Proceedings of ITC/ISHW2007

Emergence of ionization balance plasma in conﬁnement region
with the complete divertor detachment
Motoshi GOTO, Shigeru MORITA
National Institute for Fusion Science, Toki 509-5292, Japan
October 29, 2007
A spectroscopic measurement is made for the plasma in the rotating radiation belt accompanying the complete divertor detachment which is recently realized in the Large Helical Device (LHD) [J. Miyazawa, et al.,Nucl. Fusion 46, 532 (2006)]. The Balmer series lines of neutral hydrogen are clearly observed. The population distribution over the exited levels is determined from the Balmer series line intensities and is comparedwith the result of the collisional-radiative model calculation to determine the electron temperature T e and density ne . No reasonable pair of T e and ne is found when either the ionizing plasma or the recombining plasma
is assumed. A good ﬁtting is obtained under an assumption of the ionization balance plasma with T e = 1.8 eV
and ne = 2 × 1020 m−3 . The mechanism to sustain such a low temperature plasma inside the high temperature
conﬁnement region is unclear.
Keywords: radiation belt, spectroscopy, ionization balance plasma, Stark broadening

Introduction

In the study of magnetic conﬁned fusion plasma the reduction of heat ﬂux onto the divertor plate is an important
issue. A possible solution of this problem is to induce thedetached plasma in the divertor region through intentionalradiation loss. For this purpose the impurity gas puﬃng
has been attempted in various devices [1–5].
In the Large Helical Device (LHD) the complete detachment of the divertor plasma has been obtained withstrong gas puﬀ of hydrogen into the divertor region. A
salient feature of the obtained plasma in LHD is that it isaccompanied by emergence of a luminous radiation beltin the boundary region which has a helical structure andsurrounds the core plasma. Furthermore, the radiation belt
looks poloidally rotate with a frequency of, for example,
15 Hz.
Though the conditions of the discharge to obtain sucha detached plasma have been investigated in detail [6], theplasma state in the radiation belt itself is still unclear. Ourinterest is the plasma state in the strong radiation region
and its relevance to the occurrence of plasma detachment.
This paper introduces our attempt to determine the plasmastate and parameters, such as the electron temperature T eand the electron density ne , in the radiation belt from themeasured spectra in the visible wavelength range.

2Experiment

LHD is a heliotron type fusion experimental device ofmagnetic conﬁnement. It forms a steady-state structure ofmagnetic ﬁeld with a set of super-conducting coils. The
plasma has an elliptical poloidal cross section and it rotates
author’s e-mail: goto@nifs.ac.jp

with a toroidal period number of ﬁve. The major and averaged minor radii of the last closed ﬂux surface are 3.5 m–
4.2 m and 0.6 m, respectively.
We use an optical ﬁber having the diameter of 100 µm
to observe the light emitted from the plasma. One end of
the optical ﬁber is placed at the observation port, and theﬁeld of view of the optical ﬁber is collimated with a lens so
as to have a cylindrical shape with the diameter of roughly
30 mm in the plasma. The optical axis passes through theplasma center as shown in Fig. 1. The other end of the op1.0
LCMS

ergodiclayer

0.5
Z (m)

1viewing
chord0-0.5 vacuumvessel
2.0

2.5

3.0

3.5
4.0
R (m)

4.5

5.0

5.5

Fig. 1 Cross section of the vacuum vessel and the plasma forour observation. The major radius of the vacuum vessel
center is 3.9 m. The plasma is observed with a single lineof-sight shown with the arrow.

tical ﬁber is located at the entrance of a spectrometer. The
spectrometer has a focal length of 50 cm and is equippedwith three gratings of 100, 1800, and 3600 grooves mm−1 ,respectively. The spectrum is recorded with a CCD (chargecoupled device) detector. The maximum sampling rateis 200 spectra s−1 . The sensitivity of the whole observation system has been absolutely calibrated with a tungsten
lamp.

