J. Plasma Fusion Res. SERIES, Vol.7 (2006) 94-97

Simulation Study on Effects of Chemically Eroded Methane andEthylene Molecules on Carbon Impurity Transport and Net Erosionof Carbon Materials
KAWAKAMI Retsuo
Faculty of Engineering, The University of Tokushima, Tokushima 770-8506, Japan（Received: 4 October 2004 / Accepted: 24 May 2005）

Abstract
Eﬀects of chemically eroded CD4 and C2 D4 molecules on local transport of ionized C impurities and net
erosion of the C target are studied using a simulation code for plasma surface interactions. The calculated C 1+emission profile reproduces the experimental one, which indicates a stronger contribution of CD 4 . For C2+ andC3+ , the contribution of C2 D4 is stronger near the target. For their penetrations, however, the contribution ofCD4 is essential. For a high density and low temperature plasma, there is a significant influence of the chargetransfer reactions of C x Dy with D+ , by which the penetrations as well as the net erosion rates for CD 4 andC2 D4 are suppressed with their local redeposition. The net erosion rate for C 2 D4 is higher if YCD4 = YC2D4 .
If the temperature becomes high, however, the rate for C2 D4 is suppressed by its local redeposition, andapproaches that for CD4 .
Keywords:
chemical erosion, carbon, methane, ethylene, carbon impurity transport, net erosion
1．Introduction
Because of a high thermal shock resistance, C material will be used as a plasma facing material of ITER
divertor target plates. However, there is a crucial issue
in net erosion relevant to the divertor lifetime, namely,
chemical sputtering of C material. This causes penetration of hydrocarbons, such as methane (CD4 ) andethylene (C2 D4 ), to the core plasma [1]. The impurity
penetration contaminates the plasma, which results in adegradation of the plasma performance. Thus, eﬀects
of the chemically eroded CD4 and C2 D4 molecules on
the impurity penetration and the net erosion rate need
to be clear to improve the plasma performance and thedivertor lifetime.
In this study, the eﬀects on the penetrations of ionized C impurities are studied using a simulation codefor plasma surface interactions, ERIm [2]. The result iscompared with experimental data [3]. Also, the eﬀects
on the net erosion rates for a variety of plasma parameters and for the normal ITER divertor plasma predicted
by B2-EIRENE [4] are studied. The paper discusses
how the penetration depth from the C target to the coreplasma and its net erosion rate are changed by chemicalerosion (release) of CD4 and C2 D4 each.

2．Simulation code and modelOn the basis of the Monte-Carlo impurity transportmodel [5] and the binary collision model [6], ERIm
simulates the penetration depth of ionized C impurities
from a C target exposed to the plasma/impurity ions andits net erosion rate. Only the important features of thecode for this study are described here (see ref. [2] fordetails). For the penetration depth, the eroded impurities are assumed to be subject to the Lorentz and friction forces [5]. The impurity ionization, dissociation,and recombination dissociation reactions with e − andthe charge transfer reactions with D+ are included inthis code. The reaction chain by which CD4 changes
to C+ is given as the rate coeﬃcients by Ehrhardt et al.
[7]. For C2 D4 to C+ , the rate coeﬃcients by Brooks etal. are used [8], and for C0 to C3+ , those by Lennon
are used [9]. The simulation is continued until the impurities are locally redeposited on the targets or leave
the computational domain. For simplicity, the sticking
coeﬃcient is assumed to be 100 % : all of the hydrocarbons locally returned back to the target by the friction force are redeposited. For the net erosion rate,
the gross erosion/deposition by the ions impinging on
the target and the local redeposition of the eroded hydrocarbons (as described above) are taken into accountC 2006 by The Japan Society of Plasma

Science and Nuclear Fusion ResearchCorresponding author’s e-mail: retsuo@ee.tokushima-u.ac.jp

94Simulation Study on Eﬀects of Chemically Eroded Methane and Ethylene Molecules on Carbon Impurity Transport and Net Erosion of Carbon Materials[6]. Here, a word deposition is used for impurities transported by a plasma from other wall targets,and redeposition is used for those locally returnedback to the target. The energy of the impinging ionsis given by the Maxwellian distribution with an acceleration energy due to the electrostatic sheath potential, VS = T e /2 ln 2π(me /mi )(1 + T i /T e ), and the flux isgiven by ni (T i + T e )/mi 1/2 [10]. Here, T e and T i are theplasma electron and ion temperatures in front of the target, respectively, me and mi are the electron and ion
masses, respectively, and ni is the ion density. CD4and C2 D4 molecules are assumed to be released fromthe C target according to their chemical release yields,
YCD4 and YC2D4 , respectively. For the physically released C0 atoms, their release is based on the binary collision model [5]. In this study, there are no diﬀerencesin chemical properties between the deposited layer andthe bulk target.
3．Results and discussion
3.1 Carbon impurity transport

