impact of surface structures on deposition and erosion in...

Impact of Surface Structures on

Deposition and Erosion in a

Tokamak

Yushan Zhou

Doctoral thesis, 2019

KTH Royal Institute of Technology

School of Electrical Engineering and Computer Science

Department of Fusion Plasma Physics

se-100 44 Stockholm, Sweden

TRITA-EECS-AVL-2019:11 ISBN: 978-91-7873-080-3 Akademisk avhandling som med tillstånd av KTH i Stockholm framlägges till offentlig granskning för avläggande av teknisk doktorsexamen fredagen den 8 Mars kl. 14:00 i sal F3, KTH, Lindstedtsvägen 26, Stockholm.

i

Abstract

Fusion is a potentially unlimited and environmentally friendly energy

source for human society in the future. However, along the way towards

the application of fusion energy there are still unresolved complications.

Among them, deposition and erosion are two critical issues. Deposition of

fuel and impurities brings potential long-term fuel retention which may

generate safety issues and limit the economic efficiency of fusion devices.

Moreover, the erosion of the vacuum vessel wall in a fusion device

generates impurities which contaminate core plasma and can restrict the

life time of plasma facing component. The work in this thesis focuses on

deposition and erosion on tiles in the JET-ILW project, which consist of

tungsten (or tungsten coating carbon fibre composited) in the divertor

and beryllium in limiters.

For the deposition issue, micro ion beam analysis (µ-IBA) was used for

observing deuterium and beryllium distributions over tile surfaces. The

surface topography was obtained from SEM, optical microscope and

confocal laser scan microscope. Distribution maps from IBA were

compared with surface topography. To explain experimental results,

modelling of ion trajectories was applied on real and artificial surfaces.

Micro IBA results show that deuterium and beryllium accumulated in

depressed areas, e.g. pits, cracks or craters. Modelling implies that ion

gyration, surface roughness and inclination of the magnetic field could to

some extent explain this non-uniform distribution of deuterium and

beryllium. The same kind of issue, although on different scale length,

occurs also for penetration of impurities into artificial castellation

grooves, also studied experimentally in the thesis.

For the erosion issue, the thesis includes analysis of a limiter marker tile

which is designed for observing material erosion in JET. A new method to

acquire erosion data from such marker tiles is proposed, by combining

micro IBA and SEM image. This method could separate the influence on

IBA from roughness, a problem in applying IBA on rough surface. Similar

Technique is applied to improve the interpretation of IBA measurements

of deep penetration of deuterium into layered surface structures.

Keywords: Deposition, erosion, JET, micro ion beam analysis

ii

Sammanfattning

Fusion är en potentiellt obegränsad och miljövänlig energikälla för det

mänskliga samhället i framtiden. Det återstår emellertid vissa problem att

lösa. Bland dem är deposition och erosion vid ytor som är i kontakt med

plasmat kritiska. Deposition av bränsle och föroreningar ger potentiellt

långsiktig ackumulation av bränsle (tritium) som kan ge upphov till

säkerhetsproblem och försämra bränsleekonomin. Erosion av

vakuumkärlets väggar i in fusionsanläggning alstrar förorenar plasmat

och kan begränsa livstiden för väggkomponenter. Arbetet i denna

avhandling fokuserar på deposition och erosion på ytor i JET-ILW-

projektet, som består av volfram (eller volframbelagd kolfiberkomposit) i

divertor och beryllium i limiter.

För depositionsfrågorna användes mikroanalys för att observera hur

deuterium och beryllium fördelas över ytorna efter plasmaexponering.

Yttopografi erhölls från SEM, optisk mikroskopi och konfokal

laserskanmikroskopi. Distributionskartor från IBA jämfördes med

yttopografin. För att förklara experimentella resultat användes

modellering av jontrajektorior, dels på verklig experimentell topografi,

dels på förenklade modellytor. Micro IBA-resultat visar att deuterium och

beryllium ansamlas i mikroskopiskt nedsänkta områden, t.ex. gropar och

sprickor. Modelleringen visar att joners gyratation delvis kan förklara

denna ojämna fördelning av deuterium och beryllium.

För erosionsproblemet gjordes mätningar på markerplattor, konstruerade

för att observera materialosion i JET. En ny metod införs för att erhålla

erosionsdata, genom att kombinera mikro IBA och SEM-bild. Denna

metod kan skilja på inflytande på IBA-resultat från skrovlighet, vilket är

annars är ett problem IBA för på skrovlig yta. På samma sätt används

mikroanalys för att förbättra tolkningen av analyser av deuterium som

trängt in i en skiktad struktur.

Nyckelord: Deposition, erosion, JET, mikrojonstråleanalys

iii

Acronyms

CLSM

DS

EBS

H mode

ITER

IBA

ICRH

ILW

JET

LHCD

MPS

μ-IBA

NIF

NBI

NRA

OM

PIXE

PFC

PWI

PDF

RF

SEM

SIMS

SOL

TDS

Confocal laser scan microscope

Debye sheath

Elastic backscattering spectrometry

High confinement mode

International Thermonuclear Experimental Reactor

Ion beam analysis

Ion cyclotron resonance heating

ITER-like-wall

Joint European Torus

Lower hybrid current drive

Magnetic pre-sheath

Micro-ion beam analysis

National ignition facility

Neutral beam injection

Nuclear reaction analysis

Optical microscope

Particle-induced X-ray emission

Plasma facing component

Plasma wall interactions

Probability density function

Radiofrequency

Scanning electron microscope

Secondary ion mass spectrometry

Scrape-off layer

Thermal desorption spectroscopy

iv

List of papers

Thesis is based on the work presented in the following contents.

I. Microanalysis of deposited layers in the inner divertor of JET

with ITER-like wall

Zhou, Y., Bergsåker, H., Bykov, I., Petersson, P., Possnert, G., Likonen, J., Pettersson, J., Koivuranta, S. and Widdowson, A.M.,

Nuclear Materials and Energy, 12 (2017). pp.412-417.

II. The effect of gyration on the deposition of beryllium and deuterium at rough surface on the divertor tiles with ITER-like-wall in JET

Y. Zhou, H. Bergsåker,P. Petersson G. Possnert, J. Likonen and

JETcontributors

Submitted to Nuclear Materials and Eenergy

III. Modelling of effect from rough surface on deuterium and beryllium deposition on divertor target.

Y.Zhou H. Bergsåker, P. Petersson

IV. Fuel inventory and deposition in castellated structures in JET-ILW

Rubel, M., Petersson, P., Zhou, Y., Coad, J.P., Lungu, C., Jepu, I., Porosnicu, C., Matveev, D., Kirschner, A., Brezinsek, S. and Widdowson, A

Nuclear Fusion 57, no. 6 (2017): 066027.

V. Deep deuterium retention and Be/W mixing at tungsten coated surfaces in the JET divertor.

Bergsåker H, Bykov I, Zhou Y, Petersson P, Possnert G, Likonen J,

Pettersson J, Koivuranta S, Widdowson AM.

Physica Scripta. 2016 Jan 22;2016(T167):014061.

VI. Micro ion beam analysis for the erosion of beryllium marker tiles in a tokamak limiter.

v

Zhou, Y., H. Bergsåker, I. Bykov, P. Petersson, V. Paneta, and G. Possnert.

Nuclear Instruments and Methods in Physics Research Section B:

Beam Interactions with Materials and Atoms (2018).

Contribution to each paper from the PhD student Paper I: The student contributed both experimental work and data

analysing.

Paper II: The student participated experimental part of the work in this

paper and finished all other works (Modelling, data analysing and paper

writing).

Paper III: The student contributed to all the work in this paper including

writing modelling code, data analysis, and paper writing.

Paper IV: The student contributed to the data analysis for micro IBA in

this paper.

Paper V: The student participated in experimental section for micro IBA

in the paper.

Paper VI: The student took part in experimental work in this paper and

accomplished the rest of work including data analysing and paper writing.

vii

Abstract.................................................................................i Acronyms.............................................................................iii

Contents Chapter 1 Introduction .............................................................. 1

1.1 Physical background for fusion reaction ............................... 1

1.2 Approaches for fusion and Lawson criterion ....................... 5

1.3 Issues and progress in the development of Tokamak .......... 7

1.4 Thesis contents .....................................................................10

Chapter 2 Plasma wall interactions ......................................... 11

2.1 Magnetic confinement and plasma configuration .............. 11

2.2 Plasma wall interactions in divertor configuration ............ 15

2.3 Measurements for erosion and deposition ......................... 18

Chapter 3 Experimental methods ........................................... 21

3.1 Ion beam analysis ................................................................. 21

3.2 Micro ion beam analysis. .................................................... 27

3.3 Topography measurement ................................................... 31

Chapter 4 Modelling ................................................................ 37

4.1 Models for plasma and sheath ............................................ 37

4.2 Calculation of ion trajectory ................................................ 41

4.3 Computation for hitting points and data acquisition ........ 44

Chapter 5 Summary and Conclusions ..................................... 47

5.1 Results from experiments and modelling .......................... 47

5.2 Summaries of papers ........................................................... 49

Acknowledgements ................................................................. 53

Reference ..……………………………………………………………………..55

1

Chapter 1

Introduction

Fusion is always 50 years away. This is a funny and sentimental joke for

people doing fusion research. The 50 years’ delay of the thermonuclear

fusion project reflects a number of unexpected difficulties, which have

turned up along the way. But during the past 50 years, from when Lawson

introduced the criterion for a thermonuclear reactor to today, research on

the fusion project has made great achievements, accompanied with a

further understanding of plasma itself. Chapter 1 will give brief

introductions of basic physics on fusion reactions in section 1.1 and major

approaches for realising fusion in section 1.2. Section 1.3 will focus on

issues in the tokamak device and the content of the thesis will be

summarised in section 1.4.

1.1 Physical background for fusion reaction

A fusion reaction is the process of two atomic nuclei merging to form one

(or more than one) nucleus, accompanied by energy release. The concept

of a fusion reaction is easy to understand. However, for utilisation in a

power plant, the essential mechanisms behind the concept would be the

critical aspects which may bring the following questions:

Why can fusion reaction release energy?

Which fusion reactions can be exploited as energy source?

Why are we so interested in the application of fusion energy?

To explain the first and the second questions, one should look back to

concepts about the mass defect and nuclear binding energy. The first

means the mass reduction when forming a nucleus from protons and

neutrons. The mass of a nucleus is always less than the sum of individual

2 Chapter 1 Introduction

mass of protons and neutrons. Experimental support came from the mass

spectra experiments carried out by F.W. Aston, summarised in [1], who

gave a conclusive description shown that the sum of masses of four

hydrogen atoms was larger than a single helium atom. Although this

description is not accurate enough since one helium atom consists of two

protons and two neutrons instead of four hydrogen atoms. But it is quite

closed to the truth.

The mass defect of a nucleus can be represented by the binding energy,

which indicates the minimum energy to disassemble a nucleus into

separated individual nucleons (protons and neutrons). The binding

energy can be calculated thorough the equation of mass-energy

equivalence [2], which came from one of Albert Einstein articles

published on 1905. This equation shows that when the mass of a physical

system changes by Δ𝑚, the energy of the physical system changes by Δ𝑚𝑐2.

For the process of two protons and two neutrons fusing into a helium

nucleus as shown in Eq.(1.1), the masses of the proton and neutron are

1.00728 u and 1.00866 in atomic mass unit ( 𝑢 = 931.5 𝑀𝑒𝑉/𝑐2 ),

respectively [3]. The mass of helium is 4.0026 u and the reduction in

mass, calculated by the mass-energy equation, is about 27 MeV (≈6.7

MeV per nucleon)

2𝑝 + 2𝑛 → 𝐻𝑒24 (1.1)

Δ𝑚 = (2𝑚𝑝 + 2𝑚𝑛𝐻 − 𝑚𝐻𝑒) ≈ 2.9 × 10−2𝑢 (1.2)

Δ𝐸 = Δ𝑚𝑐2 = 27 𝑀𝑒𝑉 (1.3)

While for the deuterium nucleus formed by one proton and one neutron,

the binding energy is around 2.2 MeV (≈1.1 MeV per nucleon). The higher

binding energy of helium indicates that to disassemble a helium nucleus

requires more energy since the nucleons in helium are tightly bound. In

contrast, the proton and neutron in the deuterium nucleus are loosely

bound because of the lower binding energy. When the deuterium nucleus

transmutes into a helium nucleus, the energy stored in the loose structure

can be released. A similar thing happens when a heavier nucleus splits

into lighter nuclei with higher binding energy.