1PNBITi

0.5

1gas puff

02402

ne

1.0

PNBI (10 W)

20IH


120

23Wp

Ti (keV)

1.0
0.8
0.6
0.4
0.2
0
1.5

IH (10 phs/[m sr s])-3ne (m )Wp (MJ)

Proceedings of ITC/ISHW2007
of the Balmer γ (434.0 nm) to α lines are shown in Fig. 2.
It is readily noticed that the Balmer α line intensity
oscillates with a frequency of approximately 30 Hz whichis twice the frequency of the radiation belt rotation derived
from the AXUVD measurement. This is understandable
because in a cycle of the radiation belt rotation the line intensity should take the maximum twice when the radiation
region crosses the line-of-sight at the near side and the far
side of the plasma edge. The ratio of the Balmer γ andBalmer α lines is also found oscillating with the same frequency. This result suggests that the plasma states insideand outside the radiation belt are considerably diﬀerent.

00.1

H /H

H /H3



0.05
001

2time (s)3Fig. 2 Temporal development of the discharge for the presentanalysis. The measurement of the line-averaged electron density, ne with the interferometer is limited untilt = 1.2 s due to the fringe jump problem. The ion temperature, T i , is determined from the Doppler width of ahelium-like argon ion line.

Figure 2 shows the temporal behavior of a dischargefor which the complete detachment has been obtained. The
present experiment employs the magnetic conﬁguration ofRax = 3.65 m and Bax = 2.712 T, where Rax and Bax are themagnetic axis radius and the magnetic ﬁeld strength on themagnetic axis, respectively.
The plasma is sustained with three neutral beams (∼7 MW). The line-averaged electron density ne , which ismeasured with the interferometer, is feedback-controlledwith the gas puﬃng rate until t = 1 s. At t = 1 s a shortpulse massive gas puﬀ (∼ 0.1 s and ∼ 200 Pa m3 s1 ) is given
and ne suddenly increases. The ne measurement is unavailable after t = 1.2 s due to fringe jump problem.
After such an abrupt change in ne , the stored energy
Wp and the central ion temperature T i , which is determinedfrom the Doppler broadening of the heliumlike argon resonance line, are kept almost constant. During this stationary
time period the particle ﬂux onto the divertor plate, whichis measured with Langmuir probes, is found decreased andthe plasma detachment is suggested [7]. Simultaneously,
the measurement with an absolute extreme ultra violet photodiode (AXUVD) camera [8] suggests the emergence of arotating radiation belt [7].
Spectra of the emitted light from the plasma are measured with the 100 grooves mm−1 grating out of three. The
wavelength range of 300 nm to 700 nm is simultaneously
observed. Each emission line is ﬁtted with a Gaussianfunction and the corresponding intensity is derived as thearea of the line proﬁle. The temporal variations of theBalmer α (656.3 nm) line intensity and the intensity ratio

Collisional-radiative model

We use the collisional-radiative (CR) model code [10] forthe analysis of the obtained spectra. The CR model isbased on the rate equations concerning the excited levelpopulations. The time derivative of the population of alevel p, n(p), is expressed asdn(p) = Γin (p) − Γout (p),dt(1)where Γin (p) and Γout (p) stand for the population ﬂows into
the level p and out of the level p, respectively. These population ﬂows are explicitly written with various elementaryatomic processes as∑∑
Γin (p) =A(q, p)n(q) +C(q, p)ne n(q)q>p+

