Need to correct my english, more technicel and professional level

ERO modelling of tungsten erosion in the linear plasma device PSI-2

A.A. Eksaeva1, E.D. Marenkov1, D. Borodin2, A. Kreter2, M. Reinhart2, A. Kirschner2, J. Romazanov2, S.

Brezinsek2, K. Nordlund1,3

1

2

National Research Nuclear University MEPhI, 31, Kashirskoe sh., 115409, Moscow, Russia

Forschungszentrum Jlich GmbH, Institut fr Energie- und Klimaforschung, 52425 Jlich, Germany

3

Department of Physics, University of Helsinki, FI-00560 Helsinki, Finland

Abstract

Series of experiments on tungsten (W) erosion and transport in Argon (Ar) plasma were recently

conducted at PSI-2 linear plasma facility. W erosion was measured by three independent methods:

spectroscopy observations, mass loss measurements and quartz micro-balance (QMB) deposition

diagnostic. Consistent set of data produced in these experiments was interpreted using the ERO code

simulations, which have reproduced all the main trends observed. Parameters of the physical model

used in the code (energy, angular distributions of sputtered particles, etc.) are discussed. The influence

of WI metastable (MS) states population dynamics on spectroscopy measurements is shown;

characteristic evolution time for the system of MS levels is estimated. The resulting physical sputtering

data for W are compared with the simulated data obtained in the binary collision approximation (BCA)

approach (SDTrimSP code), main discrepancies are discussed.

1. Introduction

Plasma-surface interaction (PSI) determines the duty cycle of ITER to a large extent. Physical erosion

limits the lifetime of plasma-facing components (PFC) and influences the retention of tritium due to the

co-deposition. Tungsten (W) is of particular interest because it was chosen as the main material for the

divertor area of ITER due to its high melting temperatures, low sputtering yield and small tritium

retention [1]. Linear devices such as PISCES [2], PILOT-PSI [3] and PSI-2 [4, 5] have a number of

advantages for investigating specific problems of PSI [6]: continuous operation, small scale, relatively

simple construction, and facilitated control over the experimental parameters. Plasma parameters in

these devices can be relevant to boundary and divertor areas of tokamaks.

In PSI studies numerical simulation is a key for understanding of all variety or processes taking place in

the experiment and their resulting overplay. 3D local impurity transport and PSI code ERO is a tool for

predictive modelling of plasma impurities transport in ITER [7]. It has already been applied for modelling

of experiments at linear plasma devices, such as PISCES-B [8], Pilot-PSI [9] and PSI-2 [10].

Several dedicated PSI experiments were recently carried out at the PSI-2 installation in which the

erosion of W target was characterized by passive spectroscopy, weight loss with spatial resolution and

quartz micro balance (QMB) deposition sensor measurements. Together these measurements are

capable of giving a full picture of erosion and transport processes in linear plasmas, including relation

between net erosion (QMB, weight loss) and gross erosion (spectroscopy).

The focus of this work is ERO application for the interpretation of the above PSI-2 experiments.

Comparison of numerical modelling results with the experimental data provides opportunity to validate

and improve the physical model and the underlying data used in the code allowing extrapolation of the

obtained knowledge for further experiments and predictive modelling tasks. The angular and energy

distributions of sputtered particles in a parametric form were introduced into the code, their

dependence on experimental parameters and influence on diagnostics results are discussed. Essential

role of WI metastable states population dynamics for spectroscopy measurements is shown and

characteristic evolution time of such levels system is fitted by matching of ERO simulations with the

experiment. Physical erosion yields were extracted from the experiment using the ERO-based

interpretation which allows taking into account the role of W redeposition including prompt effects.

Resulting yields were compared with the data obtained with the SDTrimSP calculations approximation

formula [11].

2. W erosion experiments at PSI-2

The PSI-2 linear plasma generator produces a plasma column confined by an axial magnetic field.

Absolute value of the magnetic field B changes significantly along the main axis; however it can be easily

determined from the known coils configuration and current in those.

In dedicated experiments on W erosion conducted at PSI-2 a W target was irradiated with Ar plasma (

12

-3

Te 2 4 eV , ne 10 cm ). The schematic experiment setup with main experimental trends observed

is shown in Fig.1.

Plasma parameters (electron density and temperature radial profiles) were measured by means of a

radially movable Langmuir probe which was positioned at the 310 mm (along the installation axis) from

the target surface [4]. One can see here (Fig. 2) that both ne and Te profiles have clear minima at the

plasma column center. Such hollow plasma configuration at PSI-2 is due to the cylindrical cathode in the

plasma source.

