Measurement of gas composition ratio of H-He mixed plasmas

in Divertor Simulator MAP-II

Y. Kuwahara1)*, S. Kado2), A. Okamoto3), T. Shikama1), Y. Iida1), K. Kurihara1), F. Scotti1) and S. Tanaka1)

1)Department of Quantum Engineering and Systems Science, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan

2)High Temperature Plasma Center, The University of Tokyo, Kashiwa, Chiba 277-8568, Japan3)School of Engineering, Tohoku University, 6-6-01-2 Aobayama, Sendai 980-8579, Japan

*email: kuwahara@flanker.q.t.u-tokyo.ac.jp

P7-11

BackgroundIn divertor region of fusion reactor, plasmas are mixed with puffed molecular hydrogen, dissociated atomic hydrogen and atomic helium through fusion reaction are mixed.

CL

プ ラ ズマ 対向壁

炉心プ ラ ズマ

＝閉じ 込めら

れたプ ラ ズマ

境界層プ ラ ズマ

＝漏れて き たプ ラ ズマ

（ 壁の損耗、 不純物発生）

ト カ マ ク

中心線

core plasma: confined plasma

*S. Kado, Y. Iida, et al., J. Plasma and Fusion Res., 81, 810 (2005).

We propose the method to measure the gas composition ratio by using the ratio of hydrogen Balmer series, Fulcher-α band and helium balmer series.

In order to evaluate these atomic/molecular processed, measurement of its gas composition ratio is acquired.

Fulcher-α bandFor the ro-vibrational structure of the ground state we assume Bolzmanndistribution and calculate the emissions of each band with its parameter as rotational and vibrational temperatures. For the plasma we assumed a coronal model that is electron impact excitation from the ground state and spontaneous emission from the excited sates.

' ' ' ''' '' '' '' ' '' '

'' ''

' '' ''' ''

e' ' ' ''' '' '' ''

'' ''

dv J dv Jav J av J dv JUv J

Lv J

dv Jdv Jav JXvJ XvJdv J dv J

vJav J av Jv J

hcI A N

Ahc n R NA

λ

λ

=

= ∑∑

' ' ' 'e ' ' '' ''

'' ''0dv J dv J

XvJ XvJ dv J av JvJ v J

n N R N A− =∑ ∑Rate equation of coronal model

' '' ' ' '" "" " e' ' ' '

" " " "' '

( , ) ( )(2 1)expdv J

dv J dv J Jav J X Xav J XvJ v asdv J dv J X X

vJav J av J rot vibv J

A F J v G vhcI n R C g JA kT kTλ

∆ ∆= + − −

∑∑

Ground state (X1Σg+)

d3Πu- state

a3Σg+ state

v’=3210

v=3210

v’’=3210

J=0・・・

・・・J’=0

Boltzmann distributionBoltzmann distribution

Fulcher-α band emissionMolecular hydrogen density

d3Πu- state

a3Σg+ state

v’=3210

v’’=3210

・・・J’=0

・・・J’’=0v=3

210

2H eff

de Xn N R

radiative decay

X1Σg+ state

' ''' ''' '

' ' '' ''

d v Jav Jd v J

v J v J

N A−

−∑∑

2

' ''' ''' ' ' '

'' '' e H' ' eff'' ''' '

' ' '' ''

d v Jav Jd v J dd v J

av J Xd v Jav Jd v J

v J v J

N An N R

N Aε

−

− −

−

−

=∑∑

Rate equation

From Fulcher-α the ro-vibronic structure of d- state, Nd-v’J’ , can be obtained.

2

' 'e H '' ''' 'eff

' ' '' ''

d d v JX av Jd v J

v J v Jn N R N A

−

−=∑∑

In order to reduce the effect errors, we used the summation of 12 observed lines.

Observed Fulcher-α band

Total loss from d- state

' '

' 'eff

' '

d v JXvJ XvJ

d v J vJX

XvJv J vJ

N RR

N

−

≡∑∑∑∑

Effective reaction rate from X to d-

Hydrogen and Helium Balmer emission

Helium Balmer emission

2 22

H2

2

22

H H HH 1 2 2H(2 ) 1 2 H 2Htotal

Ful H 1H eff eff

( , , ) ( , , ).

