J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)433–436
000–000

Effect of Plasma Flow on the Gas Conductancein a Simulated Closed-Divertor
MATSUBARA Akihiro, WATANABE Tsuguhiro, SUGIMOTO Tatsunori1,
SUDO Shigeru and SATO Kuninori
1

National Institute for Fusion Science, Toki 509-5292, Japan
Dept. of Fusion Science, The Grad. Univ. for Advanced Studies, Toki 509-5292, Japan(Received: 9 December 2003 / Accepted: 23 February 2004)

Abstract
The reduction of a baffle-conductance due to the plasma flow has been experimentally investigated. For various
ion densities of the plasma flow through the aperture of the baffle, the conductance for the flow reversal of neutral
gas was derived from the neutral pressure difference between both sides of the baffle. It has been observed that thevalue of conductance is reduced continuously with increasing the ion density, indicating clearly the effect called“plasma plugging”. An effective formula expressing the reduction of the conductance is presented in consideration of
the friction between the plasma and neutral flows.
Keywords:
linear machine, closed divertor, plasma plugging, conductance, plasma flow, neutral gas, friction

1. Introduction

C will be given from the force balance between the friction
and the neutral pressure gradient in one-dimensional fluid
equations for the neutrals.

Divertor baffles in the magnetic confinement devices
remind us of the concept of gas conductance. In vacuum, theflow rate of neutral gas flowing through the aperture or duct,
Q [Pa m3·s–1], is given by
Q = C∆P,

2. Experimental setup
The experiment was carried out in the linear machine
TPD-II at the National Institute for Fusion Science (seeFig. 1) [5]. Helium plasma is continuously generated by a dc
discharge between the anode and the LaB6 cathode. As canbe seen from Fig. 1, the plasma goes into the simulated edge
plasma region (E region) and then into the divertor region (Dregion). An orifice (20 mm in length and 15 mm in diametersomewhat larger than the plasma diameter) is located 1.4 m
from the anode. This orifice serves as the opening of baffle(1)

where C [m3·s –1] is the conductance and ∆P [Pa] is thepressure difference between neutral pressures at the inlet andoutlet. If substantial dense Scrape Off Layer (SOL) plasma
passes through the opening of the baffle, the impurity flow
toward the core plasma can collide with the SOL plasma flowat the opening of the baffle, which will induce theenhancement of the friction between the plasma and neutral
reverse flows. The friction leads to the reduction in theconductance of the neutral reverse flow [1]. This effect iscalled “plasma plugging”, improving an impurity screening[2]. The plasma plugging has been clearly found in linear
machines [2-5]. The value of conductance for the impurity
was found to be reduced by a factor of 8 compared to thevalue of vacuum.
In this article, an useful formula that fairly expresses therelationship between conductance and the plasma flow will
be presented based on the experimental results obtained byusing the linear machine TPD-II (Test Plasma produced by aDc discharge) with a baffle [5]. It has been observed that thevalue of C is reduced continuously with increasing the ion
density of the plasma flow. The formula for the reduction ofPlasma source

Edge plasma region

Divertor region
HeGGLaB6
Cathode AnodePumping Baffle

BzProbes Target

1mFig. 1 Schematic of TPD-II with the baffle.

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: amatsubara@nifs.ac.jp1433

Matsubara A. et al., Effect of Plasma Flow on the Gas Conductance in a Simulated Closed-Divertor

plates in magnetic confinement devices. The electron plasma
density ne (≈ ni) is 1018~1019 m–3 under the axial magnetic
field of 0.2 T. The control in ne is achieved by varying thedischarge current Id ; ne increases as Id is increased. The valueof ne was obtained by the single cylindrical Langmuir probe
located at 1.5 m away from the anode. The probe measurement was carried out in a low neutral pressure condition(PE ≈ PD ≈ 0.1 Pa). Note that the electron temperature Te is
5 eV that is almost independent of Id . The ion flow velocity
toward the target ui (= 5 × 103 m/s) was measured from
Doppler-shift of the emission line of He II 468.57 nm, andwas comparable to the ion thermal velocity vthi for Ti ≈ 1 eV.
No change in ui with Id has been observed.
The neutral helium gas is injected into the D region,
flows against the plasma flow through the orifice, and isevacuated at the E region (the pumping speed is 0.3 m3·s–1).
The neutral gas pressures at the D and E regions, PD and PE,
were measured by using baratron gauges located in thecorresponding regions. As the flow rate of the gas injection
into the D region, QD , is increased, the value of PD increases,
and when PD becomes greater than ~1 Pa, the plasma
detachment clearly appears in the D region. Then, the positionof the ionization front, zf , moves toward the E region. Notethat in this article we deal with the case that zf remains in theD region.

