temperatures: can be calculated from the measured Doppler broadening via

mc2 ∆λ2 − ∆λ2 kT = FWHM instr (5.52) i 8 ln 2 λ2 ∆λ2 − ∆λ2 T [eV ] = 1, 692 · 108 · FWHM instr (5.53) i λ2 • plasma movement and rotation: possible to deduce using vλ ∆λ = λ − λ = 0 (5.54) 0 c

• electron density or temperature: if one of the two is known from another measurement, the second can be found based on the ratio of certain measured hydrogen Balmer lines (see subsection 5.3.1)

• particle ﬂuxes from the walls: ﬂuxes of certain particles coming from the PFMs can be calculated from the absolute intensity measurement of a spectral line of these particles by using a collisional radiative model

The experimental setup for passive light measurements is quite simple, but the interpretation of the measurements is sometimes very hard. Fortunately the study of plasmas by radiation measurement is not a new topic. It has been used already long time for the study of the sun. Of course a tokamak is very different from the sun, but a lot of techniques can be used in both cases. The wavelength range one needs to study depends on the region of the plasma one wants to study. A tokamak is characterized by a strong gradient of the electron temperature. In first approximation this gradient causes a series of concentric shells each with a different

65 predominant ionization state for every kind of particle. This simplified situation is altered by the effects of ion diffusion, especially in the plasma edge. The plasma center is extremely hot. Here the low Z ions are fully ionized. High Z species may still have some electrons left. The radiation from this part of the plasma is mostly UV and X-ray radiation. In this work one is more interested in the plasma edge where a lot of interesting processes as PWI take place. Here the electron temperature is much lower. All ions are still in low states of ionization. The radiation is mostly in the visible range. Typical condition in the 11 −3 13 −3 edge are an electron density 10 cm < ne < 10 cm and an electron temperature 1 eV < Te < 100 eV. Getting all information out of radiation measurements of a plasma is impossible without the use of models as described in subsection 5.2.3. The measured line intensities for instance give information about the concentration of excited species, while the knowledge of the concentration of the ground state species is more useful. This link can be made by modeling. Further, sometimes it is possible to trace back plasma parameters which cannot be measured directly. The models can simulate the resulting line intensities with the unknown plasma parameters as free parameters. By comparison between the reality and the model it is hence possible to determine the unmeasured plasma parameters.

5.3.1 Hydrogen atoms The theory of atomic and molecular spectra already has a quite long history and is well established. It would lead us way to far discussing it into detail. In tokamak research hydrogen and its isotopes deuterium and tritium are important species because they make up the major part of the plasma. Therefore, it is interesting to take a closer look at the spectra of these species. Quantum mechanics dictates that the electrons in every atom or molecule can only sit on certain well deﬁned discrete energy levels. This implicates that the photons emitted by electron transitions into lower lying levels also must have discrete energies. The exact quantum mechanical theory is mathematically quite complex. But for hydrogen the simpliﬁed Bohr model can already predict the main aspects of its spectrum. This model states that the electron always describes a circular trajectory around the nucleus balanced by the Coulombic and centrifugal forces. According to the wave-particle duality an electron is also a wave. Therefore, only certain discrete values are possible for the radius of the trajectories and the corresponding electron energies such that the electron wave interferes constructively with itself after one complete turn around the nucleus. It is easy to calculate the possible energy levels of the hydrogen atom based on these requirements

µe4 hcR 13.6 En = − 2 2 2 = − 2 = − 2 eV (5.55) 8n h 0 n n In equation (5.55) µ is the reduced electron mass, n is called the principal quantum number characterizing the energy level and R is the Rydberg constant with value R = 1.097373 · 107m−1. If one wants to make more detailed predictions for the hydrogen spectrum one has to rely on the complete quantum mechanical theory. The Bohr model has no mechanism for calculating transition probabilities and hence it is impossible to say something about the relative brightness of the spectral lines. Furthermore the exact theory shows that the electron shells characterized by principal quantum number n actually exist of subshells

66 Figure 5.6: The hydrogen spectrum and the Bohr model

labeled by the orbital momentum quantum number l, the magnetic quantum number ml and the spin projection quantum number ms. First order relativistic effects (fine splitting) and nuclear effects (hyperfine splitting) remove the degeneracy partially and cause very small shifts of the energy levels (maximal shifts and splittings appear for the lower lying shells and are of the order of 0.02 nm). External electric and magnetic field can cause additional splittings and shifts (Zeeman effect, Stark effect). But if the external fields are not to high and the spectral resolution of the radiation measurement is limited, the Bohr model is sufficient for explaining the spectra. Historically the discrete nature of spectra was discovered before the advent of the underlying quantum mechanical theory. The hydrogen lines were discovered in series of transitions with a common final energy level. These series were named after the scientists who discovered them: Lyman series for nf = 1, Balmer series for nf = 2, Paschen series for nf = 3, Brackett series for nf = 4, Pfund series for nf = 5 and Humphreys series for nf = 6. Of course there are also series for corresponding to the shells with nf > 6, but these did not get a name. It was found empirically that all series follow a common pattern predicted by the Rydberg formula ! 1 1 1 = R 2 − 2 (5.56) λ nf ni Later it became clear that this formula could be easily proven theoretically by the Bohr model. For this work the hydrogen lines in the visible spectrum are most interesting. Only the 4 first lines of the Balmer series are in the visible range. They were called Hα,Hβ,Hγ

67 Table 5.1: The four visible hydrogen Balmer lines and their corresponding wavelengths Name Wavelength Hα 656.28 nm Hβ 486.14 nm Hγ 434.05 nm Hδ 410.18 nm

and Hδ and correspond with the transition between the respectively initial levels ni = 3, ni = 4, ni = 5 and ni = 6 and the common final level nf = 2. Their positions can be found in table 5.1. The other Balmer lines and all Lyman lines lie in the UV region. All other series have lines with wavelengths beyond the visible region. The Balmer series was the first series of hydrogen lines to be discovered by the Swiss physicist Johann Balmer in 1885. His Balmer formula was later generalized to the Rydberg formula (5.56). The situation for deuterium and tritium is not much different. The only difference between the three isotopes is the presence of one or two additional neutrons. These cause a change in the reduced electron mass. The result is a spectrum that looks quite similar, but with the lines shifted somewhat in wavelength over a distance of the order 0.2 nm. An atom or molecule can only emit line radiation when it is in an excited state. So a system emits line radiation only when there are mechanisms populating the higher lying energy levels. Excited hydrogen atoms in a tokamak plasma can result from different processes:

• electron impact processes of cold, slowly moving hydrogen molecules released from the wall

− ∗ − H2 + e → H + H + e (dissociative excitation) (5.57) − ∗ + − H2 + e → H + H + 2e (dissociative ionization) (5.58)

• charge exchange processes with the hot plasma protons

H + H+ → H+ + H∗ (atomic charge exchange) (5.59) + + ∗ H2 + H → H2 + H (molecular charge exchange) (5.60)

• molecular ionization followed by dissociative recombination or excitation

− + − H2 + e → H2 + 2e (molecular ionization) (5.61) + − ∗ H2 + e → H + H (dissociative recombination) (5.62) + − + ∗ − H2 + e → H + H + e (dissociative excitation) (5.63) (5.64)

• electron impact processes of hydrogen atoms and ions

H + e− → H∗ + e− (collisional excitation) (5.65) H+ + e− → H∗ (recombination) (5.66)

68 The hydrogen involved in the processes (5.65) and (5.66) can originate from several of the other processes. At low electron temperatures all collisional processes are important. For higher temperatures the collisions between heavier particles dominate. Heavy particles have lower velocities and therefore, the cross section is higher. The recombination contribution is negligible for lower lying excited states in ionizing plasmas as in tokamaks [47]. The molecular reaction are only important if the amount of molecules is significant. It has been shown during last two decades that molecules are important in the plasma edge. As explained in subsection 5.2.4 the line profiles in a tokamak are significantly modified by Doppler broadening and Doppler shift. These modifications depend strongly on the temperature of the species involved. In the list above it is shown that there are a lot of possible reactions which can lead to excited hydrogen species. Each mechanism will result in particles with a different temperature (see also section 4.2). Therefore, the hydrogen lines will in general be the superposition of different Doppler profiles. Especially the components resulting from the dissociation of molecular species and charge exchange will almost always be present. Hence the interpretation of a hydrogen spectral line is not easy. There is already experimental evidence that the shape [28] and the intensity [26] of the atomic hydrogen lines are significantly influenced by the molecular contribution. In [48] it was shown indeed that the shape of the Hα line is determined by different hydrogen populations with different temperatures. Also in [49] three components were needed to explain the observations. The consequence of all this is that the hydrogen temperature is easily overestimated in low spectral resolution measurements. But the fact that the hydrogen lines are actually superpositions of the lines of different components can learn us also a lot of things. By high spectral resolution measurements it is possible to deduce the velocities of the different hydrogen populations. The velocity distribution can then be used to calculate penetration depth, fueling efficiency, recycling,... So the study of hydrogen lines will give scientists a better understanding of the recycling and neutral particle transport in a tokamak. According to [48] molecule dissociation and particle reflection are the two dominant processes in edge recycling. Beside these two processes also charge exchange represents a significant contribution to the Hα line shape.

5.3.2 Hydrogen molecules In the early days of fusion research it was assumed that hydrogen molecules do not play an important role in tokamaks. However, during the last two decades a lot of experiments have shown that the fraction of hydrogen in molecular form can be very significant, even dominant. These molecules reside in the plasma edge and can be introduced by gas puffing or by interaction of the plasma with the wall (see section 4). The molecular hydrogen fraction has proven to have a strong influence on several plasma characteristics. In some circumstances the fraction can be deduced from hydrogen Balmer line ratios [47]. Unfortunately this simple technique does not always work [25]. Therefore, more and more attention is being given to molecular hydrogen spectroscopy. Only the direct way via hydrogen molecular spectroscopy provides reliable numbers for the molecular fraction. Molecular spectra are much more complex than atomic spectra. Apart from the energy levels corresponding to different electronic arrangements also the relative position of the constituting atoms has an influence on the energy levels. This results in the existence of vibrational and rotational levels. Radiative electronic transition typically lie in the visible and UV range as for atoms, while vibrational transition are in the near IR region and

69 rotational transitions in the far IR range. The additional vibrational and rotational levels for each electronic level give rise to molecular bands in contrast to the discrete narrow peaks in the atomic case. 3 In tokamak studies one is mostly studying the Fulcher-α band emission (3p Πu → 3 2s Σg) in the relatively unperturbed red spectral wavelength range between 600 and 650 nm. Such research was for instance performed in [26], [30], [50]. Molecules can be observed readily, but the interpretation of spectra is complex due to extended energy level diagrams in comparison with atoms. The vibrational levels and their population play an important role. Because of the extensiveness of molecular band it is practically impossible to measure a complete band. Fortunately there exist techniques to reconstruct the complete molecular spectrum based on partial molecular information [51]. A good resolution R > 15000 is required for distinguishing all features of the molecular spectrum.

70 Chapter 6

Experimental setup

All experiments treated in this work were performed on the COMPASS tokamak at the Institute of Plasma Physics of the Academy of Sciences in Prague (Czech Republic). The COMPASS tokamak together with the surrounding systems (power supplies, position control and data acquisition system, diagnostics) is a quite complex device. It is impossible to discuss all components into detail. The ﬁrst section of this chapter gives a short history of the COMPASS tokamak and discusses the most important components. It is also explained why COMPASS is such an important and promising device. In last two sections the diagnostics for visible radiation measurements are treated in somewhat more detail. The Ocean Optics HR 2000+ spectrometer and the photomultiplier tubes are of primordial importance in this work.

6.1 COMPASS tokamak

The basic structure of COMPASS is that of a typical tokamak. The name COMPASS is related to the fact that it is a rather small device. It is the contraction of the words ’compact’ and ’assembly’. The appendix ’D’ is added because the tokamak has a D-shaped vessel. The most important parameters of COMPASS are given in table 6.1. It is the smallest divertor device with a clear H-mode and highly ITER relevant parameters. It scales to ITER approximately as 1:10. A schematic representation of COMPASS is given in figure 6.1. The toroidal field (TF) coils, poloidal field (PF) coils, central solenoid and vacuum chamber are indicated. The toroidal field coils are responsible for the strong toroidal magnetic field. This field provides the major contribution to the confinement of the plasma.

