J. Plasma Fusion Res. SERIES, Vol.3 (2000) 99-103

Modeling of lmpurity Radiation and Transport
during Long Pulse 'Breathing' Plasmas in LHD
PETERSON Byron J.*, RICE John E.r, YAMAZAKI Kozo, NAKAMURA Yukio, NODA Nobuaki,
TAKEIRI Yasuhiko, GOTO Motoshi, IDA Katsumi, NARIHARA Kazumichi, TANAKA Kenji, SATO Kuninori,
SHOJI Mamoru, MASUZAKI Suguru, SAKAKIBARA Satoru, OSAKABE Masaki, FUNABA Hisamichi,
OKA Yoshihide, KANEKO Osamu, TSUMORI Katsuyoshi, SATO Motoyasu, SHIMOZUMA Takashi,
KAWAHATA Kazuo, OHYABU Nobuyoshi, SUDO Shigeru and MOTOJIMA Osamu
National Institute for Fusion Science, Toki-shi, 509-5292, JA4AN
lPlasma Science & Fusion Center, Mass. Inst. of Tech.,
Cambridge, MA 0213g-42g4, USA(Received: 18 January 2000 / Accepted: 15 May 2000)

Abstract
During long pulse plasmas with a stainless steel divertor in the Large Helical Device (LHD) a slow
oscillation (t = 1.5 s) known as the 'Breathing' Plasma has been observed. Expansion and contraction
observed in the CCD video images are from changes in the radiating volume of the light impurities dueto fluctuations of the edge electron temperature. Modeling of the radiation shows that the core irondensity varies by a factor of three while carbon and oxygen densities remain constant.

Keywords:
LHD, long pulse, impurity transport, radiation

1. lntroduction[5]. In doing so we aim to learn about the role that
impurities are playing in this oscillation.
During the second experimental cycle of LHD an
oscillation in the major plasma bulk parameters wasobserved during long-pulse neutral-beam operation
which is known as the 'breathing' plasma. An exampleof the electron temperature profiles, line-averageddensity, total radiated power and light impurity line
radiation signals during a 'breathing' plasma oscillation
having a period of about 1.5 seconds is shown in Fig. 1.
One striking feature of this oscillation is the relationshipbetween the density, the total radiated power and thespectroscopic signals of the light impurities during therising phase of the density. In a typical LHD discharge

Impurity accumulation is an important issue for thesteady state operation of fusion devices as it can lead toincreased radiation and premature termination of thedischarge through radiative collapse as well as dilutionof the fueling gas. Evidence of this has been observed intokamaks, particularly in the high confinement regime[1]. Heavy impurities in particular have the ability toradiate at higher temperatures and therefore can cool thecore plasma [2]. The effect of lighter impurities islimited to the edge plasma and therefore is lessdetrimental to the plasma performance. This was seen in
the Heliotron-E stellarator through the effect of a carbon
limiter on the reduction of metallic impurities [3]. In thispaper we model the impurity radiation and transport in
LHD [4] during a long pulse discharge where a slowoscillation known as the 'breathing' plasma is observed*the radiated power rises with the line averaged density
until a density limit is reached and the plasma collapses

C orre sponding author' s e -mail : peterson@ LH D.nifs.ac.jp

99@2000 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchPeterson B.J. et al., Modeling of Impurity Radiation and Transport during Long Pulse 'Breathing' Plasmas in LHD't.0

10-25

0.8o:t....

- -trFe\-\'-./ \g)

0.6

Elo -26
O0.4=

r10 -27

o.2
0.0

1.0I

E10-289o 0.5ac 0.0600

J 400=E(L(.)

10.,^*f.oo1000

Te (ev)
Fig.2 Cooling rates vs I from ADPAK for carbon,

2000
4.0100oxygen and iron.

4.5 5.0 5.5 6.0

6.5

time (s)examine the cooling rates, Lz, as a function of theelectron temperature, 2", based on the average ionmodel, assuming coronal equilibrium [7]. These areshown in Fig. 2 for the intrinsic impurities, carbon,oxygen and iron. The impurity emissivity, 52, can becalculated from L2,2", the impurity density, n2, and theFig. 1 Time histories for shot 6690 of {a) electron
temperature profiles, {b) line-averaged density. (c)total radiated power. Cu, and Ou.

radiatively [6]. However, in the 'breathing' plasma,during the rising phase of the density the total radiatedpower is seen to rise initially reaching a peak and thento decrease while the density continues to rise.

electron density, rz", usingSz = flz n" Lr(T") .