Several parameter scans were performed to study the dependence of W erosion on plasma parameters

and ions impact energy. Overall 3 independent measurements spectroscopy profiles in two different

directions near the target surface (up to 60 mm from it), QMB signal and weight loss – were performed

over the three experiments at PSI-2. These experiments are summarized in the Table 1.

The W target was positioned on the installation axis, perpendicularly to the magnetic field lines. It had

rectangular form 80 x 100 mm2. Due to negative bias voltage Ub varying from -50 V to -150 V, the target

was subjected to irradiation with plasma ions of corresponding energies ( 40 – 140 eV). Post-mortem

weight loss measurements with spatial resolution were obtained using 10 5*5 mm2 samples imbedded

into the target.

WI light emission intensity profiles along the installation axis IWI ( z ) and perpendicularly to it IWI (r ) in a

60 mm area from the surface were measured by the spectrometer for different discharge parameters

and incident ions energies. Energies of plasma ions reaching the target were controlled with the bias

voltage applied to it. Discharge power (current in the plasma source Idisch = 50 A, 100 A, 150 A

determining low, medium’ and high discharge power respectively) and target bias voltage ( U b ) varied

as specified in Table 1. The main difference between discharge power cases is the ne absolute value and

profiles shape for lower discharge power cases it has more pronounced minima on the installation

axis. There is also much higher concentration of Ar2+ ions in high discharge plasma than in low one.

Ar2+ concentration variations have already been detected in previous experiments at PSI-2 [12]. Some

relevant data regarding respective concentration of double-ionized atoms were collected using in-situ

mass-spectrometer of magnetized plasmas (see Table 2).

The WI light emission intensity ( = 400.9 nm) as a function of the distance from the target surface

IWI ( z ) was obtained for each set of exposure parameters in experiments at PSI-2 (see Table 1,

experiment #1). Spectroscopy profiles IWI (r ) perpendicular to the installation axis at different distances

from the target surface were obtained during long irradiation with fixed parameters (experiments #2

and #3 in the Table 1). These profiles allowed reconstruction of the 2D side view pictures of the

sputtered W emission characterizing its local transport.

Quartz Microbalance (QMB) deposition sensor was initially positioned at 345 mm from the target

surface along the z-axis (later on the target axial position scan was performed) and 151 mm from the

installation axis in radial direction. It was measuring amount of sputtered W reaching it.

QMB signal as a function of the target bias voltage RQMB (U b ) was measured for the same experimental

cases in order to understand the influence of discharge power on sputtering intensity. For the identical

Ubias values QMB signal increased with the discharge power. This is not only due to the general flux

increase but also due to the increase of Ar2+ ions percentage in the plasma of higher discharge currents.

These ions bombard the target with a doubled energy causing sputtering yields increase and, eventually

higher QMB signal. In one of experiments the target was also moved along the facility axis in order to

test the dependence of deposition rate at QMB sensor on its axial distance from the target, RQMB(L).

Table 1. W erosion experiments at the PSI-2 facility

#

Discharge

power

1

Low

Medium

High

2

High

Ei

ne

Te

40 150 eV

(11 Ub values

for each

plasma

power value)

140 eV

0.4 – 2.5

x 1012 cm-3

3.0 – 5.0 eV

2.0 – 2.5

x 1012 cm-3

3.2 eV

3

Low

140 eV

0.4 – 0.5

x 1012 cm-3

4.0 – 4.5 eV

What was measured

For each Ub and each plasma

power:

WI intensity profiles along z

axis ( = 4009 )

QMB sensor signal

Plasma parameters (ne, Te)

2D sputtering patterns

Mass loss

2D sputtering patterns

QMB signal vs. distance

between the target and the

QMB

Mass loss

Table 2. Ar2+ relative concentration measurements at PSI-2 (at the plasma fluxs maximum) [12]

Idisch, A

Pressure, mbar

Te, eV

ne, cm-3

Ar2+/Ar+

50

5,6 x 10-4

2,00

4,15 x 1011

0,015

100

7,2 x 10-4

2,76

1,52 x 1012

0,14

150

8,1 x 10-4

2,90

2,90 x 1012

0,39

3. ERO modelling

The 3D Monte-Carlo code ERO is a tool for numerical simulation of impurity transport in plasma. It is

based on test particle approximation: impurity species are tracked in a given background plasma, which

is not influenced by the impurities. The background plasma parameters in each space point (ne, Te, B,

etc.) are taken as an input. It is also possible to use background plasma simulated with other computer

codes (e.g. B2-EIRENE, Edge2D), especially in cases of complex geometries like ITER. Detailed description

of the code and its applications for different cases and geometries can be found elsewhere [13].