Table 6.1: Basic parameters of the COMPASS tokamak major radius R 0.56 m minor radius a 0.26 m poloidal cross section A 0.23 m × 0.38 m plasma current Ip < 400 kA toroidal magnetic ﬁeld BT 0.8-2.1 T pulse length ∆t < 1 s triangularity δ ≈ 0.5 elongation κ ≈ 1.6

71 Figure 6.1: Schematic representation of Figure 6.2: Comparison of the poloidal the COMPASS tokamak cross sections of several ITER relevant tokamaks

Figure 6.3: Inside view of the COMPASS Figure 6.4: Close-up on part of the tokamak vacuum vessel: 1. graphite COMPASS inner vacuum vessel tiles and divertor, 2. INCONEL wall, 3. tungsten probes

The central solenoid carries the current which induced the plasma current. The poloidal field coils have different functions as discussed further on. Figure 6.2 compares the shape and dimensions of the poloidal cross section of COMPASS with that of two other ITER relevant devices: ASDEX-U and JET. A view inside COMPASS is shown in figure 6.3. The PFMs in the regions subjected to the most harsh circumstances, as the divertor region, are covered by graphite tiles. The rest of the vessel wall is made of INCONEL. That is a Ni based austenitic superalloy with Cr as second element. INCONEL also contains other elements like Fe, C, Si, Mo, Mn, P and S. An INCONEL alloy was chosen because it is oxidation and corrosion resistant and retains its strength over a wide temperature range. Besides graphite and INCONEL also tungsten is represented inside the vacuum vessel in the form of probes implanted in the divertor tiles. All these different elements in the COMPASS PFMs can enter the plasma during discharges with strong PWI. This can be seen for instance in the visible spectra (subsection 7.1.1). The close-up on part of

72 Figure 6.5: Transport of the COMPASS tokamak from Culham to Prague

Figure 6.6: COMPASS tokamak installed at the IPP ASCR, Prague the inner vacuum vessel of COMPASS in figure 6.4 clearly shows relics of erosion due to strong PWI during the quite extensive lifetime of the tokamak. The COMPASS tokamak was designed in the 1980s at the UKAEA Culham Science Center in the UK as a flexible tokamak mainly to explore magneto-hydrodynamical (MHD) physics. The first experiments on COMPASS were performed in 1989. The operation with D-shaped vessel began in 1992. The experiments at the UKAEA delivered a lot of important publications about H-mode physics, ELMs, error-field modes, ECRH,... (e.g. [52], [53], [54]). In 2001 unfortunately COMPASS was mothballed due to the growth of the spherical tokamak program at the UKAEA and the lack of manpower and hardware resources to run both the MAST and COMPASS programs. Hence the huge potential of the COMPASS tokamak was not fully exploited. Therefore, in autumn 2004 the device was officially offered by the UKAEA and EURATOM to the Institute of Plasma Physics of the Academy of Sciences of the Czech Republic (IPP ASCR) in Prague. During 2007

73 COMPASS was dismantled at Culham and transported to Prague. In the mean time in Prague the new tokamak building was constructed and the power supplies were manufactured. In December of 2007 COMPASS was installed into the new tokamak hall. After the commissioning of new power supplies, the installation of some basic diagnostics and the development of a control system, the first plasma was observed on 09/12/2008. The routine operation at the IPP started on 19/02/2009. A lot of work of course had to be done already before the first plasma was observed. First of all some theoretic studies were performed. The plasma parameters of COMPASS with its new surrounding systems were investigated by means of a self-consistent core- edge model [55]. It was found that the operational space of the tokamak is relatively broad in terms of available densities, plasma currents and magnetic fields. In [56], [57] the plasma equilibria for COMPASS with the future neutral beam injection (NBI) system were investigated numerically using the ACCOME and ASTRA codes. Further it was shown in [58] that the magnitude of the stray magnetic field around the COMPASS tokamak is low enough for the installation of the NBI system (less than 20 mT in the vicinity of the ion source). The magnetic field configuration was computed using numerical integration of the Biot-Savart law in the approximation for an infinitely thin wire. The COMPASS tokamak requires the availability of 50-60 MW of peak power for more than 1 second. At the UKAEA in Culham this power could simply be taken from the local 33 kV grid powering the JET device. At the IPP in Prague, however, the available 22 kV grid at the campus of the Academy of Sciences provides only 1 MW. Therefore, new power supplies were designed and manufactured by the CKD group. Energy of the grid is accumulated by two fly-wheel generators which can deliver about 60 MW for 1.5 seconds. This concept is also used in other tokamaks (JET, ASDEX-U, JT-60U, TCV,...). The fly- wheel generators were placed outside the assembly hall in a special sound-proof building, the local control of the power supply system, the transformers and the switching station were located in the assembly hall and the thyristor rectifiers in the tokamak hall itself. The transfer of the COMPASS tokamak from the UK to the Czech Republic was an excellent opportunity to design and develop also a completely new digital data acquisition and position control system which addresses the needs of future experiments. The long pulse durations of future discharges imply a massive amount of data. The most interesting information must be stored efficiently by the data acquisition system. Further, the control part must be able to continuously monitor and control plasma activity during the whole discharge. The toroidal geometry of a tokamak gives rise to a radial expansion of the tokamak. An external vertical magnetic field has to compensate for this effect. The plasma in COMPASS can be shaped vertically elongated. The system is then unstable to any displacement in the vertical direction. An external radial magnetic field is necessary to provide stability. Different poloidal field coils take care of the position control in both vertical and horizontal direction. The position control is split in a slow preprogrammed part and a fast feedback system (5 kHz) based on magnetic measurements. The position control and data acquisition system was redesigned and built from scratch. The most recent digital technologies were used. The hardware for the controller is based on the PICMG 3.0 Advanced Telecommunications Computing Architecture (ATCA) standard. The interface to the system is provided by the FireSignal position control and data acquisition system. It allows operators and diagnostic coordinators to configure hardware, prepare discharges, preprogram events of interest and follow results from the discharge. It will also orchestrate the data flow coming from the different diagnostics into the database

74 Figure 6.7: Poloidal field coils in the Figure 6.8: Schematic representation of COMPASS tokamak on a poloidal cross the poloidal field coils in COMPASS section and to registered data clients. Unfortunately the data acquisition and position control system do not yet work as they should. The collected data sometimes show strong noise and different channels can be shifted in time with respect to each other in an unpredictable way. This complicates of course the interpretation of the data. The fast feed-back system is not yet operational. Therefore, the shots are still not reproducible and often very short. Disruptions and strong PWI cannot be avoided without a good working control system. One is working very hard now to make both systems work properly as soon as possible. The data acquisition and position control system are indispensable for a good experimental program. More technical information about the new digital system can be found in [59]. The magnetic field system is a key component in every tokamak. The plasma is confined, shaped and positioned inside the vacuum vessel by means of these magnetic fields. The coils used now in COMPASS are still the original water-cooled copper coils. They were transferred to Prague together with the rest of the tokamak. Only the power supplies for the magnetic field system were renewed. The COMPASS tokamak has PF coils and TF coils. The PF system is composed out of 4 different parts, each with its own function

• M windings: The current through the M windings in the central solenoid is provided by the magnetizing ﬁeld power supply (MFPS). The fast change of this current induces the toroidal plasma current. The plasma current in turn provides Ohmic heating. The M windings function as the primary winding of the air transformer.

• E windings: The current through the E windings is provided by the equilibrium ﬁeld power supply (EFPS). The task of this current is to correct the position of the plasma in the COMPASS vacuum vessel over long timescales. The vertical magnetic ﬁeld prevents the plasma column from expanding its main radius.

• S windings: The current through the S windings is provided by the shaping ﬁeld power supply (SFPS). The shaping coils create the desired plasma shape. Diﬀerent

75 configurations are possible: circular, single null divertor configuration (SND), single null divertor configuration with high triangularity (SNT),... • F windings: The current through the F windings is provided by the feedback field power supply (FFPS). The fast feedback coils provide position control of the plasma on short timescales. The BR circuit creates a horizontal magnetic field for fast feedback control of the vertical plasma position, the BV circuit creates a vertical magnetic field for horizontal plasma position feedback.

The different PF coils are depicted in figures 6.7 (poloidal cross section) and 6.8 (schematic 3D view). For the moment only the M windings and E windings are used. The shaping and fast feedback system do not yet work properly. Hence the shape and position of the plasma column cannot be controlled during the shots. Located outside the PF coils, 16 equispaced TF coils provide the toroidal magnetic field BT . The maximal TF in COMPASS is 2.1 T for IBT = 92 kA. For the moment, however, shots are performed with a toroidal magnetic field field of 0.8 T. In the future the toroidal field will be increased up to its maximal value. More information on the magnetic field coils and position control can be found in [60]. Besides the new data acquisition and position control system also an new computer controlled vacuum and gas handling system was developed. A vacuum up to 10−8 mbar can be created by the new system. Conditioning of the first wall is possible by use of the inductive heating system. Typically a glow discharge in He is used for cleaning of the first wall elements. There are already some basic diagnostics available at COMPASS: magnetic sensors for measuring of the loop voltage Vloop, the toroidal plasma current Ip and the plasma position, a 2 mm microwave interferometer for determination of the electron density ne averaged over a line from top to bottom through the center of the vessel, photomultiplier tubes with the appropriate interference filters for monitoring of the Hα,Hβ or CIII line, a PMT in combination with a NaI(Tl) scintillator for monitoring of the HXR radiation, an Ocean Optics HR 2000+ spectrometer for spectrally resolved measurements of the visible region, Langmuir probes for determination of the plasma potential and a fast camera for observation of radiation in the visible range with submillisecond temporal resolution. These diagnostics provide already some basic information concerning the discharges. However, more advanced diagnostics will be added in the future. The diagnostics will be focused mainly on the plasma edge. When the shaping and position control system will be ready, the COMPASS tokamak will be able to operate in H-mode in the Ohmic regime without additional heating. In order to achieve the desired ELMy H-mode operation relevant for ITER, later two new NBI systems will be installed. Each system will have a peak power of 0.3 MW and a particle energy of 40 keV. The neutral beam injectors will be quite flexible. It should be possible to switch between co-injection, balanced injection and normal injection without to much difficulty. The original lower hybrid microwave heating system with 8 waveguides and a maximal output power of 0.4 MW at 1.3 GHz will be reinstalled. Afterwards one will also design and manufacture a new ECRH system. COMPASS may be a quite small tokamak, but it has an enormous research potential as a flexible and low-cost facility with ITER relevant parameters. Therefore, it will be able to explorate novel regimes and concepts. For the moment all discharges are produced in a hydrogen working gas. The focus of the research program of COMPASS is on edge plasma physics (H-mode studies and PWI), pedestal investigations and later also on wave-plasma

76 interaction studies (parasitic lower hybrid wave absorption in front of the antenna and lower hybrid wave coupling). A detailed description of the research program of COMPASS at the IPP ASCR is given in [61].