Generally, transmutation of nuclei from low binding energy into nuclei

with high binding energy accompanies releasing energy. Therefore, two

1.1 Physical background for fusion reaction 3

kinds of methods were created to liberate nuclear energy based on the

curve of nuclear binding energy per nucleon in Fig 1.1. One is the well-

known fission reaction, applied in commercial power plants, through

bombarding uranium nuclei with neutrons to generate an unstable

nuclear isotope, which will split into lighter elements and release large

amounts of energy. Another method combines light elements to produce

heavier elements, denominated as fusion reaction.

The nuclear binding energy curve suggests that hydrogen (and hydrogen

isotopes, i.e. deuterium and tritium), helium isotopes, lithium (lithium

isotopes), and boron isotopes could be potential candidates for fusion

energy production [4]. Because for most of the fusion reactions involving

those elements, reaction products include the stable and tightly-coupled

helium nucleus ( He4 ). Nevertheless, only some of candidates could be

Fig 1.1 Curve of average binding energy per nucleon versus elemental mass number.

Fig 1.2 Cross section for some

typical candidates of fusion

reaction.


applied in a fusion device for several reasons. One of the critical reasons

is the cross sections for those reactions, characterising the probability of

reactions. Under the same conditions, a larger cross section means that

more nuclei could experience fusion reactions and increases efficiency.

The cross-section values vary in a range covering several orders of

magnitude as seen from Fig 1.2. (Remade image based on data from [5]).

From the point of view of cross section, the D + T , D + D, and D + He23

reactions in Eq.(1.4), Eq.(1.5), and Eq.(1.6) would be good choices.

Among them, D + T has some advantages over other candidates, for

example, releasing a large amount of energy without radiative products.

The energy release from D + T is around 17 MeV, while that from D + D is

just 4.03 MeV (3.27 MeV for another branch). The D + He23 reaction could

generate 18.3 MeV but the cross section above 102 𝑚𝑏𝑎𝑟𝑛 only can be

achieved when energy exceeds 100 keV, which is far beyond the

temperature in present machine.

𝐷1

2 + 𝑇13 = 𝐻𝑒2

4 + 𝑛 + 17.1 𝑀𝑒𝑉 (1.4)

𝐷12 + 𝐷1

2 = 𝑇13 + 𝑝 + 4.03 𝑀𝑒𝑉

𝐷12 + 𝐷1

2 = H23 e + 𝑛 + 3.27 𝑀𝑒𝑉

(1.5)

𝐷1

2 + H23 e = H2

4 e + p + 18.3 MeV (1.6)

In addition, the D + T reaction also benefits from sources of primary

materials. Deuterium is a stable isotope of hydrogen with concentration ≈

0.013%~0.016% in surface water on Earth [6]. It can be enriched and

separated from common water by distillation through a heavy water plant

This method was widely used in producing heavy water from the 1960s in

industrial scale [7, 8]. Tritium, an unstable isotope which decays through

β radiation, only exists naturally in a small quantity but can be produced

artificially by neutron irradiation of lithium in fission reactors [9] and at a

later stage in fusion reactors. And lithium can be extracted from

resources in earth crust and potentially extracted from the oceans.

For those three questions raised at the beginning of this chapter, previous

discussions already show that nuclear binding energy of different

elements give rise to energy liberation during fusion. D + T reaction

would be the best candidate for practical approach to utilise fusion as

1.2 Approaches for fusion and Lawson criterion 5

energy source. The final question, about why we are interested in fusion,

will be discussed in the following context.

Several books and websites on fusion energy offer comprehensive

discussions of the advantages of fusion, for example that it is carbon

dioxide free, without long-term radiative hazards, inherent safety, that

the raw materials are practically inexhaustible and so on [10, 11]. The vital

advantage, from my view, is that fusion provides a potential unlimited

energy source for human society, since fusion reactions dominate energy

liberation in the sun. In 1920s, based on the mass-energy formula and

mass spectra results from F.W. Aston, A.S Eddington proposed a

hypothesis in which the process of four hydrogen nuclei merging into

helium acts as energy source in the Sun [12]. This hypothesis was proven

by experiments in measurement of solar neutrinos and became the

theoretical ground for nuclear fusion in the Sun [13]. Since fusion

reactions can energise the Sun for billions of years, artificial fusion on

earth may play an essential role in solving energy issue in human society

[14].

1.2 Approaches for fusion and Lawson criterion

Although fusion energy promises an attractive prospect of a future energy

source, the practical approach is far beyond a simple issue. The primary

drive for fusion reactions is the short-range nuclear force, which is

powerful only in the range of a couple of femtometres (10−15𝑚). Nuclei

need to obtain enough kinetic energy to overcome or tunnel through the

Coulomb barrier before they could reach the region dominated by the

nuclear force and achieve fusion. The term‘temperature’ represents

average kinetic energy here. The temperature needed for fusion exceeds

107 kelvins and any substance at this temperature needs to be isolated

from any solid materials.

For heating and confining the extremely hot fuel substance for fusion, two

major approaches were proposed. One is the inertial confinement method

by heating pellets, encapsulating micrograms of a mixture of deuterium

and tritium, through high-energy laser (or ion) beams [15]. Heating from

laser beams causes an explosion of the outer layer of the pellet and the

explosion further compresses the remaining part inwards, i.e. makes it

implode. Thus, the central part of the pellet reaches a high enough


temperature to initiate fusion and the burning of each pellet produces

substantial energy in a short time. The present operational inertial

confinement device is the National Ignition Facility (NIF), located at

California, USA [16]. Conceptual design of NIF began in 1994 and the

first implosion experiment was accomplished in 2o10 [17].

Another more popular confinement method is magnetic confinement by

using magnetic field. At the temperature for fusion, gaseous material

transforms into the plasma state in which particles are separated into

ions with positive charge and negatively charged electrons. Charged

particles are acted upon by the Lorentz force in an electromagnetic field,

moving along magnetic field lines with gyration and drifts. By

constructing a helical magnetic field in a torus device, as depicted in Fig

1.3, charged particles will overall follow the rotating field line and be

confined.

Approaches for magnetic confinement could be dived into two major

branches: Stellarator and Tokamak, through different techniques in

generating a helical magnetic field [18, 19]. In a Stellarator, the helical

magnetic field is generated by arranging magnetic coils into a specific

configuration without plasma current. In tokamak, besides the toroidal

filed generated with external magnetic coils, the plasma current is

introduced to provide a poloidal magnetic field. Coupling of toroidal and

poloidal field eventually forms the helical filed.

Fig 1.3 Sketch of a torus device. Red line represents the helical trajectory of ion.

1.3 Issues and progress in the development of the Tokamak 7

The Tokamak greatly simplifies design and construction of the magnetic

confinement device compared to the stellarator, since the latter requires

extra work for engineering the shape and the position of magnetic field

coils. Therefore, the tokamak, since it was invented, represents the most

promising and researched way for realizing artificial fusion on earth.

Hundreds of tokamak devices were built during the past sixty years, and

experiments on them significantly contributed to uncover plasma

properties and create operational scenarios [20]. But an intrinsic defect,

the necessity of a continuous current drive, constrains the tokamak to

work in a pulsed mode. Whereas, with the benefit from the absence of

plasma current, the stellarator could work continuously. With the help

from super computers, it becomes easier to design a stellarator. Some

stellarator-type plasma devices were already built and carried out

experiments successfully, for example the Large Helical Device in Japan

and Wendelstein 7-X in Europe [21, 22].

For either a tokamak or a stellarator, it is necessary to maintain the

plasma temperature, which may drop by inevitable energy loss through

radiations and through the contact with the vessel wall in devices.

Additional energy, from external power supplies or energy from the

fusion reaction itself, have to compensate for the energy loss. Therefore,

the ideal condition for a fusion device would be capable to provide the

compensation energy entirely by fusion reactions, so called the ignition

condition. The conditions needed for the ignition in a device can be

evaluated by Lawson’s criteria [23]. Based on those criteria, a better

figure of merits was introduced, entitled as the ‘fusion triple product’,

comprising the electron density ne , ion temperature T , and energy

confinement time τ. For the D + T reaction, the minimum triple product

is: 𝑛𝑒𝜏𝑇 = 3 × 1021 𝑘𝑒𝑉𝑠𝑚−3 and this number has not yet been achieved

in present devices [24].

1.3 Issues and progress in the development of the Tokamak

Achieving the ignition condition predicted by Lawson’s criteria will be a

milestone in the development of tokamak, though it is still in the coming

future. Several unsolved issues still restrict the realisation of the ignition

condition. Those issues could be roughly grouped into plasma heating

and performance, current drive, and materials solutions for plasma facing

components.


Plasma heating means to heat particles in the plasma to a high

temperature. It is an essential part of tokamak operation. Except for

compensating the plasma energy loss and maintaining sufficient

temperature for nuclear fusion, it also affects the plasma confinement

time significantly [25]. And the ideal condition for plasma heating would

be the self-heating by energy from fusion reaction directly, mainly

through helium particles in D + T . In early stages, ohmic heating,

proportional to the product of plasma resistance and the square of the

plasma current, dominated the heating process [26]. However, with

increasing temperature the plasma resistance decreases, and then

electrical conductivity results in the reduction of heating efficiency.

Therefore, the achievement of higher plasma temperature requires

auxiliary heating technology which is based on injection of higher energy

particle, for example Neutral beam injection (NBI), or on launching

waves into plasm, e.g. radiofrequency (RF) wave heating.

NBI is one of the particle injection methods for heating and operates in

most of present tokamak devices [27, 28]. In this approach, as it is termed,

neutral particles, generally high energy deuterium particle atoms, are

launched into the magnetically confined plasma and transfer energy to

both electrons and ions through collisions. Since neutral particles will not

be trapped by the magnetic field before being ionised, the NBI method

can heat particles in the plasma core region. In the RF methods, electrons

and ions get energy through interactions with waves respectively since

they respond to waves with different frequencies [29]. Compared to NBI,

RF heating technology can transform energy to ions (or electrons) directly

and selectively by selecting a suitable frequency, with higher efficiency

and lower cost. By taking advantage of auxiliary heating systems,

tokamak devices could operate in a high confinement mode (H mode) in

which the energy confinement time τ increases by factors of two [30, 31].

In tokamak facilities, the toroidal plasma current gives rise to the poloidal

magnetic field for plasma confinement. Thus, for sustaining plasma in a

long period of time, plasma current should be in long pulsed mode or

even steady state. An intuitive way to produce toroidal current is

generating inductive current by treating plasma as secondary circuit of a

transformer. Unfortunately, inductive current can only exist temporarily

[32]. For plasma operating in short-time pulse mode, inductive current

could maintain plasma long enough, while for a commercially attractive

1.3 Issues and progress in the development of the Tokamak 9

facility, long pulse or continuous operation scenario requires support

from additional current driving methods.

External current drive relies on particle-particle interactions and wave-

particle interactions as heating technology. the NBI can contribute to

drive toroidal plasma current by aligning tangentially to toroidal direction.

Launching waves with lower hybrid frequency, a specific frequency

characterised by plasma density and magnetic field, particles obtain

momentum from this wave when it propagates through the plasma. The

corresponding lower hybrid current drive (LHCD) is already successfully

used in present devices [33]. In addition to external current driving

methods, a self-generated current, uncovered in 1988 and named as

bootstrap current, provides a potential way for driving current efficiently

and continuously [34]. Because of relating to the inhomogeneous

magnetic field in tokamak, the bootstrap current is induced automatically

and this property may allow a tokamak to operate in a steady state in the

future [35].

If heating and current driving issues could be solved successfully, a

remaining problem consists in choosing materials which can survive

under conditions with long-pulses and high confinement plasma, for

plasma facing component (PFC) in the tokamak vessel. In practice, the

materials related issue for PFC occurs in current tokamak as well, simply

due to the extremely high temperature of the plasma state. PFC suffer

from irradiation from the plasma including bombardment by charged

particles, irradiation with high energy neutrons, and consequently

extensive heat load [36]. Details of plasma -materials interactions will be

introduced in the next chapter and some general requirements for PFC

materials will be discussed.