The simulation of the penetration depth is performed
based on the TEXTOR-94 edge plasma [11]. The electron density and temperature profiles used in this study
are the exponential functions fitted to those measured
by the Li- and He-diagnostics. They are given byne (r) = neLCFS exp −(r − 0.46 m)/0.02 m and T e (r) =T eLCFS exp −(r − 0.46 m)/0.025 m, where neLCFS (=1018 m−3 ) and T eLCFS (= 30 eV) are the density andtemperature at the last closed flux surface (LCFS), at aminor radius of r ∼ 0.46 m, respectively [3,12]. For
the impinging ions, D+ (∼ 98 %) and C4+ (∼ 2 %)are used assuming T i = T e [12].
The radial penetrations of C1+ , C2+ and C3+ generated through the reaction chains of CD4 , C2 D4 and C0
released from the target at r = 0.47 m are simulated asshown in Fig. 1. In the result, YCD4 = 3.6 % andYC2D4 = 0.9 % are assumed, which are based on the experimental data for C targets exposed to the TEXTOR94 plasma [11] and 200 eV D+ beam [1]. As shown inFig. 1(a), the C1+ penetration is in good agreement withthe measured CII light emission profile [3] (this meansthat their decay lengths are the same). The agreement
indicates that the contribution of CD4 is stronger thanthat of C2 D4 near the target. For C2+ and C3+ , however,
the opposite results occur as shown in Figs. 1(b) and1(c), which indicate the stronger contribution of C2 D4near the target. However, the contribution of CD4 isfound to be essential for the penetration of highly ionized C impurities under the low density and high temperature plasma (neLCFS = 1018 m−3 and T eLCFS = 30eV).

Fig. 1 Radial penetrations of C1+ , C2+ and C3+ generated through the reaction chains of CD4 , C2 D4and C0 released from a C target exposed to a D+
plasma including C4+ impurity (ne LCFS = 1018 m–3 ,Te LCFS = 30 eV). Open circles indicate the measured CII emission proﬁle [3].

If the density is higher and the temperature is lower(neLCFS = 1019 m−3 and T eLCFS = 3 eV), there is asignificant influence of the charge transfer reactions ofC x Dy with D+ as shown in Fig. 2 (for the low density
plasma, there is no influence). By the charge transfer
reactions, there is a suppression in the total number of
C1+ and C2+ penetrating to the core plasma [compareFig. 2(a) with Fig. 2(c), and compare Fig. 2(b) with Fig.
2(d)]. In particular, for CD4 , it is more pronounced. ForC2 D4 , there is no significant suppression, because thereleased C2 D4 molecule tends to be locally redeposited
before it changes to C1+ or C2+ . Thus, since the contributions of CD4 and C2 D4 are almost the same as shownin Figs. 2(c) and 2(d), they are found to play an important role in both the C1+ and C2+ penetrations under
the high density and low temperature plasma. Incidentally, there is no contribution of C0 to these C impurity
penetrations, because the exposure ion energy is lower
than a threshold energy below which the physical release never occurs [13].

95Simulation Study on Eﬀects of Chemically Eroded Methane and Ethylene Molecules on Carbon Impurity Transport and Net Erosion of Carbon Materials

Fig. 3 Comparison in the net erosion rate, (a) and (b),and the redeposition rate, (a’) and (b’), between
CD4 and C2 D4 chemical erosions for different
plasma densities and temperatures.

Fig. 2 Comparison in the C1+ and C2+ penetrations between the reaction chain of CD4 and C2 D4 with e– ,(a) and (b), and that with e– plus D+ , (c) and (d),under a high density and low temperature plasma(ne LCFS = 1019 m–3 , Te LCFS = 3 eV).