6.2 Ocean Optics HR 2000+ spectrometer

Table 6.2: Basic parameters of the Ocean Optics HR2000+ portable spectrometer [62] dimensions 148.8 mm × 104.8 mm × 45.1 mm weight 570 g spectral resolution 0.15 nm signal to noise ratio 250:1 integration time 10−3 - 65 s sensitivity 75 photons / count spectral range 457 - 663 nm

Figure 6.9: Outside view of the Ocean Figure 6.10: Schematic interior view Optics HR2000+ portable spectrometer of the Ocean Optics HR2000+ portable [62] spectrometer: 1. SMA connector, 2. 5 µm × 1 mm slit, 3. ﬁlter, 4. collimating mirror 5. 1200 grooves grating, 6. focusing mirror, 7. focusing lens (not present), 8. linear CCD array [62]

All spectra used during this work were taken with the HR 2000+ portable spectrometer of the Ocean Optics company. The most important parameters of the used spectrometer are given in table 6.2. A picture of the HR 2000+ spectrometer can be seen in figure 6.9. The basic components are indicated on the schematic interior view in figure 6.10. The SMA connector provides coupling with an optical fiber. The light then passes through a 5 µm × 1 mm entrance slit. A standard aluminum-coated reflective mirror collimates the light towards a 1200 grooves/mm grating (Ocean Optics grating H9). The grating is a polymer replica of a holographic master grating and is most efficient for the wavelength region 400-800 nm. The relative efficiency curve for the grating is given in figure 6.11. Another standard mirror focuses the light on the the Sony ILX511 linear silicon CCD- array detector with 2048 pixels, a dynamic range of 1300:1 which is sensitive for the

77 Figure 6.11: Relative efficiency curve for Figure 6.12: HR 2000+ spectral range the Ocean Optics H9 1200 grooves/mm and resolution as function of starting grating [62] wavelength [62] wavelength range 200-1100 nm. The mirrors and the diffraction grating are arranged in a symmetrically crossed Czerny-Turner configuration. At COMPASS one is mostly interested in the impurity lines in the visible range. Therefore, the grating was rotated and fixed such that the smallest wavelength falling onto the detector is around 457 nm. From the curve in figure 5.3 it can then be deduced that the spectral range of the spectrometer is around 205 nm and the spectral resolution between 0.14 and 0.15 nm. The sensitivity as function of the wavelength for the spectrometer depends largely on the efficiency curve of the grating and the sensitivity of the detector. More information on the HR 2000+ spectrometer and the accompanying SpectraSuite software can be found in [63], [64], [62]. The HR 2000+ was used as impurity survey spectrometer for monitoring of the most intensive spectral lines in the visible range 457-663 nm. In most shots the radiation was integrated over the complete discharge duration. Only one long shot was observed in a time resolved fashion with a resolution of 10 ms. For higher time resolution one has to rely for instance on PMTs. The study of the visible radiation of excited neutral atoms and ions from the plasma edge is very interesting, in particular for studying hydrogen recycling and the influx of impurities. The observation points and lines of sight for the HR 2000+ spectrometer and the PMTs are indicated in figure 6.13. During my first stay at the IPP the spectrometer and PMTs were installed in observation point 1 and the view was tangentially. This allowed the observation of a large plasma volume. During my second stay observation point 2 and a radial line of sight were used in order to make the interpretation of the data easier. The observed area is indicated for both cases in gray in figure 6.13. The line of sight for the 2 mm microwave interferometer was measured at another toroidal location from top to bottom through the center of the vessel. Observation point 3 will be used for future radiation measurements. During my first stay at the IPP the spectrometer and the PMTs were located about 7 m away from the tokamak in order to avoid stray magnetic fields. During my second stay the spectrometer was even moved to the diagnostic hall next to the tokamak hall. The connection between the diagnostic port and the spectrometer or PMTs is realized by means of expensive optical cables.

78 Figure 6.13: Localization of the ports for the radiation measurements on a toroidal view of the tokamak from the top. Observation point 1 and 2 were used for the HR 2000+ spectrometer and PMTs respectively during my ﬁrst and second stay at the IPP. The gray areas indicate the viewing angle. The electron density was measured along a vertical line through the center of the vessel at another toroidal location. Observation point 3 will be used for the future radiation measurements

6.3 Photomultiplier tubes

Sometimes one wants to study the time evolution of the intensity of a certain spectral line or spectral region. For this purpose the HR 2000+ spectrometer is not very useful. The sensitivity of the spectrometer detector does not allow high time resolution measurements. In this case it is more appropriate to rely on PMTs. It is then not possible anymore to perform spectrally resolved measurements, but by using an interference filter in front of the PMT it is possible to select only the light of a certain line or wavelength region. The sensitivity of a PMT is high and the processing time is only of the order of 100 ns, allowing a much better time resolution. At COMPASS PMTs are used for monitoring the integral visible light, the CIII line around 465 nm, the Hα line, the Hβ line and the HXR radiation. Selecting the desired wavelength region can be done by choosing the appropriate interference filter. For HXR radiation one also needs a scintillator which can convert HXR radiation into visible light because the photocathodes of a PMT are typically only sensitive in the visible region. If one wants to compare the signals for different lines one has to take into account that the sensitivity of a PMT is a function of the wavelength. The PMT sensitivity is determined by the photocathode absorbance, the quantum efficiency and the photoelectron escape factor. Differences can also originate from the wavelength dependent optical fiber-, filter- and window transmittance. During my second stay at the IPP the Hα and Hβ were monitored by means of PMTs. The two lines were measured at the same time with the same type of PMT. In [65] it can be found that the code M10FS25 on the PMTs stands for

79 Figure 6.14: Absolute sensitivity curves for diﬀerent photocathodes [65]

80 • M: PMT for a general measuring problem

• 10: 10 dynodes

• F: photocathode coated at the inside of the front part of the vacuum tube

• no extra indication: ordinary glass for the entrance window

• S: SbCs3 photocathode • 25: outer diameter of the PMT of 25 mm

SbCs3 photocathodes are used frequently in PMTs because of their high photoelectric efficiency and low thermionic emission [66]. The optimum sensitivity lays in the blue-green region (320-600 nm) with the maximum at 450 nm. The sensitivity curves for different photocathodes are given in figure 6.14.

81 Chapter 7

Visible light measurements on COMPASS

For my master thesis I stayed two times at the IPP in Prague. The first stay was in the summer of 2009 from 06/07/2009 till 06/08/2009. This period was very instructive. I encountered the different aspects of experimental work and data processing at the tokamak department. In the first place I learned working with the HR 2000+ spectrometer and its accompanying software SpectraSuite, accessing the experimental data on the server of the tokamak department, using IDL codes and writing some small routines myself. Further, I read a lot of articles and parts of books about the basics of tokamak research and optical spectroscopy of plasmas. The acquired knowledge allowed me then to interpret the different experimental data and to perform a study of the characteristics of some recent shots of the COMPASS tokamak. During the winter of 2010, I stayed a second time at the IPP from 24/02/2010 till 24/03/2010. I started again by acquiring new knowledge. I read some more technical articles about plasma-wall interaction, spectroscopy in tokamak research and collisional radiative models. Then I learned how to perform simulations with the FLYCHK code in order to make a comparison with the experimental results at COMPASS. In particular I tried to reproduce the experimentally measured temporal evolution of the Hα and Hβ intensities. Based on this comparison it was possible to say something more about the characteristics of the COMPASS discharges. Further, I also made a rough estimation of the time evolution of the hydrogen flux in COMPASS from the measured Hβ intensity. Finally, a study was made on the thermal ionization phase of the discharges.

7.1 First stay at the IPP

7.1.1 Study of the visible spectra The visible spectra of the COMPASS tokamak plasma obtained with the Ocean Optics HR 2000+ spectrometer contain very interesting information about the plasma. Therefore, they are treated here in a separate subsection. With the HR 2000+ it is possible to integrate the spectra over the complete discharge duration or to take multiple spectra with an integration time of 10 ms during one shot. An example of a spectrum integrated over the complete discharge duration is given in ﬁgure 7.1. A quick view learns already that the spectrum is dominated by line radiation.

82 Figure 7.1: Time integrated HR 2000+ visible spectrum (COMPASS shot 505)

The photosensitivity of the spectrometer’s detector is too low for the observation of continuum radiation or molecular radiation. Furthermore, also the spectral resolution is too low to distinguish the features of a molecular spectrum. The line radiation is emitted by the hydrogen atoms from the working gas and by the plasma impurities. Each line corresponds with a certain electronic transition in an ion. The lines are labeled by the ions with which they correspond. The numbering starts with I for a neutral atom, II for an ion with charge +1 and so on. The label CII for instance means that the line is related with a certain electronic transition between the energy levels of single ionized carbon atoms. In most cases it is possible to link the lines with their corresponding ions by consulting line position databases as that of NIST [41]. There are of course a lot of lines in each wavelength region, but one can eliminate most of them because their corresponding ions cannot be present in the COMPASS tokamak plasma. For the hydrogen working gas one can see only the Hα and the Hβ lines. The other hydrogen lines fall outside of the wavelength range of the HR 2000+ spectrometer. In most cases the Hα line clearly dominates the spectrum. There are also a lot of lines due to carbon ions. Carbon can be introduced into the plasma in many different ways, because a large part of the PFMs in COMPASS is made of graphite. The carbon atoms can enter the plasma for instance by desorption of hydrocarbons or by sputtering of graphite tiles and dust particles. The CII line at 657.8 nm is the most prominent impurity line. Finally there is also a helium line. The helium traces were left in the plasma after wall cleaning with the helium glow discharge. In figure 7.2 are given 21 different spectra, all taken sequentially during one single shot. Each spectrum corresponds with 10 ms of the discharge. For the moment this is the only good example of such a time resolved spectral measurement. Most shots in COMPASS are still limited to very short durations of around 20 ms. These durations are not sufficient to make time resolved spectral measurements with the HR 2000+ spectrometer. Longer shots as that of figure 7.2 are observed only rarely. It is not completely understood

83 Figure 7.2: Time resolved HR 2000+ visible spectrum (COMPASS shot 862)

84 Figure 7.3: Time evolution of Ip and visible radiation (COMPASS shot 862) why most shots are so short. Probably it has something to do with strong hydrogen influx from the wall caused by PWI. The plasma position control system does not yet work as it should. Therefore, the plasma sometimes touches the wall with strong PWI as consequence. The interaction between the plasma and the wall then introduces cold hydrogen species and impurities, some of them with very high Z values (tungsten, iron). These high Z impurities radiate away a lot of the plasma energy and can also cause abrupt termination of the discharge. Further, the plasma can disappear as well because of disruptions. A disruption is a complicated sequence of events. The plasma energy is lost suddenly. Major disruptions are almost always irreversible and lead to rapid decay of the plasma current and termination of the plasma discharge. The consequences of disruptions in a fusion reactor would be severe, leading to forces possibly of the order of mega-Newtons exerted on the machine structure and local overheating due to parasitic current loads. Therefore, it is very important to make the plasma control system work appropriately as soon as possible. Now back to figure 7.2. Such a time resolved measurement contains much more information about the discharge. It is possible to say something about the time evolution of a shot. In the first four spectra of shot 862 no lines are visible. The breakdown has not yet taken place. The first lines are observed only in the fifth spectrum. Here the hydrogen lines are the most prominent ones. This is logical. Starting with the breakdown the electron temperature in the plasma increases due to Ohmic heating by the induced plasma current. While the temperature is still quite low in the beginning, almost all excited species are hydrogen atoms. When the temperature increases, most hydrogen atoms will become ionized. The hydrogen lines thus decrease rapidly. Later also other species start to lose one or more electrons. The sixth, thirteenth and nineteenth spectra are much rougher than the other spectra. This is probably because during these time intervals there was strong PWI. A lot of hydrogen and impurities are then released from the walls and enter the plasma. Species coming from the wall are cold and undergo collisional excitation

85 and ionization soon after entering the plasma. This results in a lot of additional lines. In these rough spectra there are possibly also lines from tungsten and iron released by sputtering of the wall materials and tungsten probes. The last spectrum again shows prominent Hα and Hβ lines. This is because the discharge ends here and the temperature decreases again. In total there are 17 spectra which show clear lines. Hence, based on the spectral information, the discharge duration must be around 170 ms. From the graph in figure 7.3 one can also deduce information about the time evolution of shot 862. The figure shows the evolution of the plasma current Ip (from the Rogowski coil) and the integral visible radiation (from a PMT). Despite of the strong noise, these signals still have a much better time resolution than the HR 2000+ spectra. However it is not possible to obtain detailed spectral information with PMTs. They are only useful for monitoring a particular line or a certain spectral region. From the graph one can seen that the discharge starts around 960 ms and stops about 165 ms later, which is consistent with the estimation of the shot duration from the HR 2000+ spectra. The plasma current first increases steeply up to about 20 kA and after a small dip increases further less steeply up to a flat top phase at about 80 kA. The visible radiation profile starts approximately at the same time and shows a peak at the beginning and one at the end of the discharge. During the flat top phase of the current, the electron temperature in the plasma is so high that almost no radiation is emitted in the visible range. The peak at the end is probably due to strong PWI or disruptions causing the introduction of cold hydrogen and impurity atoms from the PFMs. For the conditions in the COMPASS tokamak, line broadening is dominated by the Doppler effect. Other mechanisms as natural broadening, the Zeeman effect, Stark broadening and opacity broadening of course also have an effect. But, taking into account the limited resolution of the spectrometer, these effects are so small that they can all be neglected. The only other effect that has to be taken into account is the instrumental broadening. Theoretically it is then possible to determine the temperature of the ions from the widths of their spectral lines. Both Doppler broadening and instrumental broadening give rise to a Gaussian profile. When the two effects take place at the same time one gets the convolution of two Gaussians and hence again a Gaussian. The measured FWHM of this profile is given as function of the instrumental and Doppler FWHM by the relation