Capability to withstand extensive heat load and maintain mechanical

integrity calls for materials with high melting temperature or without

melting. Besides, for the purpose to prevent the plasma from being

contaminated, materials with low atomic mass are in preference in view

of less energy loss through radiation. Finally, economy efficiency and

safety require the retention of fuel in PFC at as low level as possible. From

the 1970s, research has been carried out on materials for fusion, including

tests with beryllium, carbon, molybdenum, tungsten, and stainless steel

etc. through testing facilities all over the world [37]. Experimental results


show that none of the current materials fulfil all three requirements

optimally at the same time, hence the selection of materials is a trade-off

between those demands [38]. For example, carbon-based material could

sustain extreme heat load without deformation but chemical reactions

with hydrogen isotopes lead to erosion and substantial fuel retention [39].

Beryllium and tungsten suppress fuel retention significantly, whereas

neither of them can avoid the melting issue. A plan for combing Be and W

in one device was proposed and this material configuration will be tested

in International Thermonuclear Experimental Reactor (ITER) [40].

1.4 Thesis contents

Work in this thesis related to the materials issues mentioned above,

especially fuel retention and PFC erosion which could be influenced by

several factors. Following the general introduction in chapter 1, chapter 2

will give a brief introduction about interactions between plasma and

chamber wall, together with several aspects which contribute to the

influences on the retention and erosion.

This thesis focuses on effects of surface topography. Experiments were

carried out to measure the elemental distributions of deposited

deuterium and beryllium, and beryllium erosion on samples from Joint

European Torus (JET). Micro ion beam analysis was applied to measure

the distributions. This will be discussed in chapter 3. Optical microscope,

scanning electron microscope, and confocal laser scanning microscope

were used to obtain sample topography. Details for them will be

described in chapter 3 at the same time. Simulation of particle motion in

the sheath region under a variety of conditions will be summarised in

chapter 4. Comparison of simulated data and experimental results will be

presented in chapter 4 as well. Chapter 5 will discuss implications of the

work in this thesis and conclude results from relevant published articles.

11

Chapter 2

Plasma wall interactions

The plasma itself is a very complicated system. From the point of view of

particle motion, positive ions and negative electrons in a plasma are acted

upon by the Lorentz force. As a single object, a plasma can be treated as

an electrically conducting fluid which follows both Maxwell’s equation

and the equations for fluid dynamics. Consequences of plasma-wall

interactions (PWI) come from both particle-like behaviour of plasma and

fluid-like characteristic. This chapter will briefly survey the PWI from the

particle side. Section 2.1 will describe the rationale behind magnetic

confinement and two kinds of configuration in tokamak device, followed

by an introduction of effects on plasma and PFC from PWI in section 2.2.

Section 2.3 will summarise methods for measuring erosion of PFC and

deposition of fuel and impurities, together with basic information of JET.

2.1 Magnetic confinement and plasma configuration

In the presence of a magnetic field, the motion of charged particles (ions

and electrons) can be resolved into components perpendicular and

parallel to the magnetic field. In the parallel direction, particles move

along magnetic field with 𝑣∥. In perpendicular direction, particles move in

a circular orbit with radius rg, namely the Larmor radius, determined by

particle mass 𝑚 , charge number 𝑞 , perpendicular velocity 𝑣⊥ and

magnetic field 𝑩 as shown in Eq.(2.1) [41]. Rotation of negative particles

obeys the right-hand sense with respect to magnetic field while positive

particles rotate in the opposite direction.

Combination of motions in both directions gives rise to a helical

trajectory as depicted in Fig 2.1. Bending magnetic field lines into a circle

could bring continuous movement along the field line and eventually

confining particles. Torus shape vessel in tokamak device came from this

12 Chapter 2 Plasma wall interactions

idea. In practice, a circular magnetic field cannot accomplish its mission

perfectly since the gradient and curvature of the magnetic field exist. Both

give rise to drifts of particle orbit away from the original field line [42].

The drift velocity depends on particle mass and charge number, as

indicated by Eq.(2.2) and Eq.(2.3),

𝒗𝒈𝒓𝒂𝒅𝒊𝒆𝒏 =

𝑚𝑣⊥2

2𝑞𝐵(𝑩 × ∇B

𝐵2)

(2.2)

𝒗𝒄𝒖𝒓𝒗𝒂𝒕𝒖𝒓𝒆 =

𝑚𝑣∥2

𝑞(𝑹 × 𝑩

𝑅2𝐵2) (2.3)

thus negative and positive particle move towards opposite directions,

which will generate extra electric field, causing 𝑬 × 𝑩 drift further.

Therefore, in magnetic confinement device, helical magnetic field was

proposed (shown in Fig 1.3 in previous chapter) to compensate drift

motion.

Application of a helical magnetic field contributed to great progresses in

magnetic confinement approach. However, leaking out of particles from

the plasma remains an issue which brings irradiation damages to vessel

walls by particles impact and heat conduction. Particles escape from

confinement through cross field diffusion. Classical and neoclassical

transport theory suggest that Coulomb collisions among particles and

spatial variation of magnetic field, particle density etc. are fundamental

𝑟𝑔 =𝑚𝑣⊥

|𝑞|𝐵 (2.1)

Fig 2.1 Sketch of Spiral motion of electron in magnetic field. Heavy black line means field

line and light blue filling indicates plasma. (a) shows a negative particle rotates along

magnetic field line. (b) depicts the bending magnetic field. (c) shows directions of drifts for

positive (blue) and negative (red) particles resulting from gradient and curvature of field

through the cross-section view.

(b) (a) (c)

2.1 Magnetic confinement and plasma configuration 13

and unavoidable mechanisms for cross-field diffusion [43]. Furthermore,

experiments and simulation research prove that non-linear turbulence

dominates the transport events [44]. Even if research works out solutions

for those elusive problems and run plasma in a steady and quiescent state,

the vessel wall will still suffer from plasma irradiation. Cross field ion

transport is also necessary to remove helium ash from a burning fusion

plasma.

For protecting vessel wall, the limiter configuration, sketched in Fig 2.2,

was employed in early tokamak devices, for example Alcator A and

Alcator C [45, 46]. In this kind of configuration, limiter defines the

plasma boundary and works as a sacrificial structure by guiding

impinging of particles directly to the limiter region to defend the vessel

wall recessed behind limiter. Therefore, materials for limiter are usually

refractory metals which could sustain high temperature and retain

physical or chemical properties, for example molybdenum and tungsten

[47]. Application of limiters in tokamaks brought a much cleaner plasma

compared to previous devices. However, high-Z (high atomic number)

impurities generated by PWI in the limiter region cause contamination of

the plasma leading to plasma cool down through radiation. Energy loss in

radiation process (bremsstrahlung radiation, line radiation, and

recombination radiation etc.) suggests that high-Z materials should be

replaced by low-Z since radiation power is proportional to Z squared (for

Bremsstrahlung) [48].

Fig 2.2 Figures show the limiter configuration on the left and divertor configuration with

single null on the right. Dashed blue line denotes the outmost boundary of plasma with

closed magnetic field line. Heavy blue line represents the wall for vacuum chamber


Except for the impurity content, the limiter configuration also confronts

the pumping efficiency for exhausting helium ash. In a burning plasma

working with the D+T reaction, helium should be removed from the core

plasma after it transfers energy to fuel particles. Without effective

removal, helium ash will dilute the plasma and reduce the efficiency of

fusion the fusion power production. Thus the helium concentration

should be restricted under 10% to keep a tolerable dilution level through

efficient particle pumping [49]. In primitive limiter devices, a vacuum

pump located at vessel wall was incapable of offering sufficient pumping

rate owning to a low neutral particle pressure [50]. Optimised limiter

versions were proposed in later time by introducing the new concept of a

‘pump limiter’ which contained a pump duct near limiter to increase the

neutral particle fraction [51, 52].

For impurity content and pumping efficiency issues arose in the limiter

configuration, divertor configuration, proposed by Spitzer around the

1950s, promises a better solution [53]. This configuration generates a

more complicated magnetic field to redirect PWI to remote areas as

shown in Fig 2.2. The plasma boundary here is defined by a closed

magnetic field (Separatrix) instead of solid surface. Particles move out

across the boundary (the region outside boundary is defined as a scrape-

off layer, SOL for short) and are swept off by transport parallel to

magnetic field and are eventually retained at divertor plates. Since a

divertor plate can be placed in a separate chamber which is far away from

Fig 2.3 Sketch for poloidal cross section of a tokamak with divertor and limiter

configuration. Inset on the right describes the SOL region, located just outside separatrix

2.2 Plasma wall interactions in divertor configuration 15

the main plasma, penetration of impurities into the core plasma would be

less easy. For helium exhaust, higher pumping efficiency can be attained

via physical baffles. Baffles in the divertor region compress and neutralise

helium and other impurities to increase the neutral pressure. This had

been verified by experiments in DIII-D and Alcator C-MOD tokamaks [54,

55].

Even though the divertor configuration is very attractive, the limiter has

not been put aside completely, since it is capable to protect the vessel wall

against unstable plasma [56]. Additionally, limiters also shield auxiliary

facilities from plasma irradiation. As introduced in the previous chapter,

performing plasma operation in a tokamak requires supports from

external facilities for heating and current drive. Some of them should be

installed inside the vacuum vessel for approaching the plasma closely, for

example antennae for LHCD and ICRH (ion cyclotron resonance heating).

Those antennae should be properly protected from the plasma by

adjacent limiters [57]. Therefore, in present tokamaks, divertor and

limiter together make up the main plasma facing components as sketched

in Fig 2.3. Since PWI mainly happens in the divertor region and the SOL

directs most of the heat load to divertor plates, a limiter in this case

suffers from less heat load than in pure limiter configuration. Therefore,

low-Z material could be used in limiters, in which the heat flux becomes

lower to reduce contamination. For example, in JET with ITER-like-wall,

limiters in the main chamber are manufactured from bulk beryllium,

while divertors consist of tungsten tiles and carbon tiles with tungsten

armour [58].

2.2 Plasma wall interactions in divertor configuration

Before discussing details of physical processes in PWI, it is helpful to

clarify the definition of PWI. PWI stands for plasma-wall interaction, in

which the term ‘plasma’ doesn’t represents the core plasma with

extremely high temperature (in keV range), but the cooler and denser

edge plasma including the SOL, a region in which the magnetic field lines

get in touch with the vessel wall [59]. PWI comprises exchange of mass

and energy between edge plasma and surrounding wall materials (shown

in Fig 2.4 ) and these form a strongly coupling system. Particle and heat

flux from the edge plasma could destroy the wall, leading to erosion or

variation in mechanical properties. Density and energy loss by absorption


of particles and heat by the wall will significantly influence plasma

performance in turn.

For energy exchange, viewed from the midplane of a tokamak as

emphasised by purple dashed line in Fig 2.3, a fraction of energy from

core plasma, produced by fusion reactions and external heating, is

transported to the edge plasma (mainly SOL), in the form of particle

kinetic energy, through conduction and convection [60]. Motions of

electrons and ions moving parallel to magnetic field divert most of the

transported energy to divertor plates quickly. The remainder transfers

into radiation from impurities, or crosses field lines and deposits on the

wall. Divertor plates absorb the incident power by inertial (or active)

cooling when working with short (long) plasma pule. The peak of heat

load must be controlled to fulfil the engineering limits of divertor thus

reduction of heat from divertor is necessary for both normal operation

and off-normal event. During normal operation, optimising divertor

geometry, based on numerical simulations, can reduce heat load by

around 30% [61]. Power dispersion through radiation from intrinsic and

intended impurities further promotes reduction of heat load [62].

However, transient heat load during off-normal event, especially edge-

localised modes (ELMs), can result in melting and evaporation of vessel

components.

Mass exchange between wall and edge plasma includes recycling and

retention of fuel, and erosion and deposition of impurities.

Corresponding physical processes will be discussed in the coming

Fig 2.4 Figure for exchange of mass and energy between plasma and surrounding wall. 𝐩⊥

and 𝐩∥ denote energy transport along and cross field line. 𝐧 indicates mass exchange with f

for fuel and i for impurities in subscript.

