Proceedings of ITC/ISHW2007

Behavior of CIII to CVI emissions during recombining phaseof LHD plasmas
Malay Bikas Chowdhuri, Shigeru Moritaa and Motoshi Gotoa
Department of Fusion Science, Graduate University for Advanced Studies,
Toki 509-5292, Gifu, Japana

National Institute for Fusion Science, Toki 509-5292, Gifu, Japan(Received 15 October 2007 / Accepted 15 October 2007)

Carbon emissions of CIII-CVI during recombining phase of the Large Helical Device (LHD) plasma are studied
to understand their behaviors. For the purpose four resonance transitions of CIII (977Å: 2s2 1S-2s2p 1P), CIV(1550Å: 2s 2S-2p 2P), CV (40.27Å: 1s2 1S-1s2p 1P) and CVI (33.73Å: 1s 2S-2p 2P) are observed using absolutely
calibrated VUV monochromators and EUV spectrometers. One dimensional impurity transport code has beenused to calculate the spectral emissivity under the consideration of measured ne and Te profiles. The temporal
evolution of line emissions have been calculated and compared with the measured data. The comparison showsthat the carbon density is 3% to ne. However, the discrepancy between the calculated and measured values has
been noticed in CIII and CIV. It has been argued that three dimensional structures of CIII and CIV emissions arelikely to be the reason for this difference, which is based on the presence of relatively high-density andhigh-temperature plasmas in edge ergodic layer in LHD. It is also found that the CVI emission duringrecombining phase increases with ne whereas it is nearly constant during steady state phase suggesting thedisappearance of the edge particle screening effect.
Keywords: impurity, carbon, intensity computation, recombining phase.

1. Introduction
For the study of the impurity behavior in hightemperature plasmas impurity densities in each charge state
are usually analyzed using spectral absolute intensities
measured from spectroscopic diagnostics in combination
with a one-dimensional impurity transport code [1]. It
evaluates radial profiles of charge state and emissivity
based on measured electron density and temperature
profiles. In general the impurity transport studies havebeen done during the steady-state phase of discharges
using either of intrinsic or extrinsic impurity particles [2-5].
When the impurity time behavior is analyzed at thetransient phase, especially the plasma termination phase,the time duration is very short in the case of tokamaks
because of the abrupt disruption after the current
termination. Even if the toroidal current is controlled forthe smooth termination of the plasma, the magnetic field
topology and resultant magnetic surface structure change
so much as a function of time. In stellarator cases, on theother hand, the magnetic field for the confinement isexternally supplied and maintains steadily even during thetransient phase of the discharges. The temporal evolutionof impurity emissions from such plasmas can be easily
author’s e-mail: chowdhuri.malayl@nifs.ac.jp

computed under the presence of steady magnetic surface.
In the Large Helical Device (LHD) the helicalmagnetic field for the plasma confinement produced bysuperconducting magnetic coils makes possible the steadystate operation. The analysis is of course possible on thetransient period at initial and final phases of the discharges.
In such period the temporal variation of electron and ion
densities is mainly governed by atomic ionization andrecombination processes instead of the particle transport[6]. Therefore, the absolute intensities of edge spectral
lines emitted from fueling gas and impurities can bebasically converted to respective ion densities even if theedge temperature and density profiles are not measured indetailed. In this paper temporal behavior of edge carbon
emissions is studied during the recombining phase of LHD
discharges and the carbon density measurement isattempted with analysis of the carbon emissions as afunction of ne.