2 2 2 ∆λmeas = ∆λinstr + ∆λDoppler (7.1) Hence it is necessary first to determine the instrumental broadening of the spectroscopic system (combination of spectrometer and optical fiber). This calibration was performed in [67] for three spectral lines of the low pressure Ocean Optics CAL 2000 mercury argon calibration source. For this source Doppler broadening can be neglected and instrumental broadening is the dominant process. The FWHM is then completely determined by the instrumental broadening. The results are given in table 7.1. The instrumental FWHM ∆λinstr is of the order of 0.15 nm as expected from the spectral resolution of the spectrometer. It also follows from table 7.1 that the instrumental broadening depends significantly on the wavelength. Using equation (7.1) and taking an approximate value for the instrumental FWHM from table 7.1, the Doppler width can be calculated from the measured width. With equation (5.45) it is then possible to make an estimation for the ion temperature

86 ∆λ 2 kT [eV] ≈ m [u] Doppler (7.2) i i 7.715 · 10−5λ

Table 7.1: Instrumental broadening of the CAL 2000 calibration source lines by the HR 2000+ spectrometer [67] λ [nm] ∆λinstr [nm] 546.08 0.13 ± 0.01 576.96 0.16 ± 0.03 579.04 0.21 ± 0.02

However, the results are very meaningless in this case. The instrumental broadening is a strong function of the wavelength and is characterized by an measurement error. Furthermore, the measured broadening and the instrumental broadening are of the same order of magnitude in COMPASS. Therefore, the Doppler temperature determination is very unprecise. In [67] such a temperature determination was performed for the CII line at 657.8 nm. The instrumental broadening here was assumed to be 0.21 nm. These results are given in table 7.2. For a more meaningful temperature determination at the quite low temperatures in the COMPASS tokamak, a spectrometer with better resolution is necessary. Furthermore, the instrumental width should be determined for the wavelength of the studied line, because the instrumental width depends strongly on the wavelength.

Table 7.2: Doppler temperature determination for the CII line at 657.8 nm [67] shot ∆λmeas [nm] ∆λDoppler [nm] TCII [eV] 304 0.23 0.09 40 323 0.24 0.12 65

Finally it is also interesting to take a closer look at the Hα line. In time integrated spectra this is typically the most intense line. The study of this line can learn us a lot about hydrogen recycling processes, which are of primordial importance in tokamak research. Figure 7.4 shows a close-up of the Hα line for shot 496. The triangles represent the original data. The Hα line was so intense during this shot that the peak was cut off at the top because of the limited dynamic range of the HR 2000+ spectrometer. V. Weinzettl [68] developed a spectrum analyzer code in IDL. This routine first subtracts a smooth background fitted to the lower data. Then the remaining part of the spectrum is fitted by the sum of different Gaussian peaks with a certain threshold amplitude Amin. The code starts searching the spectrum for a peak from the short wavelength side to the long wavelength side. When a peak is found it is subtracted from the spectrum and the searching action starts again from the short wavelength side. The iterations are performed until the spectrum is everywhere lower than Amin. The spectrum analyzer was used for the shots 495-497 and 569-572. The results for the Hα line were always very similar. For all shots two Gaussians were necessary to reproduce the shape of the Hα line: one broad, large peak around 656.3 nm and a smaller, more narrow peak around 656.6 nm. These two Gaussians are depicted in figure 7.4 with dashed lines, the sum of the two Gaussians is depicted with a full line. Both peaks are indicated in figure 7.4 together with

87 Figure 7.4: Gaussian fitting of the Hα line (COMPASS shot 496) their sum. However, it is very doubtful that this result means something physical. It is more probable that the observed assymetry is only a relic from the finite resolution of the spectrometer. So also in this case a spectrometer with higher resolution is desired. With such a spectrometer it would be possible to study the combined effect of instrumental broadening, Doppler broadening, different hydrogen populations and Zeeman splitting (see subsection 5.2.4). This could learn us more about the conditions in the COMPASS tokamak plasma and the PWI processes. Further, measuring these more detailed spectra in a time resolved fashion could also be very interesting. If there are indeed multiple populations of hydrogen with different temperatures, the time evolution of the population densities could be different. This would then also be visible in the time evolution of the spectra.

7.1.2 Study of the discharge parameters Because the COMPASS tokamak was only installed in Prague by the end of 2008, the experiment at the IPP is still in its infancy. Fortunately, most basic diagnostics are already available. The discharge parameters which can be measured for the moment are

• magnetizing field current IMFPS: This current from the magnetizing field power supply (MFPS) flows through the central solenoid of the tokamak and its fast change induces the plasma current Ip.

• loop voltage Vloop: This voltage is measured by a toroidal loop of wire parallel to the plasma. It is determined by ﬂux changes due both to the magnetizing current

88 Figure 7.5: The four diﬀerent IMFPS proﬁles used during the experiments

89 IMFPS and the currents ﬂowing in the plasma itself.

• plasma current Ip: This current ﬂows through the plasma in toroidal direction due to the fast changing of the magnetizing current IMFPS. It is measured by means of a Rogowski coil (see [14] p. 501).

• electron density ne: This density is not a local value, but the average over a line from top to bottom through the center of the toroidal vessel. This is a consequence of the principle of interferometry measurements. • hard X-ray radiation HXR: X-rays are emitted by the highly ionized species in the plasma core if the temperature is high enough. Further, highly energetic plasma electrons impinging on the PFMs also cause X-ray emission. Electrons are slowed down in the dense vessel walls and emit Bremsstrahlung. • integral visible radiation allV IS: Visible radiation originates mostly from the deexcitation processes in the plasma edge, where the temperature in not very high. The signal from a PMT sensitive in the visible range without interference filter is a good measure for the evolution of the total visible radiation. • Hα, Hβ and CIII radiation: These specific lines can also be seen in the HR 2000+ spectra. However, for some applications it is interesting to monitor the lines with high temporal resolution by using PMTs with the appropriate interference filter. • Operation pressure p: Before each discharge the vacuum vessel is filled with hydrogen working gas. The hydrogen pressure before the breakdown is called the operation pressure. • discharge duration ∆t: The lifetime of a shot can be estimated by looking at the temporal evolution of the plasma current Ip, the electron density ne or the emitted radiation. • visible spectrum: As discussed in the previous subsection the HR 2000+ spectrometer delivers quite detailed spectral information on the visible radiation. How- ever the spectra cannot be used to perform studies in which very high spectral or temporal resolution is required.

These parameters allow already a limited characterization of the shots in COMPASS. In the article [1] a study was performed in which the dependence of Vloop, Ip and ∆t on p and −4 IMFPS was investigated. The operation pressure p was varied between 0.2 · 10 mbar −4 and 2.0 · 10 mbar. Four different IMFPS profiles were used during the shots and these are shown in figure 7.5. The graphs are the result of measurement. The four profiles are labeled further on by the absolute value of the current at which the fast ramp-up phase around 960 ms starts (14 kA, 12 kA, 10 kA or 8 kA). The study dealt with the shots 473-578 performed on 28/05/2009, 29/05/2009, 04/06/2009 and 10/06/2009. The main aim was to look for which conditions the shots in the COMPASS tokamak were optimized. This work was extended during my first stay at the IPP by including the radiation measurements of these shots. Making shots with a tokamak is not easy. A good discharge cannot be initiated just by pressing on some kind of ’start’ button. A whole list of precautions was taken before each shot. The most important tasks are listed below.

90 Figure 7.6: Typical waveforms for IBT , IMFPS and IEFPS at COMPASS

• Before each series of shots the COMPASS tokamak wall was baked up to a temperature of 120oC and glow discharge cleaning in He was performed for several −2 hours (UGD = 500 V, I = 0.5 A, p = 10 mbar). These measures were taken to limit the amount of impurities adsorbed to the inner tokamak wall.

• Before each shot the vacuum vessel was pumped down to a pressure of 10−7 mbar. This had to be done in order to restrict the impurities content of the vacuum vessel.

• The desired waveforms for gas puffing, toroidal magnetic field current IBT , magnetizing field current IMFPS and equilibrium field current IEFPS were prepro-

grammed. The typical profiles for IBT , IMFPS and IEFPS are shown in figure 7.6. First the current through the toroidal field coils starts to flow (this point is taken as time t = 0). After about 600 ms the toroidal magnetic field reaches its maximal

value (IBT = 35 kA or BT = 0.8 T). The data acquisitioning starts at t = 790 ms and 10 ms later IMFPS is brought to negative values. At t = 912 ms the gas puffing is started and the vacuum vessel is filled with the hydrogen working gas up to a certain operation pressure dependent on the duration of the gas puffing waveform. Eventually around 960 ms a fast ramp up of IMFPS induces the plasma current and eventually causes breakdown. At the same time the current through the equilibrium field coils reaches its maximal value. The waveform for IEFPS was always the same. dI A It starts after 961 ms and ramps up with dt = 310ms up to its maximum value of 4.8 kA.

• The breakdown in a tokamak is similar to a Townsend discharge. A few initial electrons are accelerated by the loop voltage induced by IMFPS and cause an ionization cascade. Their are always some electrons due to background radiation, but breakdown in the COMPASS tokamak is facilitated by pre-ionization of the hydrogen working gas by a UV lamp.

91 Figure 7.7: Table with the most important discharge parameters for the studied shots. From left to right: shot number, IMFPS proﬁle, discharge duration, operation pressure, maximal plasma current and maximal loop voltage. The colors indicate the IMFPS proﬁle. In green boxes are the shots with operation pressure between 43 and 92 · 10−6 mbar

92 Figure 7.8: Scatter plots with ∆t, Ip and Vloop as function of p. The colors of the data −6 points indicate the IMFPS proﬁle. The pressure range between 43 and 92 · 10 mbar is indicated with green boxes.

93 The aim of this study was to look for which conditions the shots are optimized. Good shots are characterized by a long discharge duration. The plasma current and electron density should have a phase in which they are kept approximately constant on a high level. Further it is important that so called runaway electrons do not represent a significant part of the plasma current. Runaway electrons have acquired such high velocities due to the toroidal electric field in the tokamak that they are unhampered by the drag force of the ions (cross section of the Coulomb collisions decreases with the electron velocity as 1 v2 ). They can then be accelerated with the speed of light as only limit and ’run away’. They represent a non-Maxwellian tail of the electron distribution function. The anomalous Doppler instability causes periodic interaction of the runaways with the first wall elements. Therefore, the presence of runaways can be observed as spikes on the signal of visible radiation (enhanced recycling) and X-ray radiation (strong PWI). Runaway production is E enhanced for lower plasma density and higher toroidal electric field (high p value). More information about runaway electrons in tokamaks can be found in [69], [70], [71] and [72]. A last criterion is the efficiency of the breakdown. It is very important that the necessary loop voltage for breakdown in minimized. It saves voltsecond allowing for longer shot durations and it reduces the production of runaway electrons. The most important parameters of the studied shots are listed in the table of figure 7.7. Only the shots for which all data were available are included. From left to right one has shot number, IMFPS profile, discharge duration ∆t, operation pressure p, maximal plasma current Ip and maximal loop voltage Vloop. The colors indicate the IMFPS profile. In green boxes are the shots with operation pressure between 43 and 92 · 10−6 mbar. In order to visualize the data, figure 7.8 shows scatter plots with Vloop, Ip and ∆t as function of p. The colors of the data points again indicate the IMFPS profile for that shot. The pressure range between 43 and 92 · 10−6 mbar is also here framed with green boxes. The first scatter plot shows Vloop as function of p for the different IMFPS profiles. It is clear that the loop voltage is predominantly determined by the starting value of the magnetizing field current. The higher the ramp-up phase, the higher the loop voltage. By choosing a smaller starting current for IMFPS, the loop voltage and hence also the used amount of voltseconds can be reduced. One only has to make sure that the ramp-up phase is still sufficient for breakdown. Vloop can be reduced down to 10 V for the IMFPS profile starting at 8 kA. But it appears that for these shots ∆t is always less than 10 ms and Ip always less than 30 kA. The pressure dependence for each IMFPS profile resembles the Paschen curves introduced by Paschen in the context of discharges in a parallel plate configuration (see e.g. [73]). The breakdown voltage as function of the pressure shows a minimal value. This can be understood quite easily. If the pressure is very high, there are a lot of collisions between electrons and atoms or ions. Therefore, the electrons are not efficiently accelerated by the electric field. On the other hand, if the pressure is very low, the electrons are accelerated efficiently. In that case, however, there are very few collisions and hence very few ionizations. That explains why there is an optimum pressure for breakdown. If one looks at the other two scatter plots, there appears to be a pressure region in which higher Ip and longer ∆t are favored. This region lays approximately between 43 −6 and 92 · 10 mbar and appears to be independent of the IMFPS profile. This pressure range is indicated with green boxes in figures 7.7 and 7.8. It is also clear from the scatter plots that in the high pressure range long shots with high plasma current are somehow prohibited in COMPASS. For the low pressure range no final conclusions can be made