2.2 Plasma wall interactions in divertor configuration 17

paragraphs. Generally, fuel means hydrogen and hydrogen isotopes. But

for convenience, the term ‘hydrogen’ will be used to refer to protium,

deuterium, and tritium. Impurities come from a variety of sources during

plasma operation. In present tokamaks, particles emitted from the vessel

wall (both wall materials and absorbed gases) play a significant role,

whereas in tokamak with burning deuterium and tritium, helium should

be taken into account as well [63].

Recycling denotes a dynamic process in which hydrogen leaves and

returns to the plasma. Hydrogen ions ejected from the edge plasma can

be reflected from surrounding walls through ion-atom scattering and

come back to edge plasma, mainly as neutralised atoms or molecules [64].

Around half of the ejected hydrogen ions will be back-scattered and

become slower as a result of transferring energy and momentum to the

wall [65]. Some of the slower atoms are ionised again by resonant charge

exchange with fast hydrogen ions, inducing high energy hydrogen atoms

which can either penetrate back to core plasma or strike wall [66].

Another part of the ejected hydrogen is retained somewhere within the

vessel wall by ion implantation, diffusion in bulk material, or permeation.

Retention of hydrogen results in fuel trapping, generation of bubbles etc.

Under specific conditions, trapped particles can be released through

thermal and radiation induced processes. Released particles may

experience similar reactions as that of reflected particles before they

finally come to rest [67].

As for erosion, the main physical mechanisms include melting and

evaporation in off-normal event, and sputtering generated by hydrogen

and impurities. Ions and neutrals bombardments the wall bring physical

and chemical sputtering. In physical sputtering which had been well

investigated, incoming ions transfer kinetic energy to atoms located at the

first monolayer through collisions [68]. If energy exchange exceeds a

threshold then a wall material atom can be knocked out. The value of the

energy threshold for sputtering varies with elements and species of

impinging ions [69]. Generally, with the same incident ions, high-Z

materials have a larger threshold thus physical sputtering can be

compressed by using high-Z PFC or by reducing plasma temperature in

the vicinity of PFC [70].


Chemical sputtering ,through chemical reactions between ions and wall

atoms, is much more complicated than physical sputtering since multiple

factors could influence, for example material surface temperature and

molecular potential [71]. Unlike physical sputtering, the energy threshold

for chemical sputtering is extremely small, thus ions with energy down to

tens eV could lead to substantial sputtering [72]. Besides, chemical

sputtering is sensitive to the combination of impact ion and target,

resulting in strong variation of the sputtering yield [73]. Carbon based

materials are thought to be significantly influenced by chemical

sputtering in tokamak since chemical reactivity of hydrogen promotes

reactions with carbon and the formation of volatile species [74]..

If not pumped out, eroded particles deposit at adjacent region promptly

or at remote area after traveling in vessel. Accumulation of deposits on

wall surface forms amorphous deposited layers and hydrogen is also

trapped inside through co-deposition. Deposited layers undergo the same

PWI and brings several issues for device operation. The deposited layers

have different properties compare to substrate thus the erosion on them

are much easier. The amount of trapped hydrogen increases with plasma

running time due to unlimited deposition process and eventually lead to

substantial hydrogen inventory [75]. Additionally, the peel-off of

deposition generates dust which could contain substantial hydrogen and

be harmful for staff working in device during maintenance [76].

2.3 Measurements for erosion and deposition

For operating a tokamak, erosion and deposition issues on vessel walls,

especially on PFC remain concerns. Erosion limits the life time of PFC

and the subsequent migration of eroded substances contaminates the

plasma and co-deposits with hydrogen. Co-deposition brings

accumulation of hydrogen in deposited layers with will significantly

influence the hydrogen inventory and cause safety issues for tokamaks

working with tritium. Therefore, experimental investigations of erosion

and deposition are vital to uncovering physical mechanisms and to obtain

methods for inhibiting adverse effects.

Approaches for experimental evaluation of erosion and deposition can be

categorised by their application time as in-situ analysis and post mortem

analysis and they complement each other to promote understandings of

2.3 Measurements for erosion and deposition 19

plasma behaviour and subsequent effects on PFC [77]. In-situ analysis is

applied during plasma operation and provides data for temporal variation

of erosion and deposition during one or several plasma discharges. It can

help to estimate the erosion rate of PFC and thickness change of

deposition during exposing to the plasma [78]. Additionally, short term

fuel retentions during plasma operation can be obtained from in-situ

analysis, for example gas balance which can gain insight of variation of

plasma density during operation and be helpful for density control [79].

Post mortem analysis is used after exposure to plasma for measuring the

overall erosion (or long-term deposition) and the integrated effects from

different plasma conditions after one or more operation campaigns.

Overall erosion can be estimated from the thickness variation on specific

markers by ion beam analysis (IBA) [80]. Concentration and depth

profiles of light impurities and hydrogen in the surface of deposited layer

(about 10 μm) can be measured through elastic backscattering

Fig 2.5 Cross section of vacuum vessel for JET-ILW with Be tile at main chamber and W

and W-coated CFC tiles at divertor. The blue rectangle and number 1 indicate the inner wall

guard limiter made from solid Be and some of limiter tiles contain marker for detecting

erosion degree. The red polyline shows the position of divertor. Samples from divertor were

delivered to laboratories around the world for post mortem analysis to evaluate fuel

retention.


spectrometry (EBS), nuclear reaction analysis (NRA), secondary ion mass

spectrometry (SIMS) and so on [81], while hydrogen trapping in bulk

material can be observed by thermal desorption spectroscopy (TDS).

Particle-induced X-ray emission (PIXE) can trace metal elements in

deposition which can help to survey the global impurity transport.

Works in this thesis are part of post mortem analysis of samples from

JET-ILW, shown in Fig 2.5. JET is the largest operational tokamak with

divertor configuration, located at Culham Centre for Fusion Energy, UK.

In the latest upgrades at JET, named as the ITER-like wall project (ILW),

previous carbon PFCs were replaced by new tiles manufactured from

beryllium and tungsten for testing this potential material combination for

ITER. Although those materials had been tested in other tokamaks

separately, JET-ILW project will check the integrated effect on operation.

One aim of the ILW project is to demonstrate the control of hydrogen

inventory in this material combination and try to achieve sufficient life

time for PFCs by controlling heat load [82]. Results and corresponding

extrapolations from the ILW project will play a significant role in design

and construction for ITER in the coming future.

21

Chapter 3

Experimental methods

Teamwork and cooperation are crucial for resolving complex problems.

Measuring the influences from PWI and understanding the relative

physical processes can be classified as complex problems thus

cooperation will certainly contribute to solve them. Delivering samples,

taken from tokamak, to different laboratories for post mortem analysis is

one way to make use of cooperation. This chapter will describe techniques

used in this thesis for analysing samples taken from JET. IBA will be

introduced in section 3.1 with micro IBA in section 3.2. Topography

measurement and the combination between micro IBA and topography

results for handling issues arisen from surface roughness will be

summarised in the final section

3.1 Ion beam analysis

Based on ion-atom interactions, IBA uses ion beams (projectiles) in

mega-electron volt (MeV) energy range to probe elemental compositions

and depth profiles in solid samples (targets). Major interactions include

scattering, displacement, ionisation in the inner shield of target atom,

nuclear reactions, and sputtering [83]. IBA detects the products from

those ion-atoms interactions and the spectra with counts versus energy

can be collected from signals. Analysis of the spectra can be made

through simulation codes which describe processes during ion-atom

interaction by the Monte Carlo simulation methods or by analytical

method [84, 85]. IBA used in this thesis consists of EBS, NRA, and PIXE

which will be discussed individually in following paragraphs. All IBA

measurements were carried at the 5 MV pelletron accelerator in the

Tandem laboratory at Uppsala University.

22 Chapter 3 Experimental methods

In IBA, ion beams strike solid samples and penetrate them. During the

movements in the samples, incident ions gradually lose their energy and

change direction through collisions with target atoms. Transfers in energy

from projectiles to targets can excite or ionise target atoms, leading to the

emission of electromagnetic radiation. Displacement or even sputtering

of target atoms can be expected if the amount of transferred energy is

higher than the binding energy of the atom in the material. Before the

incident ions eventually come to rest inside target, several other destinies

can be predicted. They can leave the sample through large angle

scattering if they are lighter than target atom, or disappear through

nuclear reactions [86]. Different techniques in IBA focus on different ion-

atoms interactions with variety of detectors to collect signals for acquiring

useful information on samples. EBS depends on large-angle

backscattering of incident ions and NRA focuses on the products in

nuclear reaction as shown in Fig 3.1. Instead of charged particles, PIXE

concentrates on the characteristic X-ray. In this thesis, an annular silicon

surface barrier detector was used for measuring the charged particles

while X-ray was measured by a lithium-drifted silicon detector.

Backscattering in EBS results from elastic collisions between incident

ions and target atoms, including the Rutherford scattering and non-

Rutherford scattering. During the bombardment by the ion beam of the

solid sample, the collision between projectile and target is assumed to be

Fig 3.1 Sketch for comparing EBS, NRA, and PIXE. Pink solid sphere means the

incident ions and the arrow with the same colour shows the impinging direction. In the

subset for EBS, the arrows with different colours and solid spheres indicate that the

detector collect backscattered ions from different element which can be distinguished by

blue and yellow. NRA collects the charged particles from nuclear reaction which

denoted by the hollow circles. They are usually different from the incident ions. PIXE

measures the X-ray which results from the process when outer shell electron fills a

vacancy in the inner shell.

3.1 Ion beam analysis 23

a two-body collision. In this case, there is no overall kinetic energy loss

during the collision between them. The energy of the back-scattered ion

(𝐸1) can be represented by the product of the initial energy just before

collision (𝐸0) and the kinematic factor (𝐾) which can be deduced from

conservation of energy and momentum as shown in Eq.(3.1) [87]. 𝑀1 and

𝑀2 denote the mass of incident ions and target respectively, and θ means

scattering angle in laboratory coordinate system. The expression for the

kinematic factor indicates that for a given detection angle, only 𝑀2 is the

unknown parameter, if the energy 𝐸0 and mass 𝑀1 for the incident beam

particle are known and 𝐸1 is measured. For 𝐸0, it is customary to use the

initial beam energy, namely considering the backscattering from the

outmost layer without penetration into the sample. Then 𝐸1 corresponds

to the high energy edge of the energy spectrum in Fig 3.2 and the exact

value of 𝐸1can be obtained from a calibrated energy spectrum. The energy

calibration can be made through elemental samples.

Besides identifying elemental compositions, it is possible to acquire the

amounts of specific elements in target from EBS, usually in the form of

area density. The area density is calculated as the product of atomic

density and thickness as 𝑁𝑑𝑥, thus it can be converted into thickness

when the mass density is defined. However, for samples from a tokamak,

the mass density of deposits often deviates from the bulk value when the

corresponding element stays in its pure natural state, owing to the loose

𝐸1 = 𝐾𝐸0 𝐾 = [√𝑀2

2 − 𝑀12 sin2 𝜃 + 𝑀1𝑐𝑜𝑠𝜃

𝑀2 + 𝑀1

]

2

(3.1)

Fig 3.2 Schematic figure for EBS spectrum on the right-hand side, from a monoisotopic

target on the left-hand side. Ei and YEi denote the energy and counts of particles reflected

from thin layer indicated by red hatched region in depth Δx in target. E1and E2 respond to

particles encounter backscattering from the top and bottom layer respectively.


structures in deposited layer. Therefore, the term of areal density is more

convenient in this thesis. For a thin slab of thickness For a thin slab of

thickness 𝑑𝑥 located at depth as shown by the red hatched region in Fig

3.2, the corresponding counts 𝑌𝐸𝑖 (height) at 𝐸𝑖 channel in spectrum is

determined as Eq.(3.2). Thereby, in EBS, 𝑁𝑑𝑥 can be deduced by the

counts (ordinate in Fig 3.2) in the energy spectra.