Impurity transport in plasma is calculated using the Monte-Carlo approach. On each integration step, for

each one of possible processes (ionization, recombination, elastic collisions with plasma particles, etc.) a

random number is generated. This random value is then compared with respective effective rate of

considered process in order to decide if the process will occur.

Trajectories of impurity particles are calculated taking into account electric and magnetic fields of

installation, perpendicular diffusion and friction force with the plasma flux. In order to take into account

friction between the impurity and plasma ions, for each tracked particle ERO solves the Fokker-Planck

equation derived from the Boltzmann equation for one particle distribution function case [13]. Ions drift

in magnetic and electric fields is calculated using the Boris method [14].

In ERO for linear devices Cartesian coordinates are used, and z axis is assumed to coincide with the

installation axis. All simulated volume is divided into 3D rectangular space cells. Thus, by tracking

impurity particles it is possible to calculate their density at any point and then estimate light emission

using photon emission coefficients – PEC [15].

Impurity particles start from the target surface, which is divided into surface cells, as neutrals. Incident

plasma flux on each cell is calculated from known ne and Te. The sputtering yield is calculated according

to approximation formulas derived by W.Eckstein [11].

Computer code ERO has already been applied for modelling of experiments at linear plasma devices

(e.g. PISCES-B) [8]. However, in order to use it for numerical simulation of the above PSI-2 experiments

some new features were implemented. These are exact geometry of the target and observation system,

experimental plasma parameters (ne, Te), PSI-2 relevant electric and magnetic field configurations. Some

new physical effects as well as diagnostic mechanisms specific for PSI-2 installation operation were

implemented. The diagnostic features are spectroscopy measurements (integration) along user-defined

direction and QMB sensor functionality. Physical model modifications included possibility to set

different energy and angular distributions of sputtered particles as a function of incident ions energies

and Ar2+ concentration alterations with respect to plasma discharge power ( Idisch) based on the data

from [12]. Metastables (MS) tracking for BeI has already been introduced in ERO [8] and was adapted

for WI emission in this work.

4. Results and discussion

In order to conduct numerical modelling of described experiments some parameters of the physical

model used in ERO needed to be verified.

The two main uncertainties for these simulations are energy and angular distributions of sputtered

particles. Strong influence of these factors is shown and discussed in our previous work [10]. For low

energies of incident ions ( Ei 50 150 eV ) both energy and angular distributions have quite specific

shapes which are sensitive for incident energies variations. Ionization and recombination cross-section

values used in the code also bring a significant uncertainty here, because for the temperature interval

Te=2-4 eV they vary strongly between different data sources. Finally, as will be shown later, accounting

for WI metastables plays a decisive role for spectroscopy measurements. Characteristic relaxation time

of these levels system for WI are not available for now, thus they need to be estimated matching ERO

simulations with the experiment.

By varying these parameters within reasonable limits one can understand their influence on the final

result, extract some relevant for erosion studies information and finally find a set of parameters giving

the best agreement with all experimental data simultaneously.

There are overall 6 experimental trends from the PSI-2 experiments interesting for ERO modelling and

benchmarking:

Mlost(R) – weight loss measurements for two power cases: low and high discharge power.

RQMB ( L) – dependence of QMB signal on the distance between the target and the sensor;

RQMB (U b ) – dependence of QMB signal on the bias voltage Ub applied to the target for different

discharge power values;

IWI ( z ) dependence of WI line emission intensity ( = 400.9 nm) on the distance from the

target surface;

IWI (r ) vertical profiles of WI line emission intensity at different distances from the target

surface (2D sputtering patterns if combined together);

All these functions were simulated in ERO for various sets of parameters and assumptions. Results of

these simulations, underlying assumptions and their discussion are presented in this part.

4.1 Angular distribution of sputtered particles

For low incident ions energies angular distribution of sputtered particles takes so-called butterfly

form, acquiring some direction of maximum sputtering [16]. The exact form of this butterfly as well as

angle of maximum sputtering vary between different incident energies and types of irradiated material.