94 because of the lack of data, but at first sight it seems that also here only short shots with limited plasma current are possible. Further one can also study the HR 2000+ spectra and the time evolution of the integral visible radiation, Hα, HXR, Vloop and Ip. Based on all this information it was possible to distinguish four different types of shots. A typical spectrum for each of the types is shown in figure 7.9. The typical time profiles are depicted in figure 7.10. In the high pressure region above 92 · 10−6 mbar all shots appeared to be very similar (type I). In the pressure range between 43 and 92 · 10−6 mbar there appeared to be three different types of shots (type II, III and IV). In this pressure range on the scatter plots of figure 7.8 type II events are indicated with a circle, type III events with a square and type IV events without any symbol. These indicated shots are not the only ones of their type because only the shots for which no data were missing are included in the scatter plots. First some general remarks concerning the different graphs. Figure 7.9 shows the typical spectra for all types of discharges. All these spectra are integrated over the complete discharge duration. As in the previous subsection they are characterized by line radiation. The spectra differ in the number of lines and their relative strength. The number of lines depends on the species that were present in the plasma. Shots with strong PWI and disruptions hence will result in much rougher spectra because a lot of impurities are introduced into the plasma. The variation in relative strength cannot be explained that easily. The line strengths depend both on the intrinsic transition probabilities and the plasma conditions. Therefore, the strengths can only be predicted by dedicated modeling. The plots in figure 7.10 give the time evolution of the integral visible radiation, Hα, HXR, Vloop and Ip. Hard X-rays denote PWI. An important part of the electrons impinging on the PFMs can be due to runaway electrons. They do not interact with the rest of the plasma and can thus sometimes have a better confinement and keep circulating in the tokamak for a while after the discharge has disappeared. Eventually they all bombard the tokamak first wall. This is the probably the reason why for some shots the HXR signal continues even after the end of the discharge [74]. If the discharge would be in pure hydrogen it should be possible to let coincide the integral visible radiation and Hα signal by multiplication with a factor related to the PMTs’ spectral sensitivity because the only visible lines would then be the Hα and the much less prominent Hβ line. However, in most shots the Hα line is clearly not the major contribution to the integral visible radiation signal. This clearly indicates that there are indeed a lot of impurities present in the COMPASS discharges. The startup of the discharge looks quite similar in all four plots. First Vloop increases steeply due to the ramp-up of IMFPS. When the loop voltage is high enough the few initial electrons from pre-ionization with the UV-lamp are able to cause breakdown. Ip increases exponentially. Immediately afterwards the first visible radiation is observed, also in the Hα wavelength. Ideally one then expects the following to happen. Ip should increase up to a certain level which is high enough and then stay stable for a long time till it decreases again at the end of the discharge. Vloop should drop soon after the start-up phase of the discharge. Before the breakdown the gas in the vacuum vessel has a very high resistivity. The transformer then works as a voltage source. However, after breakdown the resistivity drops down very fast and the transformer works as a current source. For the integral visible radiation and Hα one expects a peak at the beginning and a peak at the end. In the stable flat top phase of the discharge there will be almost no visible radiation because the plasma is then very hot and most radiation is emitted at shorter wavelengths. The only visible radiation then comes from impurities introduction

95 Figure 7.9: Typical spectra at COMPASS

96 Figure 7.10: Typical Vloop, Ip, allV IS, Hα and HXR proﬁles at COMPASS

97 and hydrogen recycling due to PWI. Unfortunately, for the moment, this ideal scenario is far from reality at the COMPASS tokamak. It can be due to the lack of a good working position control system, too strong PWI with high impurity content as consequence or a combination of both. Studying the data of the diﬀerent types of shots one can draw the following conclusions

• type I:

– Line spectra with a limited amount of lines (C, N, 0, He, H) and with a very prominent Hα line – Very short shots with durations of about 10 ms – Only one peak in the time evolution of Hα and the integral visible radiation

– Ip has no stable phase and starts to decrease typically already below 30 kA – Start of the HXR signal announces the extinction of the plasma

• type II:

– Very rough line spectra with lines from a lot of elements (some even comparable with the Hα line) that seems to be superimposed on some sort of a continuum – Longer shots with durations around 30 ms

– Discharges are terminated by a disruption (recognized by a peak of Vloop and a a drop of Ip – Peaks of Hα and the integral visible radiation at the beginning and end of the discharge with the peak at the end very strong due to PWI related with the disruption – HXR activity during the whole discharge indicates strong PWI

– Ip ﬁrst increases steeply up to a value of about 15 kA and then increases more slowly up to a much higher value of about 90 kA

• type III:

– Quite rough line spectra with the lines of W and C comparable with the Hα line – Longest shots up to 190 ms

– Ip shows a quite stable phase in which it is only softly decreasing due to radiation – For the rest the time proﬁles are quite similar to that of type II – HXR and the integral visible radiation were not measured till the end of the discharge

• type IV:

– Similar to type I discharges – Hα and the integral visible radiation show peaks at the beginning and end of the discharge, but the radiation does not go to zero in between the peaks

98 It is clear that the discharges at COMPASS are not yet optimized. Most shots are extremely short. Only in the pressure range between 43 and 92 · 10−6 mbar longer shots are possible. These shots are still much shorter than 1 s, but it is a start. The problem is that these lower pressures enhance the production of runaway electrons which is also not good. Furthermore, all long shots are ended by disruptions. These should of course also be avoided because they cause degradation of the PFMs. What can be done to optimize the discharges in the future?

• Operate at full values of the toroidal magnetic ﬁeld BT (2.1 T in stead of the 0.8 T which was used during my ﬁrst stay at the IPP)

• Make the feed-back system for the plasma position work as it should

• Optimize the current proﬁles for the diﬀerent coils

• Improved conditioning of the vacuum vessel

• Longer baking time and glow discharge

In [75] one had similar problems. Operation at pressures higher than a few 10−4 mbar was not possible. In the conclusion of the article it was stated that a possible reason could be the absence of an eﬃcient pre-ionization source. Therefore, one could also try the introduction of strong HF pre-ionization at COMPASS. Hopefully these measures will allow for better discharges in the future.

7.2 Second stay at the IPP

7.2.1 Analysis of the start-up phase The shots studied during my second stay at the IPP were performed at conditions quite similar to the conditions of the first stay. For all shots discussed here the ramp-up phase of IMFPS started at 14 keV. The current through the toroidal field coils IBT was 40 kA in stead of 35 kA. This current corresponds with a toroidal magnetic field of 0.9 T, which is still quite far from the maximal achievable value of 2.1 T. The operation pressures were all in the high pressure region above 92 · 10−6 mbar. Such higher pressures are more interesting in the context of fusion research. For instance, the production of runaway electrons is suppressed. A disadvantage in the case of COMPASS, as discussed in the previous section, is the fact that this higher pressures somehow prohibit longer shots. This is probably one of the reasons why typical shots observed during this period are shorter than 10 ms. Part of the work performed during my second stay at the IPP concerns the start-up phase of the tokamak discharges. This phase is very important. During the first moments of a discharge, most runaway electrons are produced. Further, the loop voltage at the breakdown influences the maximal plasma duration. A good article about the start- up phase of a tokamak discharge is [75]. The first few hundred microseconds after the breakdown is called the avalanche phase. The plasma resistance is then still very high and the tokamak transformer works in good approximation as a voltage source. During this phase the electron energy distribution is non-Maxwellian and cannot be characterized by a temperature. Both the electron density ne and the toroidal plasma current Ip increase

99 exponentially. This increase is the net result of gains by collisional ionization and losses due to diffusion and drift of the plasma particles. After a while the plasma resistance has dropped significantly. The tokamak transformer then works approximately as a current source. This transition is characterized by a sharp drop of the loop voltage Vloop. Because of the different plasma properties a new phase is said to start from this moment on: the thermal ionization phase (TIP). From the start of this phase the hydrogen lines and the electron density are clearly measurable. The electron density has increased so much that the electron energy distribution can now be approximated as a Maxwellian with a certain electron temperature Te. The TIP is said to end when ne has reached its maximal value. The predecessor of COMPASS at the IPP in Prague was the CASTOR tokamak. At this very small device studies were performed concerning the start-up phase of a tokamak discharge. An interesting article concerning an investigation of the TIP at CASTOR is [2]. In this study a simple model was established predicting the time evolution of ne and the intensity of the Hβ line IHβ during the TIP. Furthermore Te for the TIP could be estimated from this model based on the measurement of the time evolution of ne and IHβ. The model starts with the assumptions that the electron energy distribution is Maxwellian, recombination can be neglected and the amount of impurities and molecules present during the TIP is insignificant. Numerical calculations showed explicitly that practically all molecular hydrogen is dissociated already after 0.1 ms. With these assumptions, the coupled set of differential equations for the electron density ne and the neutral hydrogen density nH for a uniform hydrogen plasma can be written as

dne ne(t) (t) = Si(Te)nH (t)ne(t) − (7.3) dt τp

dnH ne(t) (t) = −Si(Te)nH (t)ne(t) + R (7.4) dt τp

The first term in both equations represents the contribution of hydrogen ionization. Si(Te) is the temperature dependent Maxwellian rate coefficient for ionization. The second term represents the contribution due to imperfect confinement. Electrons can diffuse or drift out of the vessel. This process is characterized by the electron confinement time τp. Furthermore, interaction between the imperfectly confined plasma and the first wall can result in emission of neutral hydrogen atoms from the wall. The strength of this process is expressed by the recycling coefficient R. Then one makes the following three additional assumptions

• Hydrogen atoms are only excited from the ground state

• Excited states of hydrogen decay spontaneously before collisions can take place

• Reabsorption of plasma radiation can be neglected

In this case the intensity of the Hβ line can be expressed by the following expression A I (t) = 42 Q (T )n (t)n (t) = B Q (T )n (t)n (t) (7.5) Hβ 3 14 e H e 42 14 e H e X A4i i=1

100 In this equation Aij is the transition probability for the spontaneous transition between the hydrogen shells n = i and n = j and Qij the Maxwellian rate coeﬃcient for excitation between these shells. The intensity is in this case not an energetic unit. It expresses the number of Hβ photons emitted by the uniform plasma per unit of volume and per unit of time. But IHβ is then of course still proportional to the signal measured by a PMT with the appropriate interference ﬁlter. From the relations (7.3) and (7.5) it is easy to deduce that

dn (t) ! ! e S (T ) 1 S (T ) τ (t) dt = i e 1 − = i e 1 − i (7.6) IHβ(t) Q14(Te)B42 τpnH (t)Si(Te) Q14(Te)B42 τp

1 In the last expression of this equation was written as τi(t) because it is the Si(Te)nH (t) characteristic time for ionization. If one assumes that τp >> τi and Te ≈ cte during dne the TIP, it can be stated that the time profiles of IHβ and dt have the same shape till the end of the TIP. In [2] it was shown indeed that multiplying the Hβ signal with the appropriate proportionality factor gave the same time profile as the derivative of the ne signal. Additional measurements showed that the electron temperature is indeed quite dne constant during the TIP. The time profile of dt could also be calculated analytically. Based on all previous assumptions the two coupled differential equations for ne and nH can be simplified to

dn e (t) = S (T )n (t)n (t) (7.7) dt i e H e

N = nH (t) + ne(t) (7.8) with N the initial density of hydrogen atoms. If the initial electron density ne(0) is very small compared to the initial density of hydrogen atoms N, the time evolution of ne and dne dt can be calculated to be N ne(t) = (7.9) 1 + N e−NSi(Te)t ne(0)

dn n (0)S (T )Ne−NSi(Te)t e (t) = e i e (7.10) 2 dt ne(0) −NSi(Te)t N + e

According to [75] the Te dependence of Si can be approximated in the range 5-10 eV by the semi-empirical relation

h 3 −1i −18 3 Si(Te) m s = 5.6 · 10 Te [eV] (7.11) From this relation and equation (7.10) the electron temperature during the TIP can be estimated by the formula s 3 1 Te [eV] = 3.1558 19 −3 (7.12) nM [10 m ] ∆t [ms]

dne with nM the electron density for the time at which dt is maximal and ∆t the FWHM of dne the Hβ signal or the dt time proﬁle.