𝑌𝐸𝑖 = 𝜎(𝐸𝑗)Ω𝑄𝑁𝑑𝑥 (3.2)

In order to obtain the area density 𝑁𝑑𝑥, three parameters Ω, 𝑄, 𝜎 should

be known. Ω𝑄 defines product of the solid angle subtended by detector

and the number of incident ions, or the integrated current. A Faraday cup

or a beam chopper can be used for measuring current directly. While

restricted by the chamber size and the configuration of detectors, the

integrated current was calculated by the surface height of spectrum from

elemental sample in this thesis. 𝜎(𝐸𝑗) signifies the differential

backscattering cross section at energy 𝐸𝑗, the energy of the projectile just

before collision. For Rutherford scattering, the cross section can be

deduced from an analytical function [88]. Whereas for non-Rutherford

scattering, the cross sections should be determined from experiments and

those data could be found in databases online [89].

Except the mentioned parameters, another implicit variable, 𝐸𝑗 the

energy of projectile just before collision, should be considered. Eq.(3.3) gives an expression for 𝐸𝑗 , based on the energy loss along inside path

through the integral of stopping cross section 𝜖 and target areal density

[90]. Semiempirical values of the stopping cross section for a specific

combination of incident ion and target are obtained from calculation by

energy loss theory and experimental results [91, 92]. Similar expression

can be applied for the outward trajectory after collision in Eq.(3.4) with

asterisk clarifies the different stopping cross section which varies with ion

energy. Combining Eq.(3.3) and Eq.(3.4), explicit energy value at channel 𝐸𝑖 in spectrum can be linked to the implicit variable 𝐸𝑗.

𝐸𝑗 = 𝐸0 − ∫ 𝜖𝑁

Δ𝑥

𝑜

d𝑥 (3.3)

𝐸𝑖 = 𝐾𝐸𝑗 − ∫ 𝜖∗𝑁Δ𝑥

𝑜

𝑑𝑥 (3.4)

3.1 Ion beam analysis 25

NRA focuses on the inelastic reaction when projectiles carry enough

energy to overcome the repulsion from Coulomb barrier and then

generate a nuclear reaction. Light elements are prone to undergo nuclear

reaction since the energy barrier is smaller. Therefore, NRA is more

sensitive for light elements, for instance deuterium and beryllium in this

thesis, and can be applied as a complementary method for EBS for

detecting light elements in the heavy substrates [93]. Experimental

devices used in NRA are analogous to that of in EBS with a

semiconductor detector for collecting charged particles. However, the

NRA technique has its distinctive features. In NRA, detected particles are

usually not the initial incident ions but products from nuclear reactions

with higher energy, while the initial beam energy in EBS restricts the

maximum energy of backscattered ions as shown in Fig 3.3.

Except the difference in energy, cross sections for nuclear reactions vary

complicatedly with the energy of projectiles thus, usually no analytical or

exact expression for it is available. The cross section data for a specific

reactions at a fixed detected angles can be obtained from experiments

[94]. Usually the cross section for nuclear reaction is much smaller than

elastic for elastic scattering, thus higher beam current is necessary to

fulfil statistics in NRA. In this case, large numbers of backscattered

Fig 3.3 Experimental spectra from EBS and NRA with 3 MeV proton and 4.8 MeV helium

respectively. Detected particles in EBS with maximum energy limited by kinematic factor

and the initial beam energy thus the high energy edge in EBS here is smaller than 3 MeV.

However, in NRA, energy of the reaction product mainly depends on the mass difference

between interactants and products. Fitting was done by SIMNRA.


particles may overload the detector, hence they should be filtered by

putting a thin film in front of the detector. An aluminium foil around 30

μm thickness was mounted in front of the annular detector in this thesis

and the corresponding energy loss in foil was taken into account in curve

fitting.

In this thesis, energy spectra from EBS and NRA were further analysed to

estimate the elemental concentrations through the curve fitting with the

help from the simulation code SIMNRA 6.06, assuming that the model of

the sample was laterally homogeneous and amorphous [95]. Cross section

data for both techniques were obtained from the IBANDL database. The

integrated current in EBS was derived from spectra directly as discussed

earlier, whereas in NRA, the current estimation required assistances from

PIXE.

PIXE stands for the particle induced X-ray emission and has been widely

used as a non-destructive technique in geology, art etc. since the 1980s

[96]. It depends on the emitted X-rays during the transition of an outer

shell electron to an inner shell vacancy which is left behind after the

ejection of an inner shell electron. The ejection is induced by the incident

charged particles for example protons, alpha particles or heavier ions. As

EBS and NRA, PIXE can provide a quantitative value for the elemental

concentration, especially for heavy elements, from the intensity of X-ray Y

by Eq.(3.5) and Eq.(3.6) [97]. 𝛺𝑄 represents the product detector solid

angle and current as the same in EBS. he parameter B includes other

essential variables for X-ray emission i.e. fluorescence yield 𝜔 , cross

section 𝜎 and transition probability 𝑘. Effects from the detection system

are encapsulated as well, for instance X-ray absorption coefficient 𝑇 and

detector efficiency 𝜖𝑧. The estimation of elemental concentration in the

sample can be done by comparing with standard sample or through

theoretical calculations from parameters in Eq.(3.6) with a simulation

code e.g. GUPIX [98].

𝑌 = 𝛺𝑄𝐵 (3.5)

𝐵 = ∫(𝑁𝜔𝑘𝜎𝑇𝜖𝑧)

𝑆(𝐸)𝑑𝐸 (3.6)

3.2 Micro ion beam analysis. 27

In this thesis, the intention is not to obtain sample information through

PIXE, but to calculate the incident current and to identify the scanned

area of interest. Eq.(3.5) shows that, in PIXE, the intensity of X-ray is

proportional to the incident current with the coefficient of proportionality

𝐵 which depends on the experimental conditions and sample features.

Therefore, under the same conditions and identical materials, coefficient

𝐵 should be a constant and can be deduced from the ratio of the intensity

to the current which is obtained by Eq.(3.2) from the EBS spectrum

collected simultaneously in Fig 3.4. Then in the absence of EBS, the

current can be calculated from 𝑌/ 𝐵 in reverse.

3.2 Micro ion beam analysis.

Micro-ion beam analysis (μ-IBA) is one category of IBA，carried out with

focused beam with the beam spot size in micron scale. Besides the

elemental composition or area density discussed previously, μ-IBA also

can provide additional information about spatial distributions of different

elements over the sample surfaces. IBA with broad beam (beam size in

the range of cm to mm) has been widely used in post mortem analysis for

measuring the amount of fuel retention and impurities, and the material

erosion on PFC tiles from tokamak devices [99, 100]. In recent years,

results from transmission microscopy and scanning electron microscopy

indicate that both the fuel retention and the erosion on PFC tiles contain

inhomogeneous patterns in micro meter scale [101, 102]. Outputs from μ-

IBA further confirm the existence of non-uniform distribution of trapped

Fig 3.4 Spectra from EBS and PIXE by collecting signal simultaneously from a pure

copper grid for calculating the coefficient of proportionality B.


deuterium on divertor sample in JET as well [103]. Therefore, in this

circumstance, questions about which factors lead to those non-uniform

patterns and how to handle the effect from them in IBA for samples from

tokamak emerge naturally.

Factors which influence the non-uniform deposition pattern have not

been fairly well understood, since PFC tiles experience erosion and

deposition repeatedly due to the reoccurring PWIs as discussed in chapter

2. Therefore, both the variations in plasma parameters and the changes in

the tile conditions during one operation campaign may contribute to the

non-uniform deposition. Although it is not possible to test the influence

from the variation of every parameter through the plasma operating

experiments, it is feasible to measure the lateral distributions of the major

elements in deposited layers through μ-IBA, especially μ-NRA. One could

then generalise from those distribution data for further research on

creating models or performing simulation for figuring out the dominant

factors. μ-NRA with 3He beam at 3 MeV and 4.8 MeV was chosen for the

works in this thesis for observing deuterium, beryllium and other

impurities. Emphasis was placed on deuterium since JET was fuelled by it

during the past campaigns. And beryllium was considered because it was

thought to be the major impurity, since the PFCs in the main chamber in

JET-ILW were mainly manufactured from beryllium.

Fig 3.5 Distribution maps of beryllium, carbon, and deuterium on sample located at Tile 0

from the first JET-ILW campaign. Within one map, the red patch represents higher counts

than that of yellow patch, and even lower counts on the cyan patch. Dark blue background

means the absence of the corresponding element or the amount of it is lower than the

detection limit of the device.

3.2 Micro ion beam analysis. 29

In the current line of μ-NRA located at the tandem laboratory, the

scanning of beam spot on the sample surfaces is driven by a magnetic

scanning unit with scan size in 256 × 256 steps and the spatial resolution

depends on the size of the beam spot, which is determined by the

conditions at each measurement. he Data acquisition system gets

feedback from the coordinate signals each time a particle or X-ray photon

is detected. Then the position (in the coordinates formed by the scan

steps) and the energy of a measured event (the charged particle from

nuclear reaction and the emitted X-ray) could be recorded simultaneously

[104].

Combining the coordinate information and counts on each step, the

distribution map can be obtained as exemplified in Fig 3.5. Patches in

different colours indicate the relative intensity of charged particle signals

(the yields or counts) within the scanned area. Red indicates higher

counts while cyan shows relative lower counts with dark blue background

represents the absence of the corresponding element or implies that the

amount is lower than the detection limit. Distinction among elements was

drawn from the separated peaks in the energy spectrum of NRA, resulting

from a variety of nuclear reactions between incident helium ions and

sample as shown in Table 3.1. The energy resolution for the detection

system is about 10 keV and protons from different nuclear reactions (in

Table 3.1) can be well separated.

Table 3.1 Nuclear reactions with proton in NRA in the thesis

Reaction Energy of proton (MeV)

( 𝐻𝑒3 3 MeV)

Energy of proton (MeV)

( 𝐻𝑒3 4.8 MeV)

𝐷( 𝐻𝑒3 , 𝑝) 𝐻𝑒4 11.344 10.789

𝐵𝑒9 ( 𝐻𝑒3 , 𝑝0) 𝐵11 9.923 10.647

𝐵𝑒9 ( 𝐻𝑒3 , 𝑝1) 𝐵11 8.117 8.869

𝐵𝑒9 ( 𝐻𝑒3 , 𝑝2) 𝐵11 6.174 6.958

𝐶12 ( 𝐻𝑒3 , 𝑝0) 𝑁14 5.724 6.699

𝐶12 ( 𝐻𝑒3 , 𝑝1) 𝑁14 3.745 4.744

𝐶12 ( 𝐻𝑒3 , 𝑝2) 𝑁14 2.375 3.387

Another issue raised in the first paragraph in this section is about the

non-uniform erosion pattern and the corresponding effects on IBA.


Erosion on PFCs in JET were observed by the sandwich-type marker tiles

or the common tiles with coating layers in another element. In a marker

tile, an interlayer made from different element, usually heavier element,

is used to separate the substrate and the coating layer which are

manufactured from the same material [105]. EBS is generally addressed

for measuring the thickness variation of the coating layer for further

estimating the amount of erosion and the erosion rate.

However, after exposure to plasma, the remnant of the coating layer is

rough and even only partially covers the next layer [106]. Working on a

rough surface brings a typical confusing case in IBA since the

backscattering energy spectrum can be misinterpreted as a continuous

variation of the elemental concentration, i.e. the variation on depth

profile [107]. Except the general issue, surface roughness creates a

specific problem for EBS on the marker tiles. In the energy spectrum for a

marker tile, backscattering particles from the coating layer, the interlayer

and the substrate should be well divided into individual peaks. And then

the variation of the width of the peak corresponding to the coating layer

can represent the thickness change on it. But the roughness resulting

from the non-uniform erosion in micron scale can render the separation

impossible and lead to a continuous energy spectrum.

Therefore, for either the general issue and the specific issue, it is

significant to deal with the effects from roughness. Together with the

measurement on sample topography which will be discussed in the next

section, μ-EBS can handle those issues. For the general issue, μ-EBS

records the coordinate signal of each collected backscattering particle

thus one can select data from a relatively smooth region according to the

SEM images. The simulation with a layered homogeneous model for this

smooth region can neglect the impact from roughness.

As for the specific case of the marker tiles, μ-EBS also provides the

information about the lateral distribution of thickness of the coating layer.