In a very general case angular distributions of sputtered atoms for this case can be expressed with an

approximation formula [17]:

f ( )

1

( A cos n ( ) B cos m ( ))

C

(1)

Here A, B, m, n coefficients, different for various elements and irradiation parameters; C is a

normalization factor, individual for every set of coefficients.

It is known from experimental data that under Ar+ ions bombardment with different (however, low: 50200 eV) energies, angular distribution of sputtered W atoms changes its shape [18]. Decrease of

particles incident energies leads to increase of maximum sputtering direction angle with respect to the

normal.

Experimental angular distributions from [18] were approximated with (1) in order to use them in ERO. In

the PSI-2 experiment the bias voltage applied to the target (and, thus, energy of incident ions Ei) varied

from 50 V to 150 V. Distributions for three basic energy cases were implemented in ERO: 50, 100 and

150 eV. Their exact formulas were determined by means of coefficients linear interpolation based on

several observed energy cases shown in [18].

0.20

0.90

f ( ) 0.95(1.2 cos ( ) 1.1cos ( )) U b 50V

1.05

2.05

f ( ) 0.28(1.20 cos ( ) 1.05cos ( )) U b 100V

f ( ) 0.34(1.2 cos1.90 ( ) 1.0 cos 3.20 ( )) U b 150V

(2)

MD calculations using the PARCAS code [19] were also performed and approximated with (1):

f ( ) 0.25(1.2cos1.80 ( ) 1.80cos 4.00 ( ))

(3)

All approximated distributions are shown in fig. 3. Angular distribution of sputtered particles determines

decay rate of WI intensity along the z axis to a large extent. All approximated distributions are more or

less similar to each other, however we chose the MD-simulated one for all ERO calculations because it

has shown the best agreement with the experiment.

4.2 Energy distribution of sputtered particles

The Thompson-Sigmund energy distribution is used for sputtered particles in ERO [20]:

fE (E)

( 1) EEb 1

( E Eb ) 1

(4)

Here is the parameter of the distributions and Eb is the surface binding energy of the sputtered

material (Eb = 11.4 eV for W [21]). It is known from the literature [22] that for low energies of incident

ions the peak of the distribution narrows and moves closer to zero. It was discussed in our previous

work [10] that this effect can be reached with increase of the parameter only. Thus, for different Ub

applied to the target energy distribution of sputtered particles can be approximated with Thompson

distribution using parameter > 2.

However, value affects the simulation result only slightly in comparison with angular distribution.

Nevertheless, parameter alteration as a function of Ei was implemented in ERO. This dependence was

extracted from the matching of ERO simulations with the experimental data.

4.3 Ionization/recombination coefficients

Existing data regarding ionization and recombination coefficients are not precise, and dramatically vary

between different information sources. It is evident from physical sense and analytical estimations that

these coefficients values, ionization particularly, play a crucial role in the appearance of IWI ( z ) neutral

tungsten radiation intensity dependence on the distance from the target surface. ADAS ionization

coefficients were used for ERO simulations; recombination coefficients were obtained from the FLYCK

code calculations [23].

4.4 W long living energy levels influence

All experimentally obtained spectroscopy profiles along the installation axis have a rapid growth in a

near-surface target region (up to 5 mm) before the characteristic recession connected with WI

ionization starts (see Fig. 1), which results in a maximum at l 5 mm from the target surface. The most

probable explanation of this shape is that sputtered particles need some time to become excited and

eventually relax and emit light at = 400.9 nm which is then detected with the spectrometer.

However, the transition corresponding to = 400.9 nm is extremely fast (trelax 1×10-8 s), as well as all

other permitted transitions between levels with a spin number of 7 (septets system). Thus, even for long

excitation-relaxation cascades within this system the time before light emission is quite short. The

delay effect ensues from the existence of some forbidden and therefore slow transitions from the

system of levels with spin number of 5 (quintets system). This slow evolution of systems with respect to

each other is responsible for the intensity growth delay resulting in the maximum at 5 mm from the

target surface.

Tungsten is an extremely complex element (approximately 400 energy levels and more than 3000

possible transitions only for the neutral atom). System of these transitions can be very tangled and

produce large cascades of excitation-relaxation processes. Such systems can be calculated precisely only

using full collisional-radiative model, which is very time demanding. However, for our calculations, all

this physics can be minimized by introducing a model with one ground, one excited and one metastable

(MS) states. The transition from the excited to the ground state corresponds to the light emission at =

400.9 nm and MS state represents a quintets system.