3. Experimental results and discussion
As QD is increased slowly keeping the steady state, PDand PE monotonically increase, which are shown in Figs. 2(a)and 2(b). The variation of the pressure difference between PDand PE, ∆P, is shown in Fig. 2(c). One can see that thefunctional relationship between ∆P and QD is offset-linear as∆P =QD+ ∆ P0 ,C(2)Fig. 2where, 1/C is the slope and ∆P 0 is the intercept (atQD = 0 Pa m3·s–1) of each line. The symbol C means theeffective conductance influenced by the plasma flow throughthe orifice.
The values C and ∆P0 drawn from each line are shown
as a function of the mean area density of ion, 〈n i 〉, inFigs. 3(a) and 3(b), respectively. The gas conductance forvacuum (C at I d = 0 A), C 0, is 0.027 m 3 ·s –1, which iscomparable to the value of 0.028 m3·s–1 estimated as theconductance of the short duct in vacuum [6]. It can be seenfrom Fig. 3(a) that the value of C decreases with increasing〈n i 〉, indicating that the plasma flow suppresses theconductance. On the other hand, the value of ∆P0 increases
with increasing 〈ni 〉.
The appearance of ∆P 0 suggests an additional gas
injection into the D region. This injection can arise from theplasma flow. Ions in the plasma flow come into the D region,
recombine, and become neutrals. The flow rate of the gas
injection by the plasma flow, Qp , is proportional to 〈ni 〉. Thetotal gas injection into the D region, Q, is summation of QD
and Qp : Q = QD + Qp. Equation (1) is rewritten as

Variations of PD, PE, and ∆P as a function of QD forvarious values of discharge current Id .

∆P =QD Q p+.
CC(3)By defining Qp / C as ∆P0 , eq. (3) becomes equal to eq. (2).
The experimentally obtained offset-linear scaling of eq. (2),thus, can be interpreted.
We now attempt to find a formula that expresses thechange in both C and ∆P0 as shown above. The effective
conductance C can be considered as the combinedconductance for the series-connection of C 0 and theconductance due to the plasma flow, Cp :–1⎛ 11 ⎞C =⎜ +⎜ C0 C p ⎟⎟ .
⎝⎠(4)

Equation 3 is rewritten as∆P =QD + Q p
C0+

QD + Q p
Cp.

(5)

The second term in right hand side means the pressure2434

Matsubara A. et al., Effect of Plasma Flow on the Gas Conductance in a Simulated Closed-Divertor

ζ = 2.7 x 10-17 s

3 -1

C (m s )0.03∆P ′ =(a)0.02mνn ∆ z ⎛ ui ⎞mνn ∆z ⎛ ui ⎞⎜1 + ⎟ QD + α⎜1 + ⎟ ni ui STn 0 , (9)STn 0 ⎝ un⎠
STn 0 ⎝ un ⎠where, we assume that there are no significant changes in 〈ni 〉,up, and un along with scale length ∆z. Equation (9) shows
QD- and plasma flow (〈ni 〉 ui STn0)- dependencies on ∆P’,
which is similar to eq. (6). Then we define Cp as0.01
001

2

3

4

5x10–1CP ≡ (ζ ni ) ,18-3

where, ζ is<ni> (m )6ζ =α∆P0 (Pa)543

α=31001234

5x10

18-3

<ni> (m )Fig. 3m (σ in + σ cx ) ∆ z vthi ⎛ ui ⎞⎜1 + ⎟ .
2S Tn 0⎝ un ⎠

C=Variations of C and ∆P0 as a function of the mean areadensity 〈ni 〉.

C0.
1 + ζ ni C0

difference caused by the plasma flow, and is defined as ∆P’:

QD + Q p
Cp.