The erosion makes the top coating layer become thinner and further

entails that the interlayer can be reached by incident ions with higher

energy during ion beam analysis. Thereby, the consequent backscattering

particles extend the energy spectrum of the interlayer towards the high

energy side. Conversely, the distribution map based on the extended

portion of the energy spectrum could reflect regions on the coating layer

3.3 Topography measurement 31

which share approximately the same value of thickness of the residual

coating layer. Based on this analytical method, a 3 MeV proton beam was

applied for μ-EBS in this thesis, on samples from a marker tile from the

inner-wall-guard limiter in JET-ILW. The same current line was used in

the tandem laboratory with after removal of the Al foil.

During the performance of either μ-NRA or μ-EBS, the characteristic X-

ray signals, induced by helium or proton, were collected at the same time,

i.e. μ-PIXE was carried out simultaneously. The configuration of the

vacuum chamber is depicted in Fig 3.6. As mentioned in the first section

in this chapter, PIXE was employed to obtain the integrated current from

the coefficient of proportionality 𝐵 and Eq.(3.5) through the attached

TEM copper grids within the ion beam scan regions as shown in the left

inset in Fig 3.6. Additionally, as with μ-EBS and μ-NRA, maps of

elemental distributions can be achieved from μ-PIXE as well, especially

for metals. Thus, μ-PIXE from the copper grids provides both the

information about incident current for the other two techniques and

localises the ion scan region for further comparison with the topography

of the samples.

3.3 Topography measurement

For both μ-NRA and μ-EBS in the preceding section, sample topography

is an essential part for analysis. The map of elemental distribution from

μ-NRA need to be compared with the topography for summarising the

Fig 3.6 The configuration of the chamber at the current line for micro-ion beam analysis on

the left. An annular silicon surface barrier detector collected the charged particles resulted

from backscattering and nuclear reaction at Θ1 = 165°. X-ray was measured by a Si(Li)

detector located at Θ2 = 135°. The insect on the right is the image for a divertor sample

from Tile 0 with an attached copper grid (100 mesh) on it for localising the ion beam scan

region and for the deducing of integrated current.


relevance between the sample surface structures and the deposition

pattern. And the quantitative surface topography is an important input

parameter for further simulation. For μ-EBS, the selection of a relative

smooth area requires the surface structure within the scanning region as

a reference. Therefore, in this thesis, three kinds of microscopes were

used for observing and measuring the samples: scanning electron

microscope (SEM), optical microscope (OM), and confocal laser scan

microscope (CLSM). SEM provides the sample topography in two

dimensions (2D), OM and LSM measure the roughness in three

dimensions (3D). They will be introduced individually in the following

paragraphs.

SEM is a classical microscopy for studying details of sample surface

through the interaction between sample and a focused electron beam. It

collects the backscattering electrons, the secondary electrons and other

products from the interactions to image surfaces and determine sample

compositions [108]. Usually, signals from the secondary electrons,

emitted from the surface regions (or near surface region around 10 nm),

are chosen for imaging since thy are more sensitive to the topography

than other signals [109]. In this thesis, samples from the limiter marker

tiles were imaged by SEM with the secondary electron mode. For the

purpose of selecting a smooth area within the μ-EBS detection region,

elemental distribution map was overlaid on the SEM image. The map of

copper grid from μ-PIXE align the elemental map with image from SEM

as shown in Fig 3.7. The following works on selection specific regions

Fig 3.7 The SEM images were overlaid with Ni distribution map from μ-EBS on the left

and the map of copper grid from μ-PIXE on the right. The white dashed line indicates the

ion beam scan region.


were carried out based on the overlaid image as described in Paper VI.

SEM provides the clear two-dimensional topography of the limiter

sample for choosing the relative smooth region by eyes. But for figuring

out the relevance between non-uniform deposition pattern on the

divertor samples, more details on surface structure would be necessary.

The optical microscope with the focus stacking method (also known as

the focus plane merging) can reconstruct a three-dimensional topography

and offer the quantitative value of surface structures. The focus stacking

method is a post-processing technique for combining a pile of digital

images to form a sharp image with sufficient depth of field [110].

In a photograph, the section which appears to be sharp represents the

part of an object that lies in the focus plane of the optical system, while

other sections of the object appear to be blurred on the same photo. By

focusing (moving the position of focus plane) on different sections on an

object, one can obtain a series of images with different areas in focus. By

stacking all those images together, the final image displays all parts of the

object clearly. The movement of focus plane can be done in a controlled

way to reconstruct a 3D digital topography on an optical microscope, with

a fixed lens and a monitor for the stepwise motions of the object stage

(the stage for placing sample).

Assume that the object stage locates on the xy plane in the coordinate in

Fig 3.8 and the surface roughness can be denoted by the z values. Position

1 represents the top section of the sample with z1. Position 2 can move

Fig 3.8 Sketch for the focus stacking method, viewed in the zx plane at the coordinate at

the upper right corner. The surface structure extends perpendicular to paper with a finite

length.


into the focus plane after one step motion of the object stage. The relative

difference z1 − 𝑧2 between those two positions is determined by the step

size which can be obtained from the monitor. x and y value are recorded

as pixels and the absolute values can be calibrated by an attached TEM

copper grid. Moving the object stage towards one direction repetitively

with a fixed step size and taking photo at each step can slice the sample

into multiple digital images.

Post-processing for reconstructing the 3D topography from those images

was accomplished with Adobe Photoshop and a MATLAB code in this

thesis. Step size of the stage movement settled the spatial resolution in z

direction while the lateral resolution (point-to-point resolution) was

limited by the lens with a theoretical value around 2 μm. Fig 3.9

exemplifies a result from the stacking method by showing the topography

on the same region in Fig 3.5. A pronounced relevance between the

deuterium and beryllium distribution and the surface topography can be

found with both accumulated within the crater. Paper I and Paper II

summarised more results from the comparisons of the distribution maps

with the optical images.

Fig 3.9 The optical image, obtained by the stacking method, of the divertor sample from

Tile 0 (JET-ILW) is shown on the left hand side and the 3D topography from the post-

processing stays on the right hand side. The corresponding elemental distribution

results is shown in Fig 3.5.


The focus stacking method for images from optical microscopy provides

an easy way for achieving 3D topography. However, this method cannot

fulfil the requirements for measuring the surface structures completely

since the observing area is restricted by the chosen lens. Besides, the

current update on the beam line for μ-IBA in the tandem laboratory

renders a smaller beam spot which could improve the spatial resolution

in μ-IBA significantly. Therefore, a more flexible imaging method should

be applied for compensation. As a well-known imaging tool with the

combination of high resolution and depth sensitivity, confocal laser scan

microscope can be a great candidate.

CLSM collects optical signals from sample surface by using a laser beam

as the light source. The laser beam spot scan sample surface point by

point and the reflected light (or light which is produced by fluorescence)

travels through a spatial pinhole which will block the out-of-focus light i.e.

Fig 3.10 Surface structure from CLSM for the divertor sample on Tile 0 overlaid with

deuterium distribution map. Back dashed line specifies the area scanned by μ-NRA and

the superposition of μ-IBA result on the topography was shown by the upper inset.

Topography from CLSM provides more details on surface structure than optical

microscope.


the light originates from other plane other than the focus plane. A

detector located after the pinhole records the light intensity and the

maximum value on one pixel can be transferred into position information

along the vertical direction [111]. Scanning on sample surface produce a

series of images and the stacking of those images must be done for

achieving a 3D topography. In this thesis, the CLSM was accomplished

with the Zeiss LSM 510 Pascal at AlbaNova Laser Laboratory KTH,

Sweden. Laser beam with wavelength at 543 nm was applied and a voxel

( 0.5 μm × 1.76μm × 1.76μm in z, x, and y direction respectively) was

selected for scanning. ImageJ read the raw data from CLSM and

MATLAB code reconstructed the 3D topography [112]. Fig 3.10 gives an

example for the results from CLSM for a divertor sample from Tile 0 in

JET-ILW.

For raw data from both OM and CLSM, the influence from inclination of

sample surface should be eliminated. Each divertor sample contains a

small slope inclining by several degrees, mainly resulted from the process

of cutting sample. They may confuse the results of surface structure. The

slope correction had been accomplished through subtracting a plane from

the raw data as the data levelling in the postprocessing for images from

atomic force microscope [113].

37

Chapter 4

Modelling

Scientific experiments and theory are vital tools for uncovering the

secrets of the physical world. The former observes the world under

controlled conditions by a variety of methods and equipment. The latter

explains the experimental results with hypotheses and makes predictions

for what will happen when experimental conditions change. After new

experiments confirm the predictions, this theory can be considered as a

correct description of the real world. However, for those high-cost and

high-risk experiments, or for hypotheses which contain multiple

parameters, repetitive testing for predictions through actual experiments

would be a difficult task. Fortunately, technical progress in computing

allows for computer modelling as a substitute for practical experiment.

One of the subjects in this thesis, the non-uniform distribution patterns

on PFC in JET, is such an issue, which could be affected by variety of

parameters. Therefore, a model can be a good help for understanding it.

In this chapter, some calculations for ion trajectories will be introduced.

Section 4.1 will discuss models for the background plasma, sheath and

electromagnetic filed. The calculation for trajectories of incident ions,

based on the models in section 4.1, will be summarised in section 4.2. The

final section will concentrate on the what-if scenario when relative

parameters change.

4.1 Models for plasma and sheath

As discussed in chapter 1 and chapter 2, the plasma for fusion is confined

within a finite volume in a tokamak by magnetic field with three roughly

divided regions shown in Fig 2.4. The edge plasma interacts directly with

the surrounding vessel walls which absorb impinging ions and electrons.

38 Chapter 4 Modelling

The much lighter electrons move faster than ions at the same temperature,

thereby more electrons hit the wall, generating a negative charged wall

relative to the plasma and leaving a positive region just before the wall.

The ensuing electric field retards the coming electrons and accelerates

ions. This eventually provides a shielding for the neutral plasma from the

charged vessel. The thickness of this shielding layer usually stays in the

order of the Debye length and is called the Debye sheath (DS) [114]. In

present tokamaks, for the purpose to reduce the heat flux density on

divertor tiles, the angle between magnetic field and surface should be

small, i.e. a glancing angle should be applied. The oblique magnetic field

produces a quasi-neutral magnetic pre-sheath (MPS) upstream of DS

with length scale in several ion gyro radii [115]. A schematic diagram for

the MPS and the DS is shown in Fig 4.1.

An ion which escapes from the edge plasma should travel through both

the MPS and the DS before it reaches the wall surface. For calculating ion

trajectories, the conditions (models and parameters) for the edge plasma

(background plasma in the following content) and sheath should be

clarified. In this thesis the background plasma is presumed to be an

isothermal plasma in which electrons and ions have equal temperature.

The sheaths, both MPS and DS, are supposed to be collisionless regions

and the electrostatic potential in those regions drops monotonically. The

magnetic field is fixed in both MPS and DS, while the electric fields are

Fig 4.1 Sketch for MPS and DS with the coordinate used in modelling. The pink dotted line

indicates the trajectory of the guiding centre of an ion.

4.1 Models for plasma and sheath 39

uniform, with separate values which depend on the potential drop. Those

assumptions will be discussed in the following contents.

The first assumption is about the background plasma located upstream,

which is supposed to be in isothermal equilibrium. A plasma consists of

light electrons and heavy ions and they transfer energy to the same (or

different) species through Coulomb collisions. Collisions between similar

particles i.e. between electrons or between ions drive systems which

compose the similar particles into thermal equilibrium respectively.

Collisions between different particles (electron-ions or the reverse)

transfer energy from a hotter system, usually electrons, to a cooler one.

Each mentioned process has its own time scale which can be

characterised by the average collision frequency ⟨ν⟩ in unit s−1 . For

electron-electron and electron-ion collisions, ⟨νee⟩ and ⟨ν𝑒𝑖⟩ are in similar

amount since the Coulomb force is in the same order of magnitude. ⟨ν𝑒𝑖⟩

can be determined by Eq.(4.1), which depends on particle density and

electron temperature. For a hydrogen plasma, the constants in Eq.(4.1)

can be merged into a coefficient in the magnitude of 10−11 (the density in

the unit of particles per cubic meter and the temperature in eV). Due to

the absence of ion mass in ⟨νei⟩, Eq.(4.1) should be valid for deuterium

plasma as well [116].

To establish thermal equilibrium between ions and electrons through

collisions is a much slower process. The frequency of this process 𝜏−1 is

smaller by a factor of 𝑚𝑒/𝑚𝑖 relative to ⟨νei⟩ as shown in Eq.(4.2).