Meanwhile as the total radiated power decreases the line
radiation from the light impurities, carbon and oxygen,increases sharply. This suggests two things. First of all
the decrease in the total radiated power as the radiationfrom light impurities increases indicates that iron, the(l)From looking at the cooling rates one can see thatcarbon peaks at 6 eV, oxygen at 2O eV and irondominates over the other two impurities for electron
temperatures greater than 50 eV.

3. Behavior of Carbon and Oxygen

other intrinsic impurity, is strongly contributing to thetotal radiated power. Secondly the decrease in theThe first observations of the 'breathing' plasma
appeared in the real-time CCD images which showed apulsation in the visible radiation with a period of 1.5 s.
This observation led to the name 'breathing'. The video
signal can be divided into two phases. In one phase (Fig.
3a) the visible radiating region is seen to broaden andcontract in minor radius while brightening. In the otherradiated power as the density increases indicates that theradiation from iron is decreasing rapidly due to either achange in the electron temperature decreasing thecooling rate or a decrease in the impurity density. In thispaper, using profile data from bolometer arrays forradiated power, UV line radiation measurements of thelight impurities, visible CCD video images, Thomson

phase (Fig. 3b) the radiating region narrows andexpands in minor radius while becoming dimmer.
Examination of the electron temperature profile
evolution shown in Fig. I can give a better
understanding of the video images. At t = 5.25 sscattering for electron temperature and FIRinterferometer for density, we investigate the roles that
impurities may be playing in this oscillation.

2. Gooling Rates for lmpurities from ADPAKIn order to understand the relative role that
impurities are playing in the plasma it is instructive to(corresponds to Fig. 3a) the electron temperature is at aminimum. The drop in the electron temperature at theedge results in the minor radially inward motion and100

Peterson B.J. et al., Modeling of Impurity Radiation and Transport during Long Pulse 'Breathing' Plasmas in LHD

1.5=.

6do

1.0otr

U 0.5
L!

o 0.0-t 0.50

Fig.3 Tangentially viewing CCD video image of shot
6690 at t = (a) 5.25 s and (b) 5.75 s.

do 0.40otu

broadening of the radiating region for light impurities
which corresponds to the area above the thick 50 eV
contour in Fig. 1a. This explains the peak in the light
impurity signals in Fig. lc and the image seen in Fig. 3a
as described earlier. During this period the electron
density is growing which also contributes to the increasein radiation. At t = 5.75 s (corresponds to Fig. 3b) thec 0.30
E+,

u0p!.
(r-0,20
0.10
0.00

4.5

electron temperature is near its maximum as seen in Fig.

la. This results in the radiating region for light

5.0t (s)5.5

6.0

Fig. 4 Line radiation brightness from shot 6690 for (a) Ov
and (b) C,u with transport model (*).

impurities becoming smaller and moving to the lowdensity region outside the last closed flux surface inagreement with the image seen in Fig. 3b. The
consequent reduction in the radiation from light
impurities is evident in Fig. 1c.
In order to determine what role the carbon andoxygen impurity densities may be playing in thisoscillation we have modeled the C111 and Oy signals.
This modeling was carried out using the MIST [8]transport code to determine the charge state density

profiles from the electron density and temperature
profiles and assuming a spatially invariant diffusion
coefficient of 0.2 m2ls and no inward convection (v =0.0 m/s). The emissivity profiles for the transitions inquestion can then be calculated using the collisionalradiative model of the LINES [9] code which are thenintegrated along the line of sight to give the brightness
time histories. The results of this modeling are shownwith the measured lines in Fig. 4. It was assumed thatboth the diffusion coefficient and the total impurity
densities were constant in time. The agreement between
the measured and calculated brightness histories
indicates that both of these assumptions are correct towithin the errors of the measurements. This means thatthe change in the brightness of the light impurities
during the oscillation is due mainly to the change in theelectron temperature and density and not due to largechanges in the impurity density and transport.
Besides these data from the ultraviolet, visible

r0060time (s)Fig. 5 Line radiation brightness from shot 6690 for C6tand Cs* at R = 4.025 m and Ou and Ho.