2. Experimental Setup
The experiment has been conducted with inwardly
shifted configuration of Rax=3.6m and Bt= 2.75T. A
discharge is initiated by electron cyclotron heating (ECH)Proceedings of ITC/ISHW2007
and the plasma is sustained by three negative-ion-based
neutral bean injection (NBI) devices.
Severalspectroscopic diagnostics covering visible to X-ray
wavelength ranges have been installed to monitor andstudy the impurity behaviour of LHD discharges. In thepresent study emissions from different ionization stages ofcarbon have been measured using two extreme ultra violet(EUV) spectrometers [7, 8] and two vacuum ultra violet(VUV) monochromators [9]. Two absolutely calibrated
EUV spectrometers cover 10−130Å (EUV_Short) and50−500Å (EUV_Long) wavelength range, respectively.
Back-illuminated VUV sensitive charge couple device(CCD) detectors are mounted with two EUV spectrometers
and operated in full binning mode. Data from the CCD
have been acquired in every 5 ms. Four resonancetransitions of CIII (977Å, 2s2 1S-2s2p 1P), CIV (1548Å, 2s2S-2p 2P), CV (40.27Å, 1s2 1S-1s2p 1P) and CVI (33.73Å,1s 2S-2p 2P) are mainly monitored for this study. TheCV and CVI emissions are measured using the EUV_Short
spectrometer with a spectral resolution of ~0.10Å at 40Å.
The resonance transitions from Li- and Be-like carbon ionsare observed using two 20cm normal incidence VUVmonochromators equipped with an electron multiplier tube
detector. The signal is acquired with time interval of100μs. The two VUV monochromators were absolutelycalibrated using the carbon emissions by comparing theraw signals with the absolutely calibrated EUV_Long
spectrometer for 50−500Å. Two experimental intensity
ratios of 2s2-2s3p (386.4Å) to 2s2-2s2p (977Å) transitions
from CIII and of 2s-3p (312.4Å) to 2s-2p (1550Å)transitions from CIV were adopted for the calibration.
Electron temperature and density profiles measured with
Thomson diagnostics and line-integrated electron density
measured with FIR diagnostics are used for the presentanalysis.

3. Description of Calculation
Analysis on temporal behaviors of carbon emissions
in different ionization stages are based on the calculation of
the line-integrated emissivity using one-dimensionalimpurity transport code [1]. The time behavior of theimpurity density profile is calculated by the following
equation with the ionization balance of an impurity ion;

∂n q
∂t( )

1∂
rΓq + α q −1n q −1n er ∂r+ β q +1n q +1n e − α q + β q n q n e=−

()

(1)

where nq and Γq are the ion density and particle flux of qth
charge state, respectively. The parameters of α and β
represent the ionization and recombination rate coefficients,respectively. The empirical transport model [10], of
which the validity was confirmed in LHD, using thediffusion coefficient D and convective velocity V is givenby;Γq = − D q (r )∂n q∂r+ Vq (r )n q(2)

rand Vq (r ) = − V (a ) .
a(3)Here, a, Dq and Vq are the plasma radius, diffusion
coefficient and convective velocity, respectively.
After the charge state calculation the emissivity andbrightness profiles of emission line was evaluated. The
emissivity of transition from level j to i, ε(i,j), isexpressed by the relation of ε(i, j) = Nq(j)A(i, j), where A(i,j) is the transition probability and Nq(j) is the density of thelevel j in charge state q. The emissivity is calculated fromthe level-population in the upper level.
Thelevel-population is generally determined by the collisionaland radiative processes among several quantum levels [11].
However, the coronal model is assumed in the present casefor the simplicity. This assumption really gives a good
agreement with the C-R model calculation, at least, for theH- and He-like systems. Therefore, the relation can bewritten as E(i,j) = Nq(j)A(i, j) = nqneQ(i, j), where Q(i, j) isthe excitation rate coefficient for the transition of i to j.
The excitation rate coefficient for individual line has beentaken from calculated results by Itikawa et al. [12].

4. Results and Discussions
A typical waveform of NBI discharge used in thepresent impurity study is shown in Fig.1. The time
evolution of carbon emissions has been analyzed at therecombining phase from 2.45s to the end of the plasma
termination, where the Te quickly decreases due to theabsence of the heating source while the ne stays constant.
The central electron temperature Te(0) measured byThomson scattering diagnostic was available until
t=2.620s. The CV and CVI emissions, on the other hand,
dropped to zero at 2.628s, and the CIII and CIV emissions
disappeared 15ms later because of their low ionizationenergies (I.E.) (CIII: 50eV, CIV: 68eV, CV: 367eV andCVI: 475eV). Extrapolation of the measured Te wastherefore necessary to calculate the emissivity of thecarbon emissions in different ionization stages. The Te
was calculated from magnetic energy and line-integratedelectron density <ne>. The measured and extrapolated
Te(0) and plasma radius rb at horizontally elongated plasma
cross section are plotted in Fig.2. The Te(0) and theplasma radius gradually decrease, and after t=2.550s theTe(0) begins to drop quickly. The CIII and CIV emissions
also start to increase rapidly at t=2.550s.
Temporal evolution of carbon emissions during therecombining phase has been calculated using
one-dimensional impurity transport code. The calculation
has been done on the averaged magnetic surface byProceedings of ITC/ISHW2007