(6)

(7)

where, nn and un are the neutral density and the neutral gas
flow velocity at the orifice, respectively, νn is collision
frequency, and dP’ is corresponding to the pressure difference∆P’ in eq. (6). The signs of un and ui themselves are positive;the direction of (–un) in eq. (7) is opposite to that of theplasma flow. The conservation of the neutral particle for theD region prescribes nn under the steady state [see also upper
schematic of Fig. 2]:

uQD
nn = i α ni +,un
un STn 0(13)The curves given from eqs. (12) and (13) as a functionof 〈ni 〉 are shown as solid curves in Figs. 3(a) and 3(b),respectively. From the curve fitting to the experimental data,
the parameters of ζ and α providing the best fit are ζ = 2.7 ×
10–17 s and α = 3.
The factor of α (> 1) implies necessity of a further gas
injection proportional to 〈ni 〉 . This may arise from neutrals
accompanying the plasma flow, since there exists the frictionin the upstream (the E region). The mean free path for charge
exchange collision in the E region is a few times smaller thanthe distance between the anode and the probe for present
experimental condition. This allows us to consider that theneutral flow can grow along the distance from the anode tocompensate for the ion-flux loss. Note that there is no growthof ion density due to ionization, since the mean free path forthe ionization is much larger than that for the momentumloss collision.
For estimating ζ of eq. (11), first we deduce un from theexperimental results, as follows. The neutral density at theorifice nn can be regarded as a mean value: nn = (PD + PE)/(2Tn), where, Tn is the neutral gas temperature at the orifice(≠ Tn0). Then, eq. (8) will be rewritten as

The substance of Cp can be assumed to be almost friction
between the neutral and plasma flows. For the present
experimental condition, the influence of viscosity is supposed
to be much smaller than that of the friction, because the mean
free path of neutrals becomes not much smaller than theaperture diameter of the baffle. The one-dimensional (along zaxis toward the target) equation of force balance for theneutral particle at the orifice can be written as follows:′– mnnνn ( – un – ui ) – dP = 0 ,dz(12)

Since ∆P0 is given as Qp / C [see eq. (3)], ∆P0 is⎛ 1 + ζ C0 ni ⎞∆P0 = α STn 0 ui ⎜⎟ ni .
C0⎝⎠∆P′ =(11)In derivation of eq. (11), νn = 0.5α 〈n i 〉 ( σin + σcx )v thi isadopted into νn in eq. (9), where σin (≈ 3.3 × 10–19 m2) andσcx (≈ 2.0 × 10–19 m2) are the cross sections for neutral–ionand charge exchange collisions, respectively [7]. From eqs.
(4) and (10), we obtain a formula for the effective
conductance C as(b)2(10)⎛Q ⎞ 2 Tnun = ⎜ α ni ui + D ⎟.
STn 0 ⎠ PD + PE⎝

(8)

(14)

The value of Tn , unfortunately, has not been observed, so that
we presuppose that T n is approximately equal to the wall
temperature surrounding the plasma. Then, the Id -dependenceof the wall temperature is adopted in eq. (14). In fact the wall
temperature increases from room temperature (~300 K) up towhere, S is the orifice cross-sectional area, T n0 is room
temperature (300 K), and α is a factor of 〈ni 〉 for fitting theexperimental data with the theoretical curve as shown below.
Substitution of eq. (8) into eq. (7) yields
3435Matsubara A. et al., Effect of Plasma Flow on the Gas Conductance in a Simulated Closed-Divertor~500 K for Id = 0 –120 A. The evaluated values of un lie at(1.4 ± 0.2) × 10 2 m/s and is fairly independent of thedischarge current Id. Employing this value of un and ∆z~L= 20 mm (where L is the orifice thickness), thus, the value ofζ, is estimated as 3 × 10–17 s which is comparable to theexperimentally obtained value of 2.7 × 10–17 s. This indicates,therefore, that the reduction of the effective conductance inthis experiment can be explained by means of the friction
between the neutral and plasma flows.

reduction of the conductance in this experiment.

Acknowledgment
This research was partially supported by the Ministry of
Education, Science, Sports and Culture, Grant-in-Aid for
Scientific Research (B), 15360496, 2003.

References
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C.S. Pitcher et al., J. Nucl. Mater. 290-293, 812 (2001).
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L. Schmitz et al., Phys. Plasmas 2, 3081 (1995).
A. Matsubara et al., J. Nucl. Sci. Technol. 37, 555(2000).
[5] A. Matsubara et al., J. Plasma Fusion Res. 78, 196(2002).
[6] R.G. Livesey, Foundations of vacuum science andtechnology, edited by J.M. Lafferty (John Wiley, NewYork, 1998) p. 87.
[7] M.L. Vestal et al., Phys. Rev. A 17, 1321 (1978).

4. Conclusion
The effect of the plasma flow on baffle conductance forneutral reverse flow was investigated by using the linear
machine with simulated divertor. It has been observed thatthe value of conductance is reduced continuously withincreasing the ion density of the plasma flow, indicatingclearly the effect called “plasma plugging”. By considering
the friction between the plasma and neutral flows, wepresented the formula that expresses successfully the4436