101 Figure 7.11: Data plots for a typical shot (COMPASS shot 1132). Plot 1: time evolution dne of IHβ, Ip, Vloop and ne. Plot 2: time evolution of IHβ and dt during the start-up phase. Plot 3: time evolution of ne compared with the theoretical curve from the model. Plot dne 4: comparison of the theoretical curve for dt with the experimental curve and the time evolution of IHβ shifted such that all maxima coincide.

102 Table 7.3: Parameters of the shots studied during my second stay at the IPP −4 19 −3 shot p 10 mbar Ip [kA] Te [eV] ne 10 m Vloop [V] ∆t [ms] 1121 2.6 21 8.6 1.5 27 7 1132 2.6 28 8.8 1.8 33 6 1133 2.6 33 8.2 2.4 34 7 1134 2.6 40 7.8 3.2 40 8 1135 2.6 19 6.8 1.8 29 5 1143 2.4 39 7.9 3.3 37 5 1149 18.2 30 8.4 2.6 31 7 1150 18.9 33 8.8 2.3 33 7 1155 1.89 38 9.4 2.2 35 7 1157 1.84 59 9.6 3.4 42 10 1158 1.79 60 9.4 3.8 43 10 1159 1.84 39 9.6 2.6 35 8 1160 1.84 40 8.6 1.7 45 7 1161 1.82 32 9.4 2.4 33 7 1162 1.82 41 8.4 1.8 50 6 1163 1.82 60 8.5 3.6 48 12

In analogy to the article [75] it was investigated whether the model explained above is also valid for the discharges at COMPASS performed during my second stay at the IPP. The most important parameters of the studied shots are given in table 7.3. Data plots for a typical shot are depicted in figure 7.11. The time evolution of IHβ, Ip, Vloop and ne for a typical shot are depicted in plot 1 of figure 7.11. First Vloop increases rapidly due to the fast ramp-up phase of IMFPS. When the voltage is high enough breakdown occurs and Ip starts to increase. This is the start of the TIP and is indeed characterized by a sharp drop of Vloop. It is remarkable that the signal of ne starts somewhat later than the signal of Ip. Maybe it is caused by a time shift in the A/D converter of the data acquisition system. Another reason can be the fact that ne is the average density on a vertical line through the center of the tokamak, while Ip is measured by a wire loop around the tokamak in the equatorial plane. If the discharge is somehow initiated at the edge of the tokamak and then propagates towards the center, it is logic that the ne signal is delayed somewhat compared to the Ip signal. Typical for the ne and Ip profiles is that they are quite similar and can have multiple peaks. Probably the first maximum is that predicted by the simple model described above. It corresponds with a hydrogen plasma which is almost fully ionized. The higher peaks later in the time evolution then are related to recycled hydrogen coming from PWI. Immediately after the ne signal also the profile of IHβ appears. It has typically two peaks. The first peak starts almost together with the ne signal and drops fast around the first maximum of ne when the plasma is almost fully ionized. The second maximum supports the explanation for the multiple peaks of ne and Ip. PWI releases cold hydrogen atoms from the inner walls which results of course in the emission of radiation and finally also in ionization and increase of ne and Ip. The PWI is accompanied by a new increase of Vloop. dne Plot 2 of figure 7.11 shows the time evolution of dt and IHβ during the start-up phase of the discharge. It is clear from first sight that this situation is different from that in the

103 dne model. The peak of dt appears about 0.6 ms before that of IHβ. Furthermore the peak dne of dt is signiﬁcantly wider than that of IHβ. This diﬀerence can be due to several reasons [74].

• A first possible reason for this deviation can be that the plasma at the very early phase of the COMPASS discharges is not mainly composed out of hydrogen but out of impurities. In that case it is likely that the discharge starts with a high carbon content. If the discharge starts very close to the wall of the tokamak vessel, as is also indicated by the images of the fast camera, the plasma interacts with the wall and produces carbon vapor which is then immediately ionized. Later the plasma can move to center of vessel and ionization of hydrogen working gas starts to dominate. It is only in this phase that the Hβ emission can be observed. This is the phase that can be described by the model explained above. Hence if one wants to make a rough estimation for the electron temperature during the TIP, it must be based dne on the width of the Hβ time profile and not on that of dt . This explanation can be checked in future experiments by measuring also the time evolution of a carbon line. This was not done during the shots discussed here because it was not possible to install more than two PMTs. If the explanation is valid the signal of the carbon dne line should appear simultaneously with the dt time profile. • The deviation could also be due to the different viewing angles of the diagnostics for ne and IHβ measurement. The viewing angles are indicated in figure 6.13. The interferometer and PMTs are located at different ports separated over 135o in toroidal direction. This toroidal separation should however not have much influence because of the symmetry of the system. More important is the fact that ne is measured over a line from top to bottom through the center of the vessel, while IHβ is measured from the outer edge of the vessel radially towards the center and a little bit downwards (observation point 2).

• Finally is can also not be excluded that the A/D converters of the data acquisition system are not perfectly synchronized. A time shift between the diﬀerent channels can explain the observed eﬀect as well. A delay caused by the signal formation time of the PMT cannot be the reason because typical formation times are only of the order of 100 ns.

The electron temperatures during the TIP were estimated using equation (7.12) with the width of the Hβ peak. If the first explanation is valid the electron density is not only determined by the ionization of hydrogen atoms, but also by the ionization of carbon atoms. Therefore, the model is not valid anymore for the ne signal. The temperature estimations are given in the fourth column of table 7.3. The estimations for the studied shots do not differ very much and are quite reasonable. The values go from 6.8 up to dne 9.6 eV. The theoretical time profiles for ne and dt or IHβ, given by respectively equations 7.9 and 7.10, are plotted together with the experimental data in plots 3 and 4 of figure 7.11. It is clear that the density cannot be predicted correctly by the model. For all shots the theoretical ne curve had to be multiplied by a factor around 3 in order to fit to the experimental data. The derivative of the theoretical ne curve however had to be multiplied by a factor around 2 to fit to the experimental data. Furthermore plot 4 shows dne that the experimental dt peak is significantly broader than the experimental IHβ peak or

104 the curve from the model. In plot 4 the experimental IHβ curve was shifter such that all maxima coincided and the theoretical curve could be compared with both experimental curves. To conclude one can say that the model from [2] is not completely valid for the COMPASS discharges at the moment. Probably this is due to the influence of carbon at the first moments of the start-up phase. This explanation will be checked in the future by making time resolved measurements of a carbon line. The electron temperature can only be estimated in a very rough way from the experimental IHβ profile which does not change too much by the influence of carbon. This gives an idea of the order of magnitude for the electron temperatures during the TIP. According to the calculations typically Te ≈ 8 eV. This can also be checked in the future when the Thomson scattering system will allow direct determination of the electron temperature.

7.2.2 Modeling of measured Hα and Hβ intensities with FLYCHK

During my second stay at the IPP, the Hα and the Hβ line were monitored simultaneously by means of two PMTs. As explained in section 6.3, identical M10FS25 PMTs were used for this purpose. The absolute sensitivity curve of their cesium-antimony photocathode in figure 6.14 shows that the Hα line is just at the edge of the spectral range. The sensitivity mA for the Hβ line (486.14 nm) is around 40 W , while for the Hα line (656.28 nm) it is only mA around 0.8 W . This is the main reason why the Hα signal had to be multiplied by a quite big factor in order to allow comparison of the intensity with the Hβ line. Multiplication of the signal, however, also increases the noise drastically. The Hα signals of the shots studied during my second stay are thus extremely noisy and very unprecise. It would have been better to use another type of PMT for the measurement of the Hα line, for instance one with a SbKNaCs (S20) photocathode. This is a good idea for future experiments. Both PMTs had to be equipped with an appropriate interference filter in order to allow only the light of the desired line to be transmitted. The transmittance of the Hα interference filter as function of the wavelength is given in figure 7.12, together with a typical time integrated HR 2000+ spectrum (COMPASS shot 1132). Around 656 nm light is transmitted maximally with a transmittance of about 22 %. The transmittance drops very fast to zero for lower or higher wavelengths. The only line in the neighbourhood of the Hα line which can contribute to the PMT signal is the CII line around 658 nm. The transmittance curve is very sharp. There is even significant variation over the width of the Hα or CII line. Therefore, the transmittance for the lines was calculated by averaging over the line profiles as in the following formula

R dλT (λ)I(λ) < T >= (7.13) R dλI(λ) The line shapes were taken from the time integrated HR 2000+ spectra. The calculations were performed for several shots. The results did not differ significantly from shot to shot and gave an Hα line transmittance of 19.8 % and a CII line transmittance of 6 %. Based on these values it was determined that the CII line typically has a contribution of about 7 % to the total time integrated PMT signal. Hence, the presence of the CII line influences our PMT signals significantly. Unfortunately there was no time resolved data available for the intensity of the CII line for the shots studied here. Therefore, it was not possible to separate the contributions from the Hα and the CII line in a time resolved fashion. The transmittance curve of the Hβ interference filter had a quite similar shape, but now with a

105 Figure 7.12: Transmittance of the Hα interference ﬁlter as function of wavelength

flat top centered around 486 nm. Therefore, the peak value of 65 % could be taken as the Hβ line transmittance. As can be seen in figure 7.1 there are no other lines in the direct environment of the Hβ line which can influence the PMT signal. The aim of the study described in this subsection was to reproduce the typical shape of the experimental Hα and Hβ time profiles from the PMTs with the simulation package FLYCHK [3]. FLYCHK is a suite of codes developed by the National Institute of Standards and Technology (NIST) [41]. It is freely available on the internet, fast and easy-to-use. The tool allows performing simulations of a plasma under different conditions. It can be a valuable help for the difficult task of interpreting data from plasma spectroscopy. The approximations made in the FLYCHK collisional-radiative model are described in detail in [76],[77]. A simulation with FLYCHK requires a number of input parameters. A first input parameter is the Z-value of the atomic element out of which the plasma is composed (elements up to Z = 79 are incorporated in the FLYCHK database). Molecules cannot be treated by the code. Further it is not yet possible to simulate the radiation of multiple elements at the same time. For our case Z = 1 was chosen because the discharges were always performed in a hydrogen working gas. With FLYCHK it is possible to take into account self-absorption by the plasma and the effect of radiation on the level population densities. However, these effects are negligible for typical conditions in a tokamak and hence only prolong the calculations. Further, the ion temperature can be given as input. But changing the ion temperature only influences the Doppler width of the spectral lines, not the total amount of photons in a certain line. Therefore, the ion temperature is not really of importance for this study. As explained above, it is not possible to calculate the spectra of different atomic species in one simulation. Nevertheless it is possible to include other species present in the plasma as impurities. The amount of impurities can

106 be specified by their average charge number and the percentage (by number or mass) they represent in the plasma. In this way the additional electrons coming from other species can be included. Hence one can calculate the spectra of all species present in the plasma in separate simulations, treating the other species as impurities. Indirectly it is then possible to calculate the complete spectrum by adding all spectra together. Unfortunately it is not possible to let the amount of impurities vary as function of time. This would be useful for instance in the case of PWI. Finally, the user can specify a time grid for which he gives the electron density and electron temperature. The calculations can then be performed in a time dependent fashion. The calculations typically only take a few seconds. Afterwards one can find the results in multiple files. A lot of information is given: population distributions, energy levels, transition probabilities, rate coefficients,... Most interesting in our case is the fact that one can chose to calculate the spectra at the different points of the time grid specified by the user. Together with each spectrum is a file which contains the different lines with their line-center energy, emissivity (in erg/cm3/s/srad) and line-center intensity (in J/cm2/s/Hz/srad). The line-center intensity only takes into account the photons at the center of a line and depends for instance on Doppler broadening. The emissivity on the other hand includes all photons of a line independent of the wavelength. With a PMT one also counts all photons of a certain line independent of the exact wavelength. Therefore, the emissivity is the most relevant quantity for our study. To summarize one can say that the simulations in FLYCHK require in our case only the input of ne, Te and optionally also the amount of impurities and their average charge number. The electron density is measured as function of time by the 2 mm microwave interferometer and is in the range 0.1 − 5 · 1019 m−3. For the moment there is not yet a diagnostic measuring the electron temperature. In the future time resolved temperature measurements will be provided by the Thomson scattering system. Therefore, the evolution of the electron temperature had to be estimated. In the previous subsection a simple model allowed a rough estimate of the electron temperature during the start-up phase of the discharge. This resulted in values around 8 eV. The discharges studied all had very short durations. Furthermore, no additional heating methods are applied at COMPASS for the moment. The plasma is heated only Ohmically. Therefore, the temperature can not be much higher that 10 eV during the rest of the discharge. Hence the simulations are only meaningful with an electron temperature in the range between room temperature and 15 eV. As explained already several times before, the shots at COMPASS are not yet optimized. In figure 7.13 are given the ideal time profiles of Te and ne. Such an ideal discharge can be split in three parts with different characteristics.