∑q<pF(q, p)ne n(q) + β(p)ne ni + α(p)n2e niq>p=∑C(q, p)ne n(q)

q<p+

∑

{F(q, p)ne + A(q, p)} n(q)q>p+ {β(p) + α(p)ne } ne ni ,(2)andΓout (p) =S (p)ne n(p) ++∑∑C(p, q)ne n(p)q>pF(p, q)ne n(p) +q<p∑A(p, q)n(p)

q<p
∑

C(p, q)ne= S (p)ne +q>p+∑q<p
{F(p, q)ne + A(p, q)} n(p),(3)respectively, where S (p), α(p), and β(p) are the rate coeﬃcients for the electron impact ionization, three-bodyrecombination, and radiative recombination, respectively,and C(p, q) and F(p, q) are the excitation and deexcitation
rate coeﬃcients, respectively, due to electron impacts fromProceedings of ITC/ISHW2007∑level p to level q. The expression q>p means that the summation is conducted over the excited levels located higher
than p.
The relaxation time of the excited level populations isgenerally so short that the left-hand-side of Eq. (1) is assumed to be zero except for the ground state and the ion.
In this case, a collection of Eq. (1) for the all excited levels is regarded as a set of coupled linear equations which
is solved readily. As the solution of the coupled equationsn(p) is found to be expressed as a linear combination of
two terms which are proportional to the ground state density n(1) and ion density ni , respectively, liken(p) = R0 (p)ne ni + R1 (p)ne n(1),quantum number of the upper and lower levels, respectively, is determined.
From the viewpoint of atomic processes, the line intensity I(p, q) is understood asI(p, q) = N(p)A(p, q),(6)where N(p) is the line-integrated population density oflevel p, and A(p, q) is the spontaneous transition probability. We adopt A(p, q) values of the NIST database [9] andderive N(p) from Eq. (6). In Fig. 4 N(p) normalized bytheir statistical weight g(p) is plotted with the solid squares
as a function of the ionization potential of the level p. In(4)ddn(1) = − ni = −S CR ne n(1) + αCR ne ni ,dtdt(5)810765n =34

12N0(p)-2

N(p)/g(p) (m )where the ﬁrst and the second terms are called the recombining plasma component and the ionizing plasma component, respectively, and R0 (p) and R1 (p), which are functions of T e and ne , are called the population coeﬃcients.
Equation (1) for the ground state atom and ion can be
rewritten in the form as

1011N1(p)where S CR and αCR are composed from the obtained population coeﬃcients and correspond to the eﬀective ionization and recombination rate coeﬃcients, respectively.
1010 04Results1020

2-3 (Hα)2-4(Hβ)2-5(Hγ)-1-2-1 -1intensity(photonsnm m sr s )Figure 3 shows the spectrum when the Balmer α line intensity takes maximum during the oscillation phase. This

10191018678
9101710 300

400500wavelength(nm)

600

700

Fig. 3 Spectrum at the intensity maximum averaged between t =1.2 s and 2.2 s.

result is the average of the spectra at the intensity maximums between t = 1.2 s and 2.2 s.
Since the observation system is absolutely calibrated,
the signals from the detector can be translated into theemitted photon number. Each Balmer series line is ﬁtted with a Gaussian proﬁle and the line intensity I(p, q)[photons s−1 m−2 ], where p and q stand for the principal

1
0.5
ionization potential (eV)

1.5

Fig. 4 Population distributions for diﬀerent three plasma statesin the discharge; the solid squares, open circles, andopen triangles are obtained for the intensity maximum
in the oscillation phase, before the detachment, and in
the plasma terminating phase, respectively. Fitting resultswith the CR model are also shown with the dashed lines.
The dotted-dashed lines, which are labeled as N0 (p) andN1 (p) are respectively the recombining plasma component and the ionizing plasma component in the total population N(p) of the ionization balance plasma for the intensity maximum case.

Fig. 4 the results derived for other two diﬀerent timings arealso shown.
We attempt ﬁttings of the all population distributionsin Fig. 4 with Eq. (4) by adjusting T e and ne . The open triangles in Fig. 4 are taken in the time period from t = 0.6 s
to 0.7 s. The population rapidly decreases with the increasing principal quantum number. This behavior is a typical characteristic of the ionizing plasma, for which eachlevel population is dominated by the second term in Eq.
(4). Since the dependence of the population distribution
on the electron temperature and density is generally weak,
it is diﬃcult to uniquely determine those parameters fromthe obtained population distribution. The dashed line is,for example, the calculation result with T e = 30 eV andne = 8×1018 m−3 which is normalized to the measurement.