with T eLCFS [Fig. 3(b’)]. In this calculation, the redeposition comes from the friction forces on the impurity
ions in the direction parallel to the magnetic field (nothermal forces are taken into account). Thus, at the highdensity and temperatures, the net erosion rate for C2 D4
is found to be significantly suppressed by its local redeposition.
If the charge transfer reactions with D+ are added(black and gray solid curves), both of the net erosion
rates are suppressed at the high density [Fig. 3(b)]. Dueto this addition, for example, both of the redeposition
rates at T eLCFS < 5 eV are enhanced from 0 % to 10 %[Fig. 3(b’)]. On the other hand, at the low density, there
is little influence of the charge transfer reactions [Figs.
3(a) and 3(a’)]. Thus, at the high density plasma, thenet erosion rates for CD4 and C2 D4 are expected to be
suppressed by their strong local redeposition resulting
from the charge transfer reactions.
For the normal ITER divertor plasma [4,15], the neterosion rates along the outer target plate for CD4 andC2 D4 are calculated assuming YCD4 = YC2D4 = 1.0 %,as shown in Fig. 4. At locations of z <∼ 0.1 m, i.e.,at the private region and the strike point vicinity (wherethe density increases from 5 × 1019 m−3 to 2 × 1021 m−3
with increasing z, while the temperature keeps ∼ 3 eV),
the net erosion rate for C2 D4 with e− is higher than thatfor CD4 with e− . This indicates that, for C2 D4 , the neterosion at these plasma regions would be more serious
if YCD4 = YC2D4 . In contrast, at z >∼ 0.1 m, i.e., at theSOL region (where the density decreases to 5×1018 m−3
with increasing z, while the temperature increases to 18

3.2 Net erosion of carbon material

The simulation of the net erosion rate (includingthe redeposition rate) for diﬀerent plasma densities
and temperatures is also performed based on the sameTEXTOR-94 edge plasma as described in the previous
subsection [11] (contribution of physical sputtering isincluded in this result). In order to clarify a diﬀerencein the results between CD4 and C2 D4 chemical erosions,the same erosion yields are assumed: YCD4 = YC2D4 =4.0 %. A change in the net erosion rate of the C target at r = 0.47 m with neLCFS and T eLCFS is calculated
as shown in Fig. 3 (if there is no chemical erosion, net
deposition of the impinging C impurity occurs at a lowtemperature, see ref. [14] for details).
At a low density (neLCFS = 1018 m−3 ), there is a difference in the results between the CD4 and C2 D4 reaction chains with e− . The net erosion rate for C2 D4is higher [Fig. 3(a)], although its redeposition rate ishigher [Fig. 3(a’)]. This is simply because the grosserosion for a molecule of C2 D4 is equivalent to that for
two C atoms. On the other hand, they have a similarity that they increase with TeLCFS due to an increase in
the physical erosion. However, if the density increases(neLCFS = 1019 m−3 ), there is a drastic change in thenet erosion rate for C2 D4 [Fig. 3(b)]. With increasing T eLCFS , the net erosion rate for C2 D4 increases, andthen decreases at T eLCFS > 5 eV. The further increasein T eLCFS (> 40 eV) makes it increase again, but it isalmost the same as that for CD4 . The drastic change isbecause the redeposition rate for C2 D4 increases rapidly
96

Simulation Study on Eﬀects of Chemically Eroded Methane and Ethylene Molecules on Carbon Impurity Transport and Net Erosion of Carbon Materials

4．Conclusion
The simulated C1+ penetration at neLCFS = 1018 m−3
and T eLCFS = 30 eV reproduces the experimental one,which indicates that the contribution of CD4 is stronger
than that of C2 D4 . For C2+ and C3+ , however, the opposite result occurs near the target, which indicates thestrong contribution of C2 D4 . For their penetrations,however, the contribution of CD4 is essential. For a highdensity and low temperature plasma, there is a significant influence of the charge transfer reactions of C x Dy
with D+ , by which the penetrations are significantlysuppressed. For the net erosion rate, there is also an influence of the charge transfer reactions: the net erosion
rates for CD4 and C2 D4 are suppressed by their local redeposition. Also, the net erosion rate for C2 D4 is higher
than that for CD4 if YCD4 = YC2D4 . However, if the temperature becomes high, the rate for C2 D4 is suppressedby its local redeposition, and approaches that for CD4 .

[1]
[2]
[3]
[4]
[5]
[6]
[7]

Fig. 4 Comparison in the net erosion rate (a) and the redeposition rate (b) between CD4 and C2 D4 chemical erosions for the ITER-FEAT divertor plasma[4,15].

[8][9]eV), both are almost the same. This indicates a significant suppression of the net erosion for C2 D4 , which is
attributed to the high redeposition rate for C2 D4 , as has
already been described above. As expected from the result of Fig. 3, the additional charge transfer reactions
brings about a significant suppression of the net erosion
rates at the private region and the strike point vicinity
for CD4 and C2 D4 .

[10]

[11]
[12]
[13]
[14]
[15]

97

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