Fig.1 Typical discharge for the present analysis; (a)plasma stored energy and heating pulses, (b)line-averaged electron density (solid line) andcentral electron temperature (dashed line), (c)CIII (solid line) and CIV (dashed line) emissionsand (d) CV (solid line) and CVI (dashed line)
emissions. All carbon emissions have unit of1014 photons.cm-2.sr-1.s-1. Data between t=2.45s
to 2.65s are used for analysis.
replacing the elliptical shape of LHD plasmas with thecircular shape. In this study the diffusion coefficient Dq isconsidered as an independent of q and r, and the inward
convection velocity Vq is as a function of r. Here, themaximum value of Vq is given as V(a) at average plasma
radius a (see Eq.3). The values of Dq and V(a) are taken
to be 0.2m2s-1 and 1.0ms-1 for the diffusion coefficient andinward convective velocity, respectively.
Figure 3 illustrates the total radiation power emitted
from Be-like CIII to H-like CVI, which are obtained byintegrating the whole plasma surface of LHD. The
experimental and calculated results are indicated with solidand dashed lines, respectively. In the calculation 3%
carbon density is assumed to the electron density. All thecarbon radiations gradually increase after turning off theheating power as the Te decreases. At first the CVIemissions reach the peak value at 2.60s where the Te(0) is280eV. This is in good agreement with the calculation.
Then, the CV and CVI radiations quickly decrease andbecome zero immediately at 2.625s. At this moment theTe(0) drops less than 150eV. The calculation of CV andCVI radiations also drop at 2.630s. Since the exposure
time of CCD detector is 5ms in the present experiment, thedifference between the measurement and calculation may
originate in the uncertainty of the time window.

Fig.2 Time behaviors of central electron temperature(Te(0): circles) and horizontal plasma radius (rb:diamonds) at horizontally elongated plasma
cross section during recombining phase.
Closed circles and diamonds means measured
values, and open circles and diamonds mean
extrapolated values.

Fig.3 Calculated and experimental total radiation
power of CIII to CVI. Dash and solid lines
indicate calculated and experimental data.
On the other hand, dynamic range of the CIII and CIV
emissions is really large compared to the CV and CVIcases. The voltage applied to the SEM is always adjusted
to monitor the main discharges, not the plasma termination
phase. Then, the signals of CIII and CIV are always
saturated at the plasma termination phase as seen during
t=2.628-2.632s in the figure. The calculation of CIII andCV radiations reach the peak value at 2.632s when theTe(0) becomes 12eV. The calculation after 2.633s is,however, impossible in practice, because of the extremely
low electron temperature. In the discharge very lowtemperature plasma is maintained until t=2.645s asapparently seen in the CIII temporal behavior.
During steady-state phase of discharges the carbonemissions are basically located inside the narrow shell atplasma edge. In LHD the CIII and CIV generally exist inProceedings of ITC/ISHW2007

Fig.4 Radial profiles of ne and Te ((a) and ((d)),
densities ((b) and (e)) and emissivities ((c) and(f)) of CIII to CVI taken at two different timeframes of 2.60s (a, b and c) and 2.63s (d, e andf). Abscissa means normalized radius, ρ.
the ergodic layer [13] surrounding the main plasma and theCV and CVI exist near the last closed flux surface (LCFS).
During recombining phase the width of the emission shells
is broaden as the Te decreases, and moves inside becauseof the reducing plasma size, as shown in Fig.2.
Calculated results on the radial profiles of carbon densities
and emissivities are shown in Fig.4. Figure 4 (a)-(c) and(d)-(f) are the radial profiles at t=2.60s and 2.63s in Fig.3,respectively. The CVI emission takes the maximum
value at 2.60s and the CV and CVI entirely disappear at
2.63s. Fig. 4(a) and (c) are the measured ne and Te
profiles used in the calculation. The CIII and CIV are
always located at the plasma edge in these time frameswith sharp peaks.
On the other hand, the CV and CVI emission profiles
are quite different. At t=2.60s the shell widths of the CVand CVI densities become wider (see Fig.4 (b)), andresultant emission profiles also become much wider (seeFig.4 (c)). Especially the tendency is remarkable to theCVI emission profile, because the excitation coefficient of
CVI quickly drops at Te<200eV. This effect can be seenin the difference at the peak positions of CVI density andemissivity profiles (ρ=0.67 and 0.63). At t=2.63s the CV
and CVI emissions entirely disappear as seen in Fig.4(f),whereas the CV and CVI densities increase at the plasmacenter (see Fig.4(e)). The excitation rate coefficient ofFig.5 CVI intensity (closed circles) and CVI/(ne*Q)(open circles) plotted against line-averaged
electron density <ne> for (a) recombining and(b) steady state phases. Value of Q means
excitation rate coefficient of CVI.