Proceedings of ITC/ISHW2007

niαCR=,n(1) S CRand Eq. (4) is rewritten as{}S CRn(p) = R0 (p) + R1 (p)ne ni .
αCR(7)(8)

The measured population distribution is well ﬁtted with
T e = 1.8 eV and ne = 2 × 1020 m−3 . The ﬁtting result
normalized to the measurement is shown with the dashedline in Fig. 4. The dotted-dashed lines labeled as N0 (p)and N1 (p) correspond to the ﬁrst and second terms in Eq.
(4). Equation (8) is evaluated with these parameters andn(3)/g(3) = 7.3 × 1012 m−3 is obtained. On the other hand,
the line-integrated population N(3)/g(3) is determined tobe 1.6 × 1012 m−2 in the measurement. The normalization
factor between these quantities, ` = 0.22 m, corresponds tothe thickness of the radiation belt. This result is consistent
with that of the AXUVD measurement.
It is surprising that the strong radiation area havingsuch a low electron temperature is located inside the lastclosed ﬂux surface (LCFS), while the central T i line is kept
at approximately 800 eV. No reasonable explanation has
been found to understand the fact that such an extremely
low temperature plasma steadily exists in the conﬁnement
region of a high temperature plasma.

5Discussion

The electron temperature and density are determined
mainly from the population distribution over the n = 3 ton = 6 levels, and the points corresponding to n = 7 andhigher levels apparently deviate from the expected values
as seen in Fig. 4. Since the wavelength resolution to measure their corresponding emission lines is insuﬃcient, theuncertainty of the obtained line intensity is large. In order to make clear this uncertainness, a measurement withhigher wavelength resolution has been attempted for a similar discharge. The spectrum measured with the same spectrometer but with a grating of 1800 grooves/mm is shownin Fig. 5. The synthetic spectrum with the same plasma pa10
intensity(arb.units)

The open diamonds in Fig. 4 are the result at t = 2.85 s
in the plasma decay phase after the NBI heating is terminated. The result exhibits a typical characteristic of therecombining plasma; the populations of highly excited levels are relatively large. Roughly speaking, the slope of thehighly excited level populations corresponds to T e and thelevel having the maximum population to ne . We ﬁt theresult with the ﬁrst term in Eq. (4) and the parameters ofT e = 0.2 eV and ne = 1.3 × 1019 m−3 are obtained. The
ﬁtting result is shown with the dashed line in Fig. 4.
The solid squares in Fig. 4 show a diﬀerent distribution proﬁle from those in the former two cases. No reasonable combination of T e and ne is found for the present
case when either the pure ionizing plasma or recombining plasma is assumed. Instead, we attempt a ﬁtting under
the assumption of the ionization balance plasma. Whenthe ionization rate and the recombination rate are balanced,namely, Eq. (5) is zero, the plasma is deﬁned to be in theionization balance. The ratio of ni to n(1) is expressed as3

measuredsynthetic
102

1

10370

375

380
390
385
wavelength(nm)

395

400

Fig. 5 Spectrum at the intensity maximum with a high wavelength resolution measurement. The solid line is a synthetic spectrum calculated with T e = 1.8 eV and ne =2 × 1020 m−3 and normalized to the measurement. TheStark broadening and the instrumental width are taken
into account for each line proﬁle.

rameters as derived in the analysis above, i.e., T e = 1.8 eVand ne = 2 × 1020 m−3 , is also shown in the same ﬁgure.
Here, the Stark broadening for individual line proﬁles iscalculated with the numerical calculation data [11]. Theagreement is satisfactory in both the intensity distribution
and line proﬁles, and the plasma parameters derived here
are veriﬁed.

Acknowledgments
The authors are grateful to the LHD experimental group forthe helpful support. This study has been made in part undera ﬁnancial support by the LHD project (NIFS07ULPP527).
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