Although it is a time-consuming process compared to electron-ion

collision, a plasma can be considered as thermal equilibrium if the

characteristic time scale for energy loss of electrons is longer then 𝜏. For

an edge plasma with electron density in the range of 1020 − 1019 𝑚−3 and

𝑇𝑒 ~ 10 𝑒𝑉, 𝜏 is around 10−5 − 10−4 s. Therefore, in magnetic confined

tokamak devices with the energy confinement time in the order of

millisecond, plasma can be considered as in thermal equilibrium since

⟨νei⟩ =0.5𝑛𝑍2𝑒4𝑙𝑛Λ

12𝜋32𝜖0𝑚𝑒

12𝑇𝑒

32

~ 5 × 10−11𝑛/𝑇𝑒

32 (4.1)

𝜏−1 ∝ (𝑚𝑒/𝑚𝑖)⟨νei⟩ (4.2)


electrons and ions have enough time to exchange energy and lead to 𝑇𝑒 =

𝑇𝑖.

The second assumption is for the collisions of ions in MPS and DS.

Generally, MPS and DS can be considered as collisionless regions for ions

since the mean free path λm for ion-ion Coulomb collision is much longer

than the sheath thickness [115, 117]. λm , expressed in the unit 𝑚, can be

calculated from Eq.(4.3) by the density (𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑚3⁄ ) and the

temperature (𝑒𝑉) of ions [118]. When 𝑇𝑖 ≈ 10 𝑒𝑉 and 𝑛𝑖 ≈ 1020 𝑚−3, 𝜆𝑚 is

in the magnitude of 10−2 𝑚. The thickness of DS (𝐿𝐷𝑆) is about several

Debye length λD and MPS (𝐿𝑀𝑃𝑆) has the length scale in a few ion gyro

radii which was described by the expression in Eq.(2.1). Both are much

smaller than 𝜆𝑚 under the same conditions.

𝜆𝑚 ≈ 1016𝑇𝑖2/𝑛𝑖 (4.3)

In the collisionless sheath, the motion of ions is guided by the Lorentz

force with the equation of motion in Eq.(4.4). The background plasma

contains only magnetic field, thus ions spiral along 𝑩, whereas in the

sheath regions, ions will experience accelerations and the 𝑬 × 𝑩 drift,

owing to the existence of an electric field 𝑬. This electric field be deduced

from the potential drop 𝑉𝑡𝑜𝑡𝑎𝑙 in Fig 4.1. By setting the potential of the

edge plasma to zero, the potential of the wall (i.e. the total potential drop

is over the MPS and the DS) can be indicated as Eq.(4.5) from the

derivation in [115], with 𝑘 denoting the Boltzmann constant. The

corresponding potential drop in MPS (𝑉𝑀𝑃𝑆) is given by Eq.(4.6). And

then 𝑉𝐷𝑆 can be obtained by subtracting 𝑉𝑀𝑃𝑆 from 𝑉𝑡𝑜𝑡𝑎𝑙 as discussed in

Paper II.

𝑉𝑡𝑜𝑡𝑎𝑙 = (𝑘𝑇𝑒/𝑒)0.5𝑙𝑛 (

2𝜋𝑚𝑒

𝑚𝑖

(1 + 𝑇𝑖 𝑇𝑒⁄ ) ) (4.5)

𝑉𝑀𝑃𝑆 =

𝑘𝑇𝑒

𝑒ln(cos(90 − 𝛿)) (4.6)

Based on those assumptions and models for the background plasma and

the sheath, the trajectory of a traced ion can be calculated by solving

𝑚𝑑2𝒓

𝑑𝑡2= 𝑞(𝑬 + 𝒗 × 𝑩)

(4.4)

4.2 Calculation of ion trajectory 41

Eq.(4.4). The details for computing the ion trajectory will be discussed in

the coming section.

4.2 Calculation of ion trajectory

For calculating the trajectory of an incident ion, the initial conditions of

the ion should be set, followed by the determination of ion velocity and

position. The time dependent ion motion can be deduced from the

solution of Eq.(4.4) with different configurations of 𝑬 and 𝑩, i.e. only

magnetic field should be considered in the background plasma, whereas

the electric field cannot be neglected in sheath region.

The conditions of ions are specified by their velocity and their positions.

The ion velocity 𝒗 is resolved into components perpendicular (𝑣⊥) and

parallel (𝑣∥) to 𝑩 respectively. 𝑣⊥ represents the thermal motion of ions

and follows a shifted Maxwell distribution as discussed in [119]. 𝑣∥ is

settled to be the ion sound speed cs in (4.7) since the Chodura sheath

criterion should be satisfied. This criterion emphasizes that the parallel

component of the ion velocity should be equal to or greater than the ion

sound speed at the entrance of MPS [120]. The parameter 𝛾 in (4.7)

equals unity under the isothermal equilibrium condition [115].

𝑐𝑠

2 =𝑘(𝛾𝑇𝑒 + 𝑇𝑖)

𝑚𝑖

(4.7)

As for the positions, because ions experience gyration along the magnetic

field without energy change in the background plasma, placing emphasis

on the last gyration before ions enter the MPS can simplify the calculation.

Since 𝑩 is oblique towards the wall surface with an angle 𝛿 as depicted in

Fig 4.1, different starting points of the orbit of the last gyration can lead to

a variety of conditions when the ions enter the MPS as exemplified in Fig

4.2. When ions begin their trajectories with the same value of 𝑣⊥ and 𝑣∥,

Fig 4.2 Image for illustrating the effect

from stating points on the positions of ions

at the entrance of MPS which is locating at

the z=0 plane. The red spots indicate the

locations from which ions enter the MPS.

Green lines show the gyromotion orbits of

ions, projected on zx plane.


the difference in the positions of the starting points are eventually

represented by the variation of the phase angles, the angles between 𝒗(𝑣𝑥 , 𝑣𝑦 , 𝑣𝑧) and the normal of the MPS.

Since the variation of starting points can result in the change of the phase

angles, their influences on the motions of ions should be taken into

accounted. [121] proposed a method to describe the starting point

quantitatively by the distance between the starting point and the hitting

point on MPS of an ion trajectory. This distance, denoted by 𝑑, is the

product of 𝑣∥ and the travel time. The maximum of 𝑑 appears when an ion

could finish a whole gyro orbit before entering MPS. The solid green line

in Fig 4.2 sketches a whole gyro orbit and the maximum of 𝑑 is calculated

by the gyro frequency 𝜔𝑖 in Eq.(4.8). During the simulation in this thesis,

each ion begins its orbit with 𝑑 which is randomly chosen from [0, 𝑑𝑚𝑎𝑥]

together with another two random numbers in 𝑥 and 𝑦 respectively.

𝑑𝑚𝑎𝑥 = 𝑣∥2𝜋/𝜔𝑖 (4.8)

The solution of Eq.(4.4) has a simple form in the background plasma

without 𝑬. The coordinates used for calculating ion locus and velocities in

the background plasma are shown in Fig 4.3 with the black one fixed in

space and the blue one changing with each ion. The 𝒙 axis is parallel to 𝑩,

hence the time evolution of the ion position can be expressed as Eq.(4.9),

with an assumption that the starting point for an ion is located at (-𝑑, 0,0).

Results from Eq.(4.9) are transferred into the fixed coordinate through a

rotation matrix in Eq.(4.10) with two additional parameters 𝑓 and 𝑔

Fig 4.3 The coordinate for calculating the loci of ions in the background plasma. 𝒙`, in the

coordinate denoted by blue line, has the same direction with magnetic field. The black

coordinate is fixed in space while the blue one moves on the xy plane and the movement is

identified by two displacement numbers: 𝑓 and 𝑔 . Calculation of the time-depend ion

position is done in the blue coordinate and the results can be transferred into the fixed

coordinated through a rotation matrix.

4.2 Calculation of ion trajectory 43

which indicate the displacements in the xy plane between the coordinates

[122].

𝑥` = 𝑣∥𝑡 − 𝑑, 𝑦` = −𝑟𝑔 sin(𝜔𝑖𝑡) , 𝑧` = 𝑟𝑔(1 − cos(𝜔𝑖𝑡)) (4.9)

𝒓 = [𝒓`, 1][cos(𝛿) , 0, −𝑠𝑖𝑛(𝛿), 0,1,0; 𝑠𝑖𝑛(𝛿), 0, 𝑐𝑜𝑠(𝛿); 𝑓, 𝑔, 0] (4.10)

The boundary between the background plasma and the MPS is assumed

to be planar and located at 𝑧 = 0. Ion velocity and position at 𝑧 = 0 are

saved and used as the initial inputs for the calculation in MPS. For the

boundary between DS and MPS, two kind of models were tested, where

one assumed a planar boundary and the other described the boundary

with a shape carried over from the wall surface.

In sheath regions, due to the existence of an electric field, the solution for

Eq.(4.4) becomes more complicated, but fortunately it still can be

expressed in an analytical form with the assumption of constant 𝑬 and 𝑩

in each sheath. An analytical expression was obtained from the symbolic

calculation toolbox in MATLAB [123]. The black coordinate in Fig 4.3 was

applied in sheath regions and 𝑩 is resolved into three components, as

shown in Eq.(4.11). The same process is applied to the electric field but

the values of 𝜃 and 𝜙 are different. By using this method, the analytical

expression from MATLAB could be more flexible to handle cases with

different spatial distribution of 𝑩 and 𝑬.

Bx = 𝐵𝑠𝑖𝑛(𝜙) cos(𝜃) , 𝐵𝑦 = 𝐵𝑠𝑖𝑛(𝜙) sin(𝜃) , 𝐵𝑧 = 𝐵𝑐𝑜𝑠(𝜙) (4.11)

Through the solutions of Eq.(4.4) in the background plasma and the

sheaths, the time evolution of the ion trajectories can be deduced. During

this computation, the time step is another parameter that should be

considered carefully. A too large value may reduce the precision of

velocity and position, while a too small one can increase the time

consumption significantly. Therefore, time step should be a compromise

between the precision and the computation time. For example, the time

step in the calculation in DS is set to be 10−12 𝑠 since 𝑣𝑧 in DS has the

magnitude of 1010 𝜇𝑚/𝑠 if the electron temperature in the background

plasma is 7 eV . When computing the hitting position on a surface

structure from the topography measurement in chapter 3, which has a

space resolution around 1~2 μm in z direction, this time step could keep


the traveling distance between two steps smaller than the surface

resolution.

4.3 Computation for hitting points and data acquisition

The final step in the simulation is to compute the hitting potions at the

surface structures and gain useful information for understanding the

non-uniform distribution of deposition. When an ion impinges on the

surface, the hitting position and the velocity were recorded as raw data.

The hitting positions can be affected by variations of surface roughness,

plasma temperature 𝑇𝑒, particle density 𝑛𝑒, amplitude 𝐵 and direction 𝛿

of magnetic field etc. Therefore, several calculations were performed with

what-if scenarios i.e. only one of the above parameters was changed in

each calculation. In this case, the effect on hitting positions from each

parameter can be estimated individually. Data from [124] and [125] were

used as reference for deciding the actual value and possible variations for

those mentioned parameters.

Two kinds of surface data, as exemplified by Fig 4.4 , were used. One

came from the topography measurement for real samples as discussed in

section 3.3 and another was created artificially. The intention of using an

actual sample surface is to directly compare the modelling results with

the elemental distribution from μ-IBA as discussed in Paper II. On the

other hand, the artificial surfaces were applied for testing the influence on

hitting positions from various surface topographies. Those artificial

Fig 4.4 Surface data used in the simulation. The inset on the left shows the cross section of

an artificial sinusoidal surface which can be characterised by 𝑝𝑥 and 𝑝𝑧 . The surface

extends perpendicular to paper. The inset on the right gives a cross section for a sample

surface obtained from optical microscope.

4.3 Computation for hitting points and data acquisition 45

surface were generated by sinusoidal functions which were characterised

by amplitude 𝑝𝑧 and period 𝑝𝑥 in Paper III.

The comparison between the hitting positions and the surface structure

provides the primary information about where the incident ions will

accumulate before other physical reactions occur. Fig 4.5 gives an

example for this comparison with a sinusoidal surface and the

quantitative information is presented by the probability density function

(PDF) versus the locations in Paper II .