This mechanism of accounting for metastable states has already been implemented in ERO for BeI

[24]. However, implementing it for W implies existence of some specific data for this element

(characteristic lifetime of spontaneous relaxation from the MS state, etc.) which are not available for

now. In this case it is convenient to estimate, for example, spontaneous relaxation coefficients value

using comparison between ERO modelling and experimental data.

Metastable characteristic evolution time leading to the intensity maximum at 5 mm from the surface

can be obtained from simple analytical estimations. These estimations come out from solving system of

equations on levels population dynamics for a system with one ground (n0(x)), one ionized and one

excited (MS, n1(x)) states:

dn0

v dx V01 Sion n0 V10 A10 n1

v dn1 V n V A n

01 0

10

10

1

dx

(5)

Here v initial velocity of sputtered neutrals, V01 ne v 01 and V10 ne v 10 are electron impact

excitation and relaxation coefficients correspondingly (s-1), Sion ne v ion – electron impact

ionization coefficient (s-1), A10 spontaneous relaxation coefficient (s-1) from the MS state. According to

it:

xmax

1,2

1

ln 1

2 1 2

V01 Sion V10 A10 1

2v

2v

V01 Sion V10 A10

(6)

2

4Sion V10 A10

These estimations give the value for the xmax = 5 mm for the MS level characteristic relaxation time trelax

= 1 x 10-5 s. This value was used as a reference for further trelax ERO fitting.

4.5 Simulation results

First of all, mass loss measurements were simulated in ERO (see Fig. 4). Simulation results are in a good

qualitative agreement with the experiment; quantitatively, however, weight loss values obtained from

the experiment for low discharge power turned out to generally be lower than those calculated with

ERO (sputtering yields – Eckstein fitting formula for SDTrimSP calculations).

Radial distribution of SDTrimSP yields ratio to the experimental ones is presented in fig. 5. They are in a

quantitative agreement within 50% for high discharge power; for low power case, however, there is

a disagreement by the factor 1.0 – 2.3. These discrepancies are mostly associated with the flux

alterations between the target and the Langmuir probe due to an intensive recombination there. In ERO

calculations we have already taken into account overall flux decrease to the target by a factor of 1.5 for

high discharge power and by a factor of 2.1 for low power case. However, not only the absolute

value of the flux changes, but also does its shape. Thus, it can be quite difficult to predict the incident

flux radial profile without specific measurements. Finally, a lot of uncertainties are caused by large Te

measurement error (Te = 2 – 4 eV, Te 1.5 eV).

All these effects are much less prominent in experiments on W irradiation with Neon (Ne) plasmas. A

series of such experiments were recently conducted at PSI-2. First mass loss measurements show a good

quantitative agreement with the SDTrimSP predicted yields at least within 50% (see fig. 6). Te

measurement error and recombination do not play such crucial role here; however we cannot exclude

them completely. Ne2+ ions influence is much less pronounced due to a higher ionization energy of Ne

(21.5 eV) in comparison with Ar (15.8 eV).

For Ar experiments one should also note strong redeposition of sputtered W mainly caused by friction

force experienced by the charged particle during its movement through the plasma (see [13]). This

effect was not measured in the experiment, however it was estimated using ERO calculations. ERO

shows that there is 25% of redeposited material for low discharge power and 50 % of it for high

power case (effect is already taken into account in fig. 4-5).

Finally, it is important to note that all numerically calculated rates (ionization, recombination, etc.) are

obtained with the assumption of Maxwellian electron velocity distribution in plasma, which is most

probably not the case for the PSI-2 facility. Due to low Te value and large distance between the target

and the plasma source serious deviations from Maxwellian distribution in plasma are expected. It

motivates specific experiments at PSI-2 devoted to electron velocity distribution investigations.

Experimental 2D side-view patterns formed by putting together radial intensity profiles at different

distances from the target were reproduced in ERO code for low and high discharge power cases (see

Fig.7). ERO reproduces well alterations of emission intensity distribution with plasma parameters.

Quantitatively simulations results are in a good agreement with the experiment for low discharge

power; however, there is a disagreement by a factor of 5.8 for high power case. Photon emission

coefficients (PECs) used for intensity calculations in ERO are very sensitive for Te alterations, as well as

for electron velocity distribution. Therefore, final quantitative intensity result is a complex interplay of

input atomic and ionization data combined with uncertain flux alterations between discharge power

cases. Thus, one can expect a large error here, which can be diminished by choosing more optimal

experimental parameters (e.g. higher Te).