107 Figure 7.13: Ideal time evolution of electron temperature and density during a shot

• phase 1: Before this first phase pre-ionization is provided for instance by a UV lamp. Therefore, in phase 1 ne starts at a small, non-zero value. Te starts around room temperature and increases steeply due to Ohmic heating as soon as the Ip starts to flow. Also ne then starts to increase very fast due to an avalanche of ionizations. The rate of collisions between ions or between ions and electrons is inversionally proportional with the center of mass velocity. Therefore, collisional processes are dominant in this first quite cold phase of the discharge. Furthermore the rate coefficients for collisional excitation and ionization are much higher than that of collisional recombination. Both ion-ion collisions (e.g. charge exchange) and electron-ion collisions are important.

• phase 2: Ohmic heating still increases Te, but this heating is limited. The increase is now very slowly because Ohmic heating is not very efficient. In an ideal discharge this phase is characterized by a stable and flat ne profile. Collisional processes now are less frequent and the ion-ion collisions dominated because ions are heavier and hence slower. Furthermore Ohmic heating is also very inefficient for heating ions.

• phase 3: In the ﬁnal phase the discharge is ended. The magnetic ﬁelds, ne and Te decrease in a controlled way without disruptions or too strong PWI. Collisional processes are again more frequent, both ion-ion and ion-electron collisions are important.

In figure 7.13 it is shown in dotted lines that the discharges in COMPASS are far from ideal. ne starts to decrease too soon. Shots with a flat phase for ne are very rare. One thinks that it is due to strong hydrogen recycling during PWI. The high flux of cold hydrogen atoms and molecules coming from the inner wall materials can end the discharge. In figure 7.14 the time evolutions of ne,Hα and Hβ are plotted for a typical shot (COMPASS shot 1132) performed during my second stay at the IPP. The ne signal typically increases initially up to a first maximum, then stays quite constant for a while, increases again and finally decreases abruptly at the end of the discharge. The Hα signal was multiplied with a factor of 164, taking into account the difference between the Hα and Hβ radiation in transmittance of the interference filter and in sensitivity of the PMT photocathode. Both signals were smoothed, especially the Hα signal, because of the noise. For almost all shots the Hα and Hβ time profiles show two peaks. One peak around the first maximum of the ne profile and one peak during the steep decrease of ne at the end of

108 the discharge. There is no clear trend with respect to the relative magnitudes of the two peaks. In some shots the ﬁrst peak the highest, in other shots the second peak is more intense.

Figure 7.14: Experimental time proﬁles of ne,Hα and Hβ (COMPASS shot 1132)

Figure 7.15: Simulation of Hα and Hβ radiation with FLYCHK. Left: Te and ne time proﬁles used as input for the simulation. Right: Hα and Hβ time proﬁles resulting from the simulation.

The ne time profile could simply be taken as input for FLYCHK. The Te profile and the amount of impurities had to be guessed such that the typical time profiles of Hα and Hβ were reproduced. It was not possible to obtain absolute correspondence with the experimental results because FLYCHK gives the emissivity of the lines. Conversion

109 of the PMT signal into emissivity is very difficult. It requires precise calibration of the PMT and exact knowledge of the position of the plasma and the volume and solid angle of the observation area. Furthermore, the simulations with the FLYCHK code do not correspond completely with reality. First of all in each collisional-radiative model certain approximations have to be made. It is impossible to take all interactions and energy levels into account. Further, with FLYCHK spatial gradients and PWI cannot be taken into account. Also the effect of hydrogen molecules is not included in the simulations. Finally the experimental Hα signal is very noisy and it is influenced significantly by the CII line. These are several reasons why it was only possible to reproduce the general characteristics of the Hα and Hβ time profiles. Figure 7.15 shows the result of such a simulation in FLYCHK. The plot at the left shows the Te and ne profiles that were used as input. The ne profile was simply the measured profile of COMPASS shot 1132. Based on the theory from the previous subsection, it was assumed that Te first increases very rapidly during the start-up phase, up to a value of about 8 eV. During the next few milliseconds the temperature was kept constant. This evolution of temperature together with the experimental evolution of the density resulted already in the reproduction of the first peak of the Hα and Hβ profile measured with the PMTs. This peak is related with the complete ionization of the hydrogen working gas and can be modeled very well by FLYCHK. This first peak had to be followed by a phase in which almost no hydrogen radiation is observed. Finally the discharge had to be terminated with a second peak in the time profiles of Hα and Hβ. Both properties could be modeled by letting Te drop quite steeple during the steep increase of ne. This drop in temperature together with the increase of density can be explained by hydrogen recycling due to PWI. It is possible that due to lack of good position control the plasma starts to interact strongly with the wall after a few milliseconds. This then results in the emission of cold hydrogen atoms and molecules from the wall into the plasma. The cold hydrogen gas lowers the temperature of the plasma and in the end causes termination of the discharge. This second part of the discharge is more difficult to model with FLYCHK because the effects of PWI cannot be taken into account properly. The evolution of Te is also very unsure. Therefore the evolution in the second part is given in dashed lines in figure 7.15. The simulation was performed with an impurity content of 5 % and an average impurity chargez ¯ = 2.2. Without impurities the second peak became too high. Slight changes of the temperature profile or the impurity content change the radiation profiles significantly. The problem is strongly non-linear and difficult to predict. One can conclude that the main aspects of the experimental observations can be reproduced by the temperature profile shown in figure 7.15 and a small amount of impurities. The used temperature profile and the impurities can be justified by the effects of plasma wall interaction. However, there are still deviations between the general shape of the experimental profiles and the simulated profiles. For instance, the Hα signal of the PMTs shows a clear assymmetry in the first peak. The first peak is also much broader than that simulated in FLYCHK. This can be related to the fact the the CII line is also transmitted significantly by the Hα transmission filter.

7.2.3 Determination of hydrogen and carbon fluxes One of the most important applications of visible spectroscopy is the determination of atomic or molecular fluxes coming from the inner walls. These fluxes can be calculated

110 from measured atomic line or molecular band intensities [78]. The theoretic background is not very difficult. Let Iij be the observed photon flux, corresponding with the spontaneous radiative deexcitation between the energy levels i and j of the atomic or molecular species A. These photons can for instance be observed with the combination of a PMT and an appropriate interference filter. It is assumed that for the observed plasma collisional excitation is compensated by radiative deexcitation. Hence, collisional deexcitation and excitation by absorption of radiation are neglected. Further it is assumed that excitation only takes place from the ground state. Population by cascades from high levels is disregarded. These assumptions are justified by the low electron densities in tokamaks. For typical tokamak conditions the population densities of excited levels are far below the population densities according to the Boltzmann distribution. The population densities of excited levels are orders of magnitude lower than the population of the ground state. The ground state density can then in good approximation be replaced by the overall particle density. Taking into account that observation involves integration along the line of sight, the observed photon flux Iij can be approximated as

r2 Z Iij = Bij nA(r)ne(r) < σex,give > dr (7.14) r1

Bij is the branching ratio for the spontaneous radiative decay from level i to level j, nA is the density of the ground state species A and < σex,give > is the rate coefficient for collisional excitation from the ground state to state i, averaged over the electron population. The integration path is taken along the line of sight. For typical tokamak conditions all radiation from particles entering the plasma eventually vanishes by entering the next ionization state. Such a plasma is called an ionizing plasma. For an ionizing plasma the number of ionizations equals the number of particles penetrating into the plasma, i.e. the particle flux. The flux of neutral particles A hence can be written as

r2 Z ΦA = nA(r)ne(r) < σI ve > dr (7.15) r1 with < σI ve > the averaged collisional ionization rate coeﬃcient for the species A. Only electron impact ionization is taken into account, stepwise ionization is neglected. In the case of transitions in the molecular band structure also the dissociation rate should be included. The ionization cross section should then be substituted by the sum of the ionization cross section and the dissociation cross section. If the ratio <σI ve> does not <σex,give> depend strongly on temperature or density, one can combine the equations (7.14) and (7.15) in order to get the simple relation

S ΦA = Iij (7.16) XiBij with S =< σI ve > and Xi =< σex,give >. For a better accuracy S and Xi can be substituted by rate coefficients provided by an appropriate collisional-radiative model, S considering excitation and deexcitation processes from all possible levels. The XB ratio can also be seen as the number of ionization events per emitted photon. Hence, in this way the determination of the flux is not extremely difficult. A PMT with interference filter gives the time evolution of the light of a certain transition. By calibration the PMT

111 S Figure 7.16: XB ratio in the case of Hα for hydrogen atoms and molecules as function of ne for diﬀerent values of Te [47]

S signal can be converted into a photon flux. With a CRM the XB ratio can be determined for this transition. This requires of course also the knowledge of ne and Te as function of time as input for the CRM. Hence diagnostics must be installed in order to measure ne S and Te. Simple multiplication of the time resolved photon flux with the time resolved XB ratio then gives the time resolved particle flux. One of the most interesting species to look at is of course hydrogen. For this purpose mostly Balmer line measurements are performed. One then looks at excited atoms and dissociatively excited molecules. Various collisional-radiative models were developed for hydrogen. The first model for hydrogen atoms was set up by Johnson and Hinnov [43]. Some later models also treat hydrogen molecules. A good example of such a CRM for S hydrogen atoms and molecules is [47], [44]. The XB ratios for Hα radiation resulting from this model are given for atomic and for molecular hydrogen in figure 7.16. The most recent collisional-radiative model for atoms is that of the Atomic Data and Analysis Structure (ADAS) [4]. It is an interconnected set of computer codes and data collections. S It is also possible to determine the XB ratio experimentally by using a beam with a fixed particle flux [79]. From figure 7.16 it is clear that there is a big difference between Hα S radiation from hydrogen atoms or hydrogen molecules. For Hα radiation the XB ratio of hydrogen molecules is one order of magnitude higher than that of hydrogen atoms. This is due to the difference between atomic excitation and molecular dissociative excitation. Hence, it is important that the molecular contribution to the hydrogen flux from the wall is taken into account. Otherwise the hydrogen fluxes will be underestimated significantly (typically a factor of 2 [25]) from Balmer line measurements. This complicates the situation. It is indispensable to perform also molecular spectroscopy in order to estimate the molecular contribution. For this purpose one looks typically at Fulcher-α band emis- 3 3 sion (3p Πu → 2s Σg) in the range 600-650 nm. This requires a spectrometer with high spectral resolution (around 0.02 nm) and a detector with high photosensitivity. In [26] it

