23G06
Heat conduction analysis of a composite metal
プラズマ照射された金属複合材の熱伝導解析
Hiroto Matsuura,Ryohei Ohyama,Shotaro Turu, A.Rusinov,Mizuki Sakamoto
松浦 寛人, 大山亮平, 鶴昭太朗,A. ルシノフ, 坂本瑞樹
Res. Org. for Univ.-Comm. Collabo., Osaka Pref. U.,
Gakuen-cho 1-2, Naka-ku, Sakai, Osaka 599-8570, Japan
大阪府立大学地域連携研究機構、〒 599-8570 大阪府堺市中区学園町 1-2
Absorbed heat ﬂux from plasma to solid target is diﬃcult to determine experimentally. It
depend not only on plasma parameters but also on surface condition, which can not monitor insite easily. In this work, a bulk composite target is irradiated by He plasma, and temperature
data with an Inferred Camera thermometer and thermocouple are compared. From these data,
modeling of heat conduction process are also conducted. For exact heat estimate, heat sinkmust be treat carefully.

1. Introduction
Sheath heat ﬂux from plasma to solid surface has large impact on the divertor plate offusion plasma, the substrates in semi-conductor
processing, the wall material of space vehicles.
It is found from direct heat ﬂux measurementwith thermal probes that sheath heat ﬂux depends not only plasma parameters but also thematerial and surface condition of the probe
tips [1]. Tungsten is the ﬁrst candidate of theﬁrst wall material of fusion reactors. Recently,
however, it suﬀers various surface damage under the helium plasma irradiation [2]. So it isimportant to study the eﬀect of these surface
damage on the sheath heat ﬂux. Moreover,surface damages aﬀects Inferred Camera thermometer (IRC) data and surface temperature
data with it can not provide absorbed heat
content in the bulk material.
In this work, we use a bulk target material with three thermocouples (TC), obtainthe temperature data obtained with IRC andTC, and compare them with heat conduction
model.
2. Experimental setup and target
Experimental device used here is the compact PWI simulator, APSEDAS [3]. By keeping gas pressure in the chamber as about 35[mTorr], Helium plasma is produces with aRadio Frequency helical antenna of 13.56 [MHz].
In this work, RF power is 300 ∼ 400 [W] and,hence so-called Helicon jump does not occur

Fig.1: Schematic drawing of composite target.
The target consists of Tungsten (1cm thick)and Copper ( 2cm thick ).

and plasma density is not so high ( order of1016 [m−3 ].
Bulk irradiation target is shown in Fig. 1.
which is set on the water cooled support stage.
This target consists of of Tungsten with thethickness of L1 = 10.0 [mm] and Copper of
L2 = 20.0 [mm]. Its cross section facing plasma
is S = 30 × 30 = 9.0 × 102 [mm2 ] and surface temperature is measured with two IRCs (Chino IR–CAQ series ) with diﬀerent temperature range. Bulk temperature is measured
with three type-K TCs, which are set at 5.0,12.0,
and 22.0 [mm] from Tungsten irradiation surface.
3. Experimental result and discussion
Figure 2 shows an example of target temper-Steady State 1D heat conduction result
350
IRC
TC1
TC2
TC3
stage

300

temp.[deg.]

250

200

150

100

5000

2000

4000

6000
Time[s]

8000

10000

12000

Fig.2: Example of temperature evolution. RF
power for plasma production is about 400[W].
Discharge duration is 90 [mini.].

50
t1t2t3WCu
45

40

temp.[deg]ature evolution. Plasma parameters measured
with a Langmuir probe are ne = 5.9×1016 [m−3 ],Te = 10[eV], Vs = 38[V], Γi = 5.7×1020 [He/m2 s],
respectively. Surface temperature ( IRC data,red line ) shows rapid increase to 315[deg.] atdischarge start, keeps almost constant during
the irradiation, and drops rapidly to 295[deg.]at discharge end. But bulk temperature data
(TC1,TC2,TC3) show slow increase and steadystate does not establish even at discharge end( 90[min.] ).
By using Tungsten thermal diﬀusivity α1 =λ1−42
c1 ρ1 = 0.695 × 10 [m /s], heat diﬀusion time
for characteristic length of L1 + L2 is τ1 =L2
α = 12.95[s]. By using Copper value, τ2 isabout 70%. So if plasma irradiation is longer
than one [min.], temperature proﬁle is expected
to reach steady state. But Fig. 2 contradicts
this prediction. The stage temperature is also
monitored with TC and shows similar behavior. ( Ideally, this temperature should be kept
constant. ) So the characteristic length mustbe much larger than L1 + L2 .
Recently we obtain an analytical solutionof heat conduction for a composite slab [4].
One example is shown in Fig. 3. This solution
is obtained for large characteristic length L =L1 + L2 + Lex , where this expanded length
Lex denotes the heat resistance between thetarget and the stage. If Lex = 0, the stage
acts as a perfect sink. In the real APSEDAS
experiment, Lex must be very large and steadystate hardly establishes.
After irradiation phase, three TC data andIRC data are identical within the experimental error and the decay constant is about 750[s](12.5 [min.]). Since the heat capacity of sample
target can be estimate as (c1 ρ1 L1 + c2 ρ2 L2 ) ×
S = 72.5[J/K] and temperature increment justbefore discharge stop was 190[deg.], total heatloss was 72.5 × 104 × 190/750 = 18.4[W]. If
this heat loss occurs only through heat conduction to the stage, heat ﬂux density alongnormal direction was 20.4[kW/m2 ] and temperature drop in W layer is estimated to beabout 1[deg.], while in Cu layer it is similarvalue.
Unfortunately, TC2, and also TC(stage),show a small drop (a few degree ) at discharge
start timing and recover at stop timing. So inorder to check above estimation, direct measurement of temperature gradient will be necessary for farther improved experiment.

3530

25-0.005

00.005

0.01

0.015
x[m]

0.02

0.025

0.030.035

Fig.3: Calculated temperature proﬁle. Initial temperature is assumed to be 30 [deg.],
plasma irradiation starts at t = t0 = 10 [s],and three proﬁles for t − t0 = 1.0, 10.0, and50.0 [s] are plotted. Lex = 100L1 is assumed.

Acknowledgements
This work was supported in part by the Collaborative Research Program of Research Institute for Applied Mechanics, Kyushu University.

References[1]

H.Matsuura et al.: Proc. 2nd Int. Forum. Heat
Trans., Tokyo, 2008.

[2]

S.Takamura et al.: Plasma and Fusion Research
1, 051(2006).

[3]

Y.Higashizono et al.: Plasma and Fusion Research 4, 043(2009).

[4]

M.Ishihara: private communication.