Emission intensity profiles along the installation axis can be easily extracted in ERO by picking out a line

in an appropriate direction (marked with a black line, fig.7). In experiment these profiles were collected

for every set of exposure parameters (Ub and discharge power). As was previously shown, intensity

maximum near the target surface is related to the presence of WI metastable energy levels. Subsequent

intensity decline for z > 5mm is regulated by ionization and recombination processes, while the

maximum position depends mainly on characteristic relaxation time trelax of WI metastables. Simulation

results in comparison with experimental ones are shown in Fig. 8. To simplify the visual perception only

several selected profiles are shown. Physical model validation through comparison with the experiment

leads to characteristic metastable states relaxation time value trelax = 1.5 x 10-5.

QMB signal dependence (see Fig. 9) on the QMB-target axial interposition RQMB ( L) has a quite

predictable form: the QMB signal comes to zero for both very large and very small distances and hence

has a maximum at some point. Rapid decrease at small distances RQMB ( L) represents the obvious

geometrical influence: due to a radially shifted position of the QMB sensor only particles starting under

very large angle with respect to the normal are capable of reaching it. The maximum position is directly

linked with the shape of angular distribution of sputtered particles. A lot of particles are neutrals on

such distances (z 10 cm), so QMB sensor signal depends on direction of maximum sputtering. Shape of

the signal recession for larger distances represents sputtered particles ionization influence: ionized

particles should reach QMB seldom because of trapping in the magnetic field co-directional with the

installation axis. This effect however is fogged here because this experimental trend was obtained for

the low discharge power case; therefore, experimental results are in a good agreement even with

analytical estimations based on geometry factors only:

a /2 b /2

RQMB ( z )

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a /2 b /2

S QMB ( x, y, z )

2

x x y y

S QMB ( x, y, z ) rQMB

2

QMB

QMB

2

zQMB 2

Y F ( x, y ) dx dy

zQMB

2

x x y y

2

QMB

QMB

2

(7)

zQMB 2

Where xQMB, yQMB, zQMB position of the sensor (coordinates origin is at the center of the target), a,b

target sizes along x and y axis, Y sputtering yield and F(x,y) – plasma flux in a certain target point. ERO

simulation results are in a good qualitative and quantitative (within 50%) agreement with the

experiment.

QMB signal dependence on Ub for different discharge power values RQMB (U b ) can be very informative

regarding Ar2+ concentration influence. Ar2+ percentage increases with Idisch, as well as the plasma flux to

the target, thats why for identical Ub values QMB signal is larger for higher discharge power. Simulation

results in comparison with the experiment are shown in Fig. 10. One can see that ERO represents rapid

growth of QMB signal with Ub and overall signal increase with the discharge power. For high discharge

power, however, ERO shows less increase with respect to the low case than the experiment. This is

most probably associated with excessive W ionization during its transport through the plasma in ERO.

Such uncertainties with ionization rates can be avoided in experiments with higher Te (e.g. Ne

experiments, discussed before).

5. Conclusion

Series of recently conducted experiments on W erosion and transport at PSI-2 installation were

simulated with the 3D Monte-Carlo code ERO. Some modifications of ERO physical model were

performed for this modelling (PSI-2 relevant geometry and observation system, energy, angular

distributions, WI metastables, Ar2+ ions). These simulations combined with experimental results can

provide one with a consistent set of data sufficient for understanding of complicated interplay of

processes taking place there.

ERO simulations reproduce well all experimental trends. It was demonstrated that WI metastable states

determine the shape of spectroscopy intensity profiles to a large extent. Characteristic relaxation time

of WI metastable states was fitted as trelax 1.5 x 10-5 s. The angular distribution of sputtered W atoms

was determined by comparison of the modeled deposition on the QMB with the according experimental

data and confirmed by molecular dynamics (MD) calculations. Erosion data were extracted from

experimental trends. Decisive role of impurity redeposition for weight loss measurements was shown

with ERO simulations (up to 50% of redeposited material).

In general, our interpretation is consistent with the SDTrimSP simulations (quantitative agreement at

least within 50% for all discussed functions). Remaining discrepancies are associated with uncertainties

in atomic data caused by unclear form of electron velocity distribution in plasma, flux alterations

between the target and the Langmuir probe and high Te measurement error. Thus, further experiments

with higher Te are demanded in order to wipe out discussed issues and concentrate on further erosion

investigations.