Fig.6 CIII intensity against line-averaged electron
density <ne> for recombining (closed circles)
and steady state phases (open circles).
CVI at Fig.4(f) (Te(0)=70eV) decreases 30 times compared
to Fig.4(c) case (6×10-17m3.s-1 at Te(0)=280eV).
Calculation of the total radiation power from the CV
and CVI shows the good agreement with the experiment
under assumption of 3% carbon density. However, theCIII and CIV results are ten times larger than theexperimental values. The reason is not fully clear atpresent. At least it is known that the emission distribution
from low ionized ions and neutral atoms is toroidally andpoloidally inhomogeneous because of the presence of theProceedings of ITC/ISHW2007
ergodic layer. Indeed, recent studies indicate that theemissions from CIII and CIV have the asymmetric featuresreflecting the field line structure of the ergodic layer [14].
Especially, the vertical profile of CIV exhibits four peaks.
The four peaks are formed at the inboard side near theX-point in addition to the top and bottom edge peaks at thehorizontally elongated plasma cross section. It is reported
that the particle recycling is enhanced at the inboard side[15]. It is also observed that the inhomogeneous poloidal
distribution of neutral emissions arises mainly frominhomogeneity in the neutral particle density, not from thenonuniformity of the electron temperature and density [16].
This is likely to be one of the reasons for the difference.
Finally the CVI emission is examined for several
discharges at the peak value during the recombining phase,where the plasma begins to shrink and the size becomes alittle smaller than the LCFS. The CVI emission during
steady-state phase is also studied for the comparison.
Intensities of CVI are plotted against <ne>, as shown inFig. 5(a) and Fig. 5(b) for the recombining and steady statephases, respectively. CVI intensities normalized to theelectron density <ne> and excitation rate coefficient, Q,(CVI/(ne*Q), which means the carbon density of CVI), arealso plotted in the figures. The excitation rate coefficientis calculated against the electron temperature at the LCFS
for steady state phase and at the central electron
temperature for recombining phase. This choice isreasonably correct since the CVI emission location isestimated from the CV radial profile. The difference
between two phases is very clear. The CVI intensities
from recombining phase increase with <ne> but those fromsteady-state phase decrease with <ne>. Thus, we find aclear difference in the carbon density behavior with <ne>.
That is to say, the CVI density is nearly constant with <ne>for recombining phase, but it definitely decreases with<ne> for steady state phase. On the other hand, the CIII
intensities, which suggest the carbon influx for the ionizing
plasma like during steady state phase, increase with <ne>for both phases, as shown in Fig.6. The CIII intensities
for recombining phase are saturated at densities greaterthan 5×1019 m-3. The reduction of the CVI density forsteady state phase may suggest the impurity screening
effect. Increasing the density in the ergodic layer, thefriction force becomes large, which leads to the impurity
screening.
In case of the recombining phase theunderstanding of carbon emissions is not really simple,
because the CIII emissions do not indicate simply theinflux. In addition, the origin of the carbon source is very
unclear since the plasma shrinks and is completely
detached from the divertor plates and vacuum wall. We
need further investigation on the study of carbon behavior
during the recombining phase.

4. Summary
Temporal evolution of carbon emission during therecombining phase of the discharges has been studied
through the calculation of spectral emissitvity using 1-dtransport code. From the calculation of CV and CVI
radiation it indicates that carbon density is 3% of electron
density, ne. The discrepancy between computed andexperimental CIII and CIV radiation has been found.
Although the reason behind this is not fully clear it isargued that the three dimensional structure of CIII and CIV
emissions might be responsible for the differences alongwith localized sources of carbon. Comparison of CVI
emissions during steady state and recombining phasereveal its different dependence with ne. From thisobservation it is also suggested that impurity screening
effect increases with ne during the steady state phase and it
disappears during the recombining phase of the discharges.

Acknowledgements
The authors would like to thank the members of LHD
experimental group for their technical support. This work
was carried out partly under the LHD project financial
support (NIFS06ULPP527).
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