Except for the variation in those parameters, other physical reactions e.g.

reflection and sputtering could change the final position at which ions

come to rest. Although considering influences from those reactions is not

the major purpose in the modelling in this thesis, but additional

processing on raw data were applied for deriving impact angles respect to

surface normal. The local impact angle on every hitting position

(illustrated in Fig 4.4) can be derived from the velocity vector 𝒗 and the

normal 𝒏 of the patch at hitting position by Eq.(4.12). The local impact

angle is significant for the reflection of ions especially for cases in which

the ion energy is comparable to surface binding energy with a

glancing incidence angle [126]. Besides, ion-induced sputtering yield

depends on the incident angle as well with the lowest value with normal

incidence [127]. But only the simulations of artificially constructed

surfaces can provide the local impact angle in this thesis. Results for the

local impact angle are represented by PDF, as shown in Fig 4.6.

Additionally, angles between incident ions and magnetic field at the

hitting positions were extracted as well. In deposited layers on samples

𝑙𝑜𝑐𝑎𝑙 𝑖𝑚𝑝𝑎𝑐𝑡 𝑎𝑛𝑔𝑙𝑒 = 𝜋 − arcos (𝒗 ⋅ 𝒏

|𝒗||𝒏|) (4.12)

Fig 4.5 An example for the results of

hitting position of incident deuterium

ions comparing to a sinusoidal surface

with the amplitude and the period in

10 μm.


from JET, column-like structure enriched with deuterium and cone-like

structures which may mainly consist beryllium were observed to be

oriented towards a specific angle respecting to magnetic field [103, 128].

Those observations may be interpreted as that ions come to the PFC

surface from similar angles and the accumulation of them lead to a

column-like structure tilted to a specific angle. Therefore, it would be

worthwhile to test this hypothesis from simulation. Eq.(4.12) was used for

calculation but the surface normal 𝒏 should be replaced by vector which

could indicate the magnetic field direction and an example is shown in

Fig 4.7.

Fig 4.6 PDF for the local impact

angle for deuterium ions on a

sinusoidal surface with the

amplitude and the period in

10 μm . The ion temperature in

the background plasma is 7 eV.

Fig 4.7 Angle between incidence and magnetic field at the hitting positions for both

deuterium and beryllium. The sample came from Tile 0 in JET-ILW.

47

Chapter 5

Summary and Conclusions

As the final section, this chapter will summarise the work that has been

done in this thesis, together with major scientific conclusions and their

potential applications. Several papers have been finished based on the

works in this thesis. Overviews for those papers will be presented at the

end of this chapter.

5.1 Results from experiments and modelling

This thesis focuses on the influences from surface structures on the issues

of deposition and erosion in JET-ILW. For the deposition issue, this

thesis tries to measure and explain the microscopic distributions of Be

and D on the samples (Paper I-V). For the erosion issue, the emphasis is

placed on the marker tiles, which are designed for the erosion

measurement (Paper VI). The main experimental methods are μ-IBA,

optical microscope and SEM. Several calculations for the trajectories of

incident ions are applied for the deposition issue as well.

Paper IV , Paper V and Paper I discussed the distributions of Be and D

on two kinds of surface structures on PFCs in JET-ILW. One is the tile

surface topography which is carried over from the original tile surface or

generated during PWI. The corresponding experimental results from μ-

IBA are shown in Paper I and Paper V. Another kind of surface structure,

discussed in Paper IV, is the castellation structure which is produced

artificially to improve the thermo-mechanical properties.

On the tile surfaces, the distributions of the deposited Be and D show a

complicated pattern. Be distributes uniformly over the tile surface while

D accumulates on some depressed areas on the sample with a thick

deposition layer (thickness is around 30-50 μm [129]), However, on the

48 Chapter 5 Summary and Conclusions

sample with a thin deposited layer (the thickness is several microns [129]),

both Be and D stay on the depressed areas preferentially. Furthermore,

although Be and D appear to be non-uniform over the tile surface, their

distribution patterns are different from each other. The corresponding

details are discussed in Paper I and Paper V. Since the distribution of Be

and D relates to the topography on the tile surfaces, Paper II compares

the distribution patterns and the surface topography. A sample,

containing a thin deposited layer, was selected for measuring the surface

topography by optical microscope. The distribution patterns were

obtained by μ-IBA. Those results suggest that Be deposited at a lower

region than that of D. The trajectories of the incident ions and the

corresponding impact positions on the divertor sample surface were

calculated. The computed results show that the gyration of ions could

result in the non-uniform distributions of Be and D.

In order to get insight into the results in Paper II, the works in Paper III

applied an updated code to compute the trajectories and the impact

positions on different sinusoidal surfaces. Results from the modelling

suggest that a rough surface could generate the non-uniform distribution

even though the surface roughness is much smaller than the Larmor

radius of the incident ions. Increasing the width of sinusoidal surface

brings a higher probability for D and Be ions to arrive a lower position.

Paper III also tested the effect from the variations on the magnetic field

and the ion temperature. Under the same temperature, Be ions tend to

stay at a lower position than that of D ions. For D, a lower temperature

makes the ions move to a deeper position. Those two results imply that,

from the view point of particle motion, the incident ions with a lower

velocity attempt to ‘smooth’ the surface roughness.

The experiments and the computations on the topography of the tile

surfaces focus on those structures which range from ten to hundred micro

meters. While in the castellation structures, the width of the grooves and

the gaps is in the magnitude of a millimetre. The deposition pattern of D

on those structures also appears to be non-uniform. Samples from the

castellated limiter tiles in JET-ILW were measured by μ-IBA in Paper IV.

The spatial distribution suggests that D accumulated at entrance to gaps.

5.2 Summaries of papers 49

Paper VI discusses the erosion issue on the beryllium limiter marker tiles

in JET-ILW. Those specific tiles were designed for the ex-situ IBA to

measure the material erosion. However, the rough surfaces, generating by

PWIs, obscured the results from the broad beam IBA (beam spot size in

mm or cm). For the purpose to separate the influence from surface

roughness on IBA, Paper V proposed a possible method by analysing

microscopically flat regions. Based on this method, the works in Paper VI

tried to obtain the erosion data from limiter maker tiles by employing μ-

IBA and SEM. μ-IBA provides elemental maps for the lateral distributions

and the depth profiles from flat regions. Combining the results from μ-

IBA and images from SEM, one could estimate the erosion with less

effects from the surface roughness. Therefore, the combination of μ-IBA

and SEM can a potential method for measuring material erosion on a

rough sample.

5.2 Summaries of papers

Paper I: Microanalysis of deposited layers in the inner divertor of JET with ITER-like wall

The non-uniform distribution of the impurities and the trapped fuel

particles on PFCs remains an unsolved mystery which could affect the

selection of the fuel removal methods. Therefore, the works in this paper

carried out μ-IBA on several divertor samples from JET-ILW. It extended

the microanalysis to the high field gap closure (HFGC) tiles. Deuterium

and beryllium were found to accumulate on the depressed areas which

were either carried over from the fibres of the CFC substrate or were

generated during PWIs.

Paper II: The effect of gyration on the deposition of beryllium and deuterium at rough surface on the divertor tiles with ITER-like-wall in JET

The emphasis in this paper was placed on the non-uniform accumulation

of deuterium and beryllium on depressed areas which were carried over

from the original tile surface structure. The surface topography on the

selected divertor samples were measured quantitatively through optical

microscope by the focus stacking method. The surface topography was

compared with the elemental distribution maps from μ-IBA. The

modelling for the ions motion at the sheath regions was done for


estimating the effects from the first step in deposition process, i.e. the

imping of incident ions on tile surface. Gyration of ions could bring non-

uniform distribution of the impact positions on the tile surfaces. This can

qualitatively explain part of the experimental results.

Paper III: Modelling of effect from rough surface on deuterium and beryllium deposition on divertor target

The surface on the actual PFC tiles contains a variety of structures. The

motions of ions in the edge plasma could be influenced not just by those

different surface structures, but also can be affected by the variations in

magnetic field or other parameters. Assessments of the effects from each

of those factors are necessary for understanding the mechanisms behind

the non-uniform deposition patterns. Some computations for the gyration

of ions and the corresponding impact positions on sinusoidal surfaces

were performed in this paper. Computed results suggest that increase the

width of sinusoidal surface brings a higher probability for D and Be ions

to arrive a lower position. And the variations on ion species and

temperature were summarised as the difference in ion velocity. Slower (or

cooler) ions tend to stay at lower part and may ‘smooth’ the rough surface.

Paper IV: Fuel inventory and deposition in castellated structures in JET-ILW

Castellations(gap) are essential for the PFCs to endure high thermal

stresses during the plasma operations. Re-deposition in the castellations

is a critical issue for fuel inventory in tokamak since the surface area of

castellation is greater than that of PFCs. This work focused on the

castellated beryllium tiles from JET-ILW. μ-IBA, IBA, and modelling etc.

were applied for analysing the fuel deposition in gaps and grooves in the

castellations. Experimental results suggest that deuterium accumulates at

the entrance of the gaps with a steep decay length. The amount of

deuterium deposition increased with the width of the gaps which implied

that narrow gaps in the castellated PFCs would be necessary for future

devices.

5.2 Summaries of papers 51

Paper V: Deep deuterium retention and Be/W mixing at tungsten coated surfaces in the JET divertor

μ-IBA and SEM were applied on samples from a poloidal set of divertor

tiles in JET-ILW. On those samples, D trapping was found non-uniformly

in a scale of 10-100 μm. Combination of μ-IBA and SEM made it possible

to extract spectra from microscopically flat regions on the sample

surfaces. Analysing for those spectra can provide more accurate

information about elemental concentration, with less effect from the

rough surfaces.

Paper VI: Micro ion beam analysis for the erosion of beryllium marker tiles in a tokamak limiter

PWIs on the limiter tiles results in a rough surface with several pits and

craters. The exist of those structures can obscure the results of material

erosion from EBS, due to an ambiguity between roughness and elemental

depth profile. The work in this paper applied μ-IBA (μ-EBS and μ-PIXE)

to address this issue and proposed a method by comparing the lateral

distribution map of an interesting element with the images from SEM.

With this method, one could separate the influence from the rough

surface and obtain a clear interpretation for IBA results.

53

Acknowledgements

Working and living in a country far away from home for more than four

years is not an easy task even though this country is so beautiful. But

fortunately, I met a lot of kind persons who support both my work and my

life in Stockholm.

I would like to show my gratitude to my supervisors Henric Bergsåker

and Marek Rubel firstly, for all their guidance and suggestions during the

past four years. Then I would like to heartily thank Per Petersson for his

excellent helps and patience for both my work and my endless questions.

Without the help from all those three people, I may not be able to finish

my project. Besides the works for the doctoral project, courses are

another essential part in the last four years. Therefore, I would like to

express my gratitude to Per Brunsell, Thomas Jonsson, and Jan Scheffel

for their supports and comments for my courses, especially to Jan for

reviewing my thesis. Special thanks to Jonas Åström at Uppsala

University for his great help in the experiments in the Tandem laboratory.

I also received a generous support for the CLSM experiment from

Hjalmar Brismar at AlbaNova Laser Laboratory KTH. During work and

studying, I got great support from Ann Marklund, Visén Mikael and Silvia

Cardenas for paperwork. Thank you very much for their helps, patience

and especially their smiles which make me feel warm.

I really enjoyed the lunch time and the fika time with my colleagues. I

experienced a wonderful world through the conversations with Armin

Weckmann, Petter Ström, Alvaro Garcia Carrasco and Estera Stefániková.

Thank you very much for all those nice talks. I want to express my thanks

to Jesper Freiberg for sharing so many knowledges about foods, cultures

and other interesting things about Sweden which make me know more

about this country. I would like to thank my other colleagues for sharing a

wonderful time in this department：Håkan Ferm, Lorentzo Frassinetti,

Pablo Vallejos Olivares, Kristoffer Lindvall, Sunwoo Moon and Erik Saad.

Last but not least, I would like to show my greatest appreciations to all

my other friends: Shuai Shi, Shuang He, Mousong Wu, Jie Fu, Jie Hao,

Chao Zheng, Xiaojing Wang, Yansong Ren, and Han Zhang for sharing a

nice time here in Sweden. Best wishes to all of you.

55

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