What is plasma-surface interaction (PSI) and how does it determine the duty cycle of ITER?

  

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 )

Don't use plagiarized sources. Get Your Custom Essay on
What is plasma-surface interaction (PSI) and how does it determine the duty cycle of ITER?
Just from $13/Page
Order Essay

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.
References
[1] V. Philipps, Tungsten as material for plasma-facing components in fusion devices. Journal of Nuclear
Materials. Vol. 415, Issue 1, Pages S2S9 (2011)
[2] R.P. Doerner, M. J. Baldwin and K. Schmid, Phys. Scr. T111 (2004) 75.
[3] G. J. van Rooij, V. P. Veremiyenko, W. J. Goedheer, B. de Groot, A. W. Kleyn, P. H. M. Smeets, T. W.
Versloot, D. G. Whyte, R. Engeln, D. C. Schram, and N. J. Lopes Cardozo, Appl. Phys. Lett. 90, 121501
(2007).
[4] Kreter, Arkadi, et al. “Linear plasma device PSI-2 for plasma-material interaction studies.” Fusion
science and technology 68.1 (2015): 8-14.
[5] A. Pospieszczyk et al., Spectroscopic characterization of the PSI-2 plasma in the ionizing and
recombining state. Journal of Nuclear Materials, Volume 438, Pages S1249S1252 (2013).
[6] A. Kreter. Reactor-relevant plasma-material interaction studies in linear plasma devices. Fusion
Science and Technology. Volume 59, Issue 1 T, (2011) Pages 51-56
[7] A. Kirschner et al. Modelling of tritium retention and target life time of the ITER divertor using the
ERO code. Journal of Nuclear Materials, 363-365, 91-95 (2007).
[8] D. Borodin et al. Modelling of Be transport in PSI experiments at PISCES-B, Journal of Nuclear
Materials, 390391, 390-391 (2009).
[9] D. Borodin et al. Modelling 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)
[10] E. Marenkov, et al. Modeling of plasma-material interaction experiments at PSI-2 with the 3D
Monte-Carlo code ERO. Journal of Nuclear Materials, Volume 463, August 2015, Pages 268-271.
[11] W. Eckstein. Sputtering Yields. Topics in Applied Physics, Vol. 110, (2007), 33-187
[12] Sorokin, Ivan, Igor Vizgalov, and Olga Bidlevich. “In-situ Mass-spectrometry of Magnetized
Plasmas.” Physics Procedia 71 (2015): 428-432.
[13] A. Kirschner, et al. Simulation of the plasma-wall interaction in a tokamak with the Monte Carlo
code ERO-TEXTOR. (2000) Nucl. Fusion, 40, 989.
[14] C. Birdsall, Plasma physics via computer simulation, McGraw-Hill, Singapore 1985
[15] H.P. Summers. The ADAS User Manual (2004), version 2.6; http://adas.phys.strath.ac.uk.
[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?

Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
× How can I help you?