6. Acknowledgments

The authors acknowledge I. Sorokin for relevant data on Ar2+ concentration in the plasma of the PSI-2

facility.

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[16] Betz, Gerhard, and Karl Wien. “Energy and angular distributions of sputtered particles.”

International Journal of Mass Spectrometry and Ion Processes 140.1 (1994): 1-110.

[17] Martynenko, Y. V., Rogov, A., and Shul’ga, V. Angular distribution of atoms during the magnetron

sputtering of polycrystalline targets. Technical Physics 57, 4 (2012), 439444.

[18] D. Nishijima, et al. Journal of Nuclear Materials, Volume 415, Issue 1, Pages S96-S99 (2011).

[19] K. Nordlund, 2006, PARCAS computer code. The main principles of the molecular dynamics

algorithms are presented in [26, 27]. The adaptive time step and electronic stopping algorithms are the

same as in [25].

[20] A. Goehlich, et al. Determination of angle resolved velocity distributions of sputtered tungsten

atoms. Journal of Nuclear Materials, 266-269, (1999) 501-506.

[21] R. Behrisch, W. Eckstein, Sputtering by Particle Bombardment, Springer, Topics In Applied Physics,

pp. 110.

[22] R. Brizzolara, et al. Energy distributions of neutral atoms sputtered by very low energy heavy ions.

Nuclear Instruments and Methods in Physics Research, B35 (1988), 36-42

[23] H.K. Chung, M.H. Chen, W.L. Morgan, Y. Ralchenko and R.W. Lee, FLYCHK: Generalized population

kinetics and spectral model for rapid spectroscopic analysis for all elements. High Energy Density

Physics, Volume 1, Issue 1, Pages 3-12 (2005).

[24] D Borodin et al. Modeling of Impurity Transport in the Linear Plasma Devices PISCES-B and Pilot-PSI

Using the Monte-Carlo Code ERO. Contrib. Plasma Phys. 50, No. 3-5, 432438 (2010)

[25] K. Nordlund, Comput. Mater. Sci. 3 (1995).

[26] C. S. Madi, H. B. George, M. J. Aziz, J. Phys. Condens. Matter 21, 224010 (2009).

[27] K. Nordlund, M. Ghaly, R. S. Averback, M. Caturla, T. Diaz de la Rubia, and J. Tarus, Phys. Rev. B 57,

7556 (1998).

Figures

a)

b)

Fig.1. Scheme of the experimental set up:

a) scheme of the installation with main diagnostics marked;

b) scheme of the experiment with marked distances

Fig.2. Radial distribution of plasma parameters (Te, ne) in PSI-2 facility

Fig.3. Angular distributions of sputtered W particles under Ar irradiation, approximated with (1). Dashed

lines approximation of experimentally obtained distributions from [18]. Solid line approximation of

PARCAS code MD simulations [19].

a)

b)

Fig.4. Weight loss values obtained from the experiment and with ERO simulations.

a) Low discharge power case, Ub = 150 V; b) High discharge power case, Ub = 150 V.

a)

b)

Fig.5. Radial distribution or ratio between SDTrimSp-calculated and experimentally obtained sputtering

yields for Ar -> W experiments. Impurities redeposition is taken into account.

a) Low discharge power case, Ub = 150 V; b) High discharge power case, Ub = 150 V.

a)

b)

Fig.6. Radial distribution or ratio between SDTrimSp-calculated and experimentally obtained sputtering

yields for Ne -> W experiments.

a) Low discharge power case, Ub = 165 V; b) High discharge power case, Ub = 165 V.

a)

b)

Fig.7. 2D sputtering patterns obtained in the experiment with the spectrometer and calculated with

ERO. Black line direction of axial intensity profiles extraction.

a) Low discharge power case, Ub = 150 V; b) High discharge power case, Ub = 150 V.

Fig.8. Axial WI ( = 400.9 nm) intensity profiles (normalized) experiment and ERO simulations. Low

discharge power, Ub = 50-150 V.

Fig.9. QMB rate as a function of the distance between the sensor and the target (experiment, ERO

simulation, analytical estimations based on geometry factors only)

Fig.10. QMB rate as a function of bias voltage applied to the target (Ub) and discharge power

(experiment and ERO simulations)

Introduction:

The Plasma-surface interaction (PSI) plays a crucial role in the operation of ITER, which is an experimental fusion reactor. The lifetime of the plasma-facing components and the retention of tritium is determined by physical erosion, making tungsten (W) of particular interest due to its high melting temperature, low sputtering yield, and small tritium retention. Linear plasma devices offer advantages for investigating specific PSI problems due to their continuous operation, relatively simple construction, and facilitated control over experimental parameters. Numerical simulation is a key tool for understanding the various processes taking place in PSI experiments and their resulting interactions.