112 S Table 7.4: XB ratio for Hβ as function of ne and Te [4] −3 Te [eV] / ne cm 1,00E+12 2,00E+12 5,00E+12 1,00E+13 2,00E+13 0,2 0,212 0,289 0,524 0,887 1,600 0,3 0,712 0,953 1,590 2,620 4,630 0,5 2,000 2,600 4,210 6,770 11,700 0,7 3,120 4,090 6,730 10,900 19,100 1,0 4,590 6,040 10,100 16,500 28,700 2,0 6,510 8,640 14,600 23,900 41,700 3,0 8,340 11,100 18,600 30,400 52,600 5,0 11,500 15,200 25,400 41,200 70,200 7,0 16,600 21,900 36,200 57,800 97,200 10,0 21,300 28,000 46,200 73,700 123,000 is explained how the information from molecular spectroscopy can be used to determine the molecular fraction of the hydrogen flux. This information then allows to deduce the correct hydrogen flux. The determination of the hydrogen fluxes in tokamaks is very interesting. It allows to study hydrogen recycling and its dependence on tokamak and plasma conditions. But also the fluxes of impurity species like carbon and tungsten coming from the PFMs are interesting to look at. This information can for instance be used to make an estimation of the impurity content of the plasma. Passive visible light spectroscopy is used frequently for the study of recycling and impurity influx. Often the visible radiation is obtained by means of diagnostic arrays allowing poloidal reconstruction of fuel and impurity radiation. Optical spectroscopy has contributed considerably to the elucidation of physical and chemical particle release mechanisms from either metallic, carbonized, boronized PFMs. The most difficult part is the development of suitable CRMs required for the interpretation of the experimental results. Nowadays it is still very valuable technique in tokamak research. It would be interesting to perform similar studies at COMPASS. However, at the moment it is not yet possible to get precise quantitative results. The HR 2000+ spectrometer is not suitable for molecular spectroscopy. The resolution is not good enough and the detector sensitivity is too low. Therefore, it is not possible to take into account the effect of molecules. The hydrogen fluxes calculated from the Balmer line intensities hence will be underestimated significantly. The results can thus only be used for qualitative studies. It is possible for instance to study for which tokamak conditions or discharge parameters hydrogen recycling is favored. By monitoring hydrogen and carbon lines simultaneously, one can also look at the ratio of the hydrogen and carbon fluxes for different tokamak conditions or discharge parameters. This can learn us a lot about the relation between tokamak conditions, discharge parameters and fluxes from the PFMs. As explained before, both the Hα and Hβ lines were monitored by means of a PMT. It is best to use the Hβ signal because the Hα signal has a lot of noise and is influenced significantly by the neighboring CII line. The PMT signal should be converted into the Hβ photon flux. This was done by calibration with the Ocean Optics HL-2000 tungsten halogen light source, emitting in the complete visible and near infrared spectral region (360-2000 nm). It was calculated that multiplying the PMT signal with the 15 photons factor 3.95 · 10 cm2 gives the Hβ photon flux. This time resolved photon flux then

113 Figure 7.17: Hydrogen ﬂux deduced from the Hβ signal (COMPASS shot 1132)

S should be multiplied with the time dependent XB ratio for Hβ calculated with a CRM. The electron density needed as input for the CRM was measured by means of the 2 mm microwave interferometer. The electron temperature is unfortunately not measured for the moment. Hence, the evolution of Te can for the moment only be estimated from the study of the thermal ionization phase (subsection 7.2.1) and the simulations in FLYCHK (subsection 7.2.2). Later the Thomson scattering system will allow direct measurement of Te as function of time. In figure 7.17 is depicted an estimate for the time evolution of the hydrogen flux for COMPASS shot 1132. It was deduced from the PMT Hβ signal. All data points were first multiplied with the same calibration factor for conversion of the S signal into the photon flux. Finally each point was multiplied with the corresponding XB ratio. This ratio is a function of time because of the variation in ne and Te. For ne the data from the 2 mm microwave interferometer were taken. The temperature profile was S approximated by the profile from figure 7.15. The values for the XB ratio were taken from the ADAS database [4] and are given in table 7.4.

114 Chapter 8

Conclusions and suggestions for future experiments

The COMPASS tokamak was installed at the IPP in Prague only recently. The amount of diagnostics already available is limited. Therefore, it is not yet possible to characterize the discharges completely. For instance, there is no diagnostic for measuring the electron temperature. Further, the data acquisition system is not yet fully optimized. The data are sometimes shifted in time or show strong noise. Also the plasma shaping and position control systems do not yet work as they should. That is the major reason why the discharges are not yet reproducible. The lack of position control frequently allows the plasma to touch the plasma facing materials. This results in strong hydrogen and impurity fluxes into the plasma. Therefore, most discharges are extremely short and have absolutely no stable plasma current phase. Longer discharges are often terminated by disruptions. Hence, it is clear that for the moment it is not yet possible to perform the promising H-mode studies and pedestal investigations for which COMPASS was designed. People at the tokamak department are now working very hard to solve the problems with the data acquisition, shaping and position control system. One is also developing an advanced tomographic optical system and a Thomson scattering system for measuring the electron temperature [80]. In order to achieve the desired ELMy H-mode operation - the standard scenario for ITER - two new NBI systems will be installed [58],[56]. The original lower hybrid microwave heating system will be reinstalled. Finally a completely new ECRH system will be designed and manufactured. Fortunately, with the diagnostics already available at COMPASS, it was possible to perform some smaller studies on the characteristics of the present discharges at COMPASS. Especially the observation of the visible radiation can give a lot of information about the plasma. In a first study the spectra measured with the Ocean Optics HR 2000+ spectrometer were investigated. Almost all spectra were integrated over the complete discharge duration. The spectra at COMPASS are clearly dominated by line radiation. The hydrogen Hα en Hβ lines are typically the most prominent lines. Often one also observes lines of carbon and helium. Carbon comes from the PFMs and can enter the plasma due to different PWI processes. Helium is a relic from glow discharge cleaning. In discharges with strong PWI or disruptions a lot of additional lines are observed. For instance, tungsten can be sputtered from the tungsten probes in the divertor plates. The line widths in COMPASS

115 are dominated by instrumental and Doppler broadening. Theoretically it is then possible to determine the ion temperatures from the experimentally measured widths. It was shown, however, that the resolution of the HR 2000+ spectrometer does not suffice for this purpose. The limited resolution also prohibited the detailed study of the Hα line shape. In [1] a study of the discharge parameters in COMPASS was made. For this project the study was continued by including also the radiation measurements. The main aim of the study was to look for which conditions the shots at COMPASS are optimized. The most important result was the fact that for the moment in COMPASS there exists a pressure range (43 - 93 · 10−6 mbar) for which longer discharge durations and higher plasma currents are favored. Not all shots in this pressure region were longer. Based on the discharge parameters it was possible to distinguish three types of shots with different characteristics. For higher pressures all shots were very short and quite similar. For lower pressures no final conclusions could be made due to the limited amount of data, but it appears that also for lower pressures only very short shots are possible. Unfortunately, even the longer shots were still limited to durations shorter than 100 ms. The longer shots were also always terminated by disruptions. Furthermore, in the context of nuclear fusion it is much more interesting to perform discharges at higher pressures. Hence, the discharges at COMPASS are not yet fully optimized. Some measures that can help improving the shots in the future are

• Operate at the maximal value for the toroidal magnet ﬁeld

• Make the feedback system for the plasma position work as it should

• Optimize the current proﬁles for the diﬀerent coils

• Improved conditioning of the vacuum vessel

• Longer baking time and glow discharge

• Strong HF pre-ionization

In another small study the thermal ionization phase (TIP) of the COMPASS discharges was investigated. It was tried to describe the experimentally observed time evolution of the electron density and Hβ intensity analytically with the simple model presented in [2]. It was shown that the experimental data and the model deviate signiﬁcantly. The reason for this is not completely understood. Some possible explanations are

• The initial discharge might contain a lot of carbon

• The interferometer and PMT have a diﬀerent observation angle

• It is possible that the A/D converters of the data acquisition system are not perfectly synchronized

More research is needed in order to state with certainty what the reason is. Based on the same model a rough estimation was made for the electron temperature during the TIP. The calculated temperatures were for all shots close to 8 eV. Another part of this work was performed with the simulation code FLYCHK [3]. This online, freely available code allows to simulate the spectra of a plasma under diﬀerent

116 conditions. The aim of the study was to reproduce the time evolution of the Hα and Hβ intensities measured with the PMTs. The FLYCHK code requires the input of the time evolution of the electron density and temperature. Optionally also the amount of impurities and their average charge can be defined. The evolution of the electron density was measured by means of the 2 mm microwave interferometer. Typically the electron density increases first up to a stable phase during the TIP. Then it starts to increase again up to much higher values followed immediately by a fast drop ending the discharge. The electron temperature is not yet measured at COMPASS. Therefore its time profile had to be estimated. Fairly good qualitative agreement was obtained with a temperature profile that first increases rapidly up to 8 eV at the beginning of the TIP, then stays constant until it decreases again steeply from the moment the electron density increases for the second time until the end of the discharge. The two peaks that typically occur in the time profiles of the Hα and Hβ intensities could be reproduced. The first peak is related to the complete ionization of the hydrogen working gas. The second peak is probably related to the introduction of cold hydrogen and impurities due to PWI. Finally also a rough estimation was made for the time evolution of the hydrogen flux from the Hβ signal. The PMT signal in volts was converted into the Hβ photon flux by S calibration with the Ocean Optics HL-2000 calibration source. The XB ratios for Hβ as function of the electron density and temperature were taken from the ADAS database [4]. With these ratio’s it was possible to convert the Hβ photon flux into the hydrogen flux. However, one has to remark that the influence of hydrogen molecules was not taken into account. Therefore, the calculated hydrogen flux is only a rough estimation of the real flux. The real flux can be up to a factor of 2 higher. The studies performed in this work are only introductory. A lot of other studies related to visible radiation measurements can be performed in the future. A few ideas

∆λ • In the near future the high resolution ( λ = 72000) spectrometer from the ISTTOK tokamak [81] will be installed at COMPASS. It will be used for the study of the CII (2s3s33D → 2s3p33P 0) line. In stead of a holographic grating with high groove density, a double monochromator conﬁguration is used in this spectrometer. This results in a higher throughput. The spectrometer has a small spectral range of about 2 nm around the central wavelength λc = 465 nm. It will allow the measurement of the plasma rotation based on Doppler shift measurements and the determination of the ion temperature based on Doppler broadening.

• Zeff can be calculated from Bremsstrahlung radiation measurements in the line free region slightly above 520 nm. This Bremsstrahlung can be measured for instance by a PMT with the appropriate interference ﬁlter. When electron density and temperature are known, Zeff can be determined [82]. It gives a good idea of the impurity content of the plasma. • The installation of a high sensitivity, high resolution spectrometer in the range 600-650 nm would allow the study of the molecular hydrogen Fulcher-α band. With this additional information it would be possible to make more precise calculations for the hydrogen ﬂux.

• High resolution spectroscopy of the Hα line could also deliver a lot of interesting information. Multi Gauss ﬁtting of the Hα line gives the contributions and temperatures of the diﬀerent hydrogen populations. Comparison with PWI simulations

117 allows to estimate the importance of diﬀerent hydrogen production mechanisms. The information can also be used as input for edge models.

• After the installation of the Thomson scattering system, both the electron temperature and the electron density can be measured at COMPASS. The only free parameter in the simulations in FLYCHK is then the amount of impurities and their average charge. In discharges without disruptions the plasma is in good approximation composed out of hydrogen and a little bit of carbon. It is possible with FLYCHK to perform simulations for hydrogen and carbon separately treating the other species as impurities. If a hydrogen line and a carbon line are monitored simultaneously by means of PMTs with interference ﬁlter, it is possible to look with FLYCHK for which carbon concentration and average charge the ratio of the intensities of the two lines can be reproduced correctly. In this way it is then possible to make an indirect estimation of the carbon content.

These are only a few examples of possible applications of plasma spectroscopy. There are of course much more possibilities. In [34] a lot of other applications are treated. Very promising also is the planned installation of a completely new advanced optical system for visible plasma radiation measurements [83], [80]. The multichannel system will have a large observation angle (70o-80o). It will consist out of a 35 channel visible light diagnostic, a 35 channel soft X-ray semiconductor sensor and two arrays of absolute extreme ultraviolet (AXUV) bolometric detectors with 20 channels each. All channels integrate the radiation along vertically stepped lines of sight with spatial resolution of about 1 cm. The visible light detectors will be located far away from the tokamak because they are sensitive to X-ray radiation from the plasma. A narrow wavelength range can be selected as usual by means of an interference filter. A similar arrangement of detectors located at the same poloidal cross-section will allow fast tomography and a correlation analysis of turbulent plasma events. With this advanced system it will be possible to study neutral atom densities, impurity inflow, recycling processes, particle confinement time and much more. To conclude one can say that the COMPASS tokamak has a large potential for ITER relevant studies. One is working very hard in order to be able to make ITER relevant discharges with a clear H-mode as soon as possible. The visible radiation measurements give already a lot of information about the present COMPASS discharges. In the near future other spectrometers and an advanced opticle system will allow to obtain even more information. The visible radiation diagnostics will be a very important tool also in the study of the ITER relevant discharges later on.

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