e e e e e pp pd d

e X X

n N R p n T N R p n T A R A N RN Rn N R R

εε

←← ← + = = +

Hydrogen Balmer emissionPopulation coefficient Hydrogen CR model*

2 1 2 1

22

He He2 1He 1 12 2He He

totalFul HH eff eff

( , , )(2 ) .s s

se e e L p L p

d de X X

n N R p n T A R AL p NNn N R R

εε

+ ++

← ←← = =

Gas composition ratio, NH2:NH:NHe ,can be obtained

Population coefficient Helium CR model**

*T. Fujimoto, K. Sawada and K. Takahara, J. Appl. Phys., 66, 2315 (1989).**T. Fujimoto, Quant. Spectrosc. Radial. Transfer., 21 (1979) 439

Experimental deviceDivertor simulator MAP(material and plasma)-II

Condition

@target chm.

radial profile

P:3.3mTorr, Idis: 45A, Vdis: 86V

Source gas: H2: 50sccm, He: 50sccm

Te and ne measurement: electrical probe

DC arc discharge，H2 & He plasma

Abel inversionObserved emissions are line integrated along the viewing chordAbel inversion is needed to obtain the local emission at each point.

we measure the emission profile of each line by means of a CCD and wavelength-tunable filter system*.

plasma Particular wavelength

Wavelength-tunable filter: liquid crystal based Lyotfilter, 400-720nm

CCD: 1024x256 pixel, 14bit

Plasma flowbackground

*Related Poster: P11-02

Density profile

Because the degree of ionization is assumed to be less than 10%, the density profile of He should be flat.

In the outer region the density rises.The Te and ne errors can affect the density distribution.

Expected He density

Population coefficient of He

For Te<4eV, the value of population coefficient greatly changes.An error of 0.1eV can result in 30% error of density if Te<3eV and 60% error if Te<2eV

This implies a big error in the evaluation of density for r>15.Precise measurement of Te is need in order to obtain the density profile.The dependence is the same for R1 for other levels.

**T. Fujimoto, Quant. Spectrosc. Radial. Transfer., 21 (1979) 439

Population coefficient of 41S state of He

Population coefficient of H

As in the case of helium, the population coefficient changes greatly around Te<3eV.For n=2 level, the change of R1 is relatively slow. (especially the effect of ne error is much smaller than that of n=6 state)

If we can use Lyman a line, the effect of Te and ne errors can be reduced.

*T. Fujimoto, K. Sawada and K. Takahara, J. Appl. Phys., 66, 2315 (1989).

Gas composition ratioThe region where R1 of He and H largely change is close.

The errors on Te and ne can directly affect on the density profile.However, the effect of Te and ne errors on the gas composition ratio at the same position can be small because the effect of error may cancel each other.The effect of error is still big in the region of Te<2.The obtained gas composition ratio is assumed to be within the error of several tens percent.

Gas composition ratio

SummaryWe proposed a method to measure the gas composition ratio of H-He mixed plasma, and applied it to the divertor simulator MAP-II.The population coefficient of H and He can be largely affected by the errors on Te and ne.An error of ∆Te=0.1eV can result in 60% error on density if Te<2eV.A precise measurement of Te and ne is needed in order to measure the density profile.In case of gas composition ratio, the effect of errors on Te and ne can　be reduced because they are canceled out each other.If Te>3, an error of ∆Te=0.1eV result in less than 10% error of gas composition ratio.If the density profile of a particular species can be obtained with another method like LIF, the density profile of the others can be obtained from the gas composition ratio.

Principle -effective reaction rate-The effective reaction rate considering the ro-vibrational structure is used.

4x10-10

3

2

1

0

<σv>

X->d

[cm

3 /s]

1086420Te [eV]

1.5

1

0.5

0

Ne=

<σv>

beam

/<σv

> eff

(a)

(b)

<σv>eff

<σv>beam

Ne fit_Ne

There is no data of reaction rate of molecular hydrogen, by using Gryzinski’s semi- classical model we calculate the cross section and then obtained the reaction rate.

It is know that the reaction rate of Gryzinski agree with the experimental one if Ne=1.

In order to obtained the reaction rate more precisely, we normalized the effective reaction rate calculated under the condition of beam experiment(Tvib=0, Trot=room temp.) to the experimental reaction rate** .

If we normalize around 10eV, Ne is 0.85. But around low temperature region it does not agree. So we obtained Ne as a function of Te.

**G. R. Möhlmann and F. J. De Heer, Chem. Phys. Lett., 43, 240 (1976).*M. Gryzinski, Phys. Rev., 138, A305 (1965).

' '

' 'eff

dv JXvJ XvJ

d v J vJX

XvJvJ

N RR

N=∑∑∑

Gry e ( )Q N f E d E= ∆ ∆∫shape factor

Gryzinski’s Ne factor: absolute value

Appendix