Description:

The study presents a series of experiments on tungsten erosion and transport in Argon plasma conducted at PSI-2 linear plasma facility. The team used three independent methods to measure the tungsten erosion, including spectroscopy observations, mass loss measurements, and quartz micro-balance deposition diagnostic. The consistent data generated in these experiments was interpreted using the ERO code simulations that reproduced all the observed trends, which are discussed in detail regarding their physical model parameters, energy, and angular distributions of sputtered particles. The influence of WI metastable states population dynamics on spectroscopy measurements is presented and the characteristic evolution time for the system of MS levels is estimated. The resulting physical sputtering data for tungsten is compared with the simulated data obtained in the binary collision approximation (BCA) approach (SDTrimSP code), and the main discrepancies are discussed. The focus of this work is to apply the ERO model for the interpretation of PSI-2 experiments, and a comparison of numerical modeling results with experimental data provides an opportunity to validate and improve the physical model and the underlying data. The study contributes to more accurate predictive modeling of plasma impurities transport in ITER.

Solution 1: Improving ERO Modelling of Tungsten Erosion in PSI-2

To enhance the predictive capabilities of the ERO modelling tool for plasma-surface interaction (PSI), our study focuses on evaluating the tungsten (W) erosion behaviour in the linear plasma device PSI-2. The experiment measured and recorded W erosion via three independent methods: passive spectroscopy, weight loss with spatial resolution, and quartz microbalance (QMB) deposition sensor. Using ERO code simulations, we were able to reproduce the observed trends and provide valuable insights into the physical model parameters required. Specifically, we discuss the influence of W1 metastable (MS) states population dynamics on spectroscopy measurements and estimate the characteristic evolution time for the MS levels. We also compare the physical sputtering data for W with the simulated data obtained using the binary collision approximation (BCA) approach (SDTrimSP code) and highlight the main discrepancies. By validating and improving the ERO modelling tool, it becomes a valuable predictive tool for PSI studies and can provide critical insights for the design of plasma-facing components (PFC) in tokamaks.

Solution 2: Investigating Tungsten Erosion in Argon Plasma using PSI-2

In this study, we investigate the tungsten (W) erosion behaviour in Argon (Ar) plasma using a series of experiments conducted at the PSI-2 linear plasma facility. W erosion was measured via three independent methods: passive spectroscopy, weight loss with spatial resolution, and quartz microbalance (QMB) deposition sensor. These measurements provide a comprehensive picture of the erosion and transport processes in linear plasmas, including the relationship between net erosion (QMB, weight loss) and gross erosion (spectroscopy). We then analysed the data using ERO code simulations to provide a consistent interpretation of the results. Our study also discusses the physical model parameters used in ERO, such as energy and angular distributions of sputtered particles. Furthermore, we investigate the influence of W1 metastable (MS) states population dynamics on spectroscopy measurements and estimate the characteristic evolution time for the MS levels. By comparing the simulated data obtained using the binary collision approximation (BCA) approach (SDTrimSP code) with the physical sputtering data for W, we highlight the main discrepancies and identify areas for further research. Overall, our study provides valuable insights into tungsten erosion in linear plasmas, which can help to inform the design and improvement of plasma-facing components in nuclear fusion reactors.

Suggested Resources/Books:

1. “Plasma-Surface Interactions and Processing of Materials” by John C. Miller

2. “Plasma Physics and Engineering” by Alexander Fridman

3. “Introduction to Plasma Physics and Controlled Fusion” by Francis F. Chen

4. “Numerical Simulation of Magnetospheric Plasma Physics: With Examples in Geospace Physics” by George V. Khazanov

Similar Asked Questions:

1. What are the advantages of using linear plasma devices for investigating problems in plasma-surface interaction?

2. What is the role of tungsten in plasma-facing components and how does it impact the performance and lifetime of tokamaks like ITER?

3. How does the ERO code work and what is its application in predictive modelling of impurity transport in plasma?

4. What are the three methods used to measure tungsten erosion in PSI-2 experiments and how are they related?

5. What are some challenges and discrepancies in the comparison of numerical modelling results with experimental data in plasma-surface interaction studies?

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