emission from fully ionized carbon (C6*) shows that
there is only about a20Vo change in the carbon density,
as seen in Fig. 5. On the other hand, C5*, which has adependence on the electron temperature, shows a muchlarger variation similar to that seen in Oy and Cn1.

r0lPeterson B.J. et al., Modeling of Impurity Radiation and Transport during Long Pulse 'Breathing' Plasmas in LHDt.2

4. Behavior of lron lmpurity
While carbon and oxygen should radiate from the1ot3/cms)

1.0

low temperature edge plasma, iron should dominate theradiation inside r = 0.8 where T" > 50 eV. Therefore wecan calculate the iron density profile evolution for thisregion from the measured radiated power, electron
density and temperature profiles and the iron coolingF. 0.8 \. ,:r..(n--$7'r'-ft/a\tr 0.6otr o.4

rate from Fig.2 using Eq. l. The result of thiscalculation at r = O.4 is shown in Fig. 6. One notes incontrast to the light impurities that the iron density iso.20.0

strongly oscillating in time, varying by a factor of 3 inamplitude. The oscillation in the emissivity at this radius
can be nearly completely attributed to the oscillation in
the iron density as the electron density is'oscillating outof phase and the temperature dependence of the iron(u)nr"(1otr/cm3)

25o'EC',

20. l5E!

Iv,cooling rate at this temperature range is weak. The time
derivative of the electron temperature is well correlated

l0504.O

with the amplitude of the iron density indicating thatradiation from iron is cooling the plasma at this radius.

4.5 5.0 5.5 6.0 6.5time (s)Additional data from the vacuum ultraviolet region
for a similar shot show radiation from iron oscillatingout of phase with that from the lighter impurities as seenin Fig. 7. This is in agreement with the phasing of theradiation at p - 0.4 shown in Fig. 6 compared with thephasing of the lighter impurities shown in Fig. 1. Also,
similar oscillations have been observed in spectorscopic
signals from F"xy1 [10].

Fig. 6 Local parameters at p = 0.4 from shot 6690 (a) Inn nr" and (b) S-r.

roEoq
C

5. Gonclusions and Discussion

jThe expansion and contraction evident in the video
images of 'breathing' plasma are due to the motion andoO

ithe change in size of the radiating volume for light
impurities resulting from the rise and fall of the edgeo.

electron temperature. However, transport analysis of thejd=

light impurities shows that their densities are not,,, *-:l:*:::"*"-rtr#tEIochanging significantly during the oscillation. On theother hand, calculation of the core iron density showsthat it is changing significantly and its radiation is
cooling the core electrons. Therefore we conclude thatiron is playing a major role in this oscillation in contrast
to carbon and oxygen whose radiation is oscillating only

jd-qdQ.Olx)z^.-t:.

,r,t..
..r'(d) r,-.- -t{)-.-.-'"''--.:
5.0

in reaction to the change in the edge electron
temperature and density. The most likely candidate forthe source of iron is the stainless steel divertor as thisoscillation was only seen in experiments before theinstallation of carbon divertor tiles.

5.5,r.0

timc (:)

4.5

5.0

Fig. 7 Global parameters and spectroscopic signals fromshot 6650.

performing the experiments.

Acknowledgment
We would like to thank the member of LHD
Experimental Groups I and 2 for their cooperation in

References

tll G. Fussman et al., J. Nucl. Mater. 162, 14 (1989).
t02

Peterson B]. et al., Modeling of Impurity Radiation and Transport during[2] R.J. Hawryluk et al.,Nucl. Fusion 19, 1307 (1979).
t3l K. Kondo et aI., J. Nucl. Mater. 196-198, 303

Long pulse .Breathing' plasmas in LHD

t7l D.E. Post e/ al., At. Data Nucl. Data Tables 20,397(r977).

(1992).

[8] R.A. Hulse, Nucl. Tech./Fus. 3,259 (1983).
[9] M.A. Graf, Ph. D. Diss., MIT (1995).

t4l O. Motojima et aI.,Phys. Plasmas 6,1843 (1999).
t5l Y. Takeiri et al.,Plasma Phys. Control. Fusion,42,[10] S. Morita and M. Goto, Ann. Report of National
Inst. for Fusion Science, (1999) p. 151.

r47 (2000).

[6] B.J. Peterson et al., Proc. 26th EPS, Europhysics
Conl Absts. 23J,1337 (1999).

r03