J. Plasma Fusiorr Res. SERIES, Vol.5 (2002) 409412

Transient Response of Electron Temperature
to Abrupt Plasma Edge Gooling on LHD
INAGAKI Shigeru, NAGAYAMA Yoshio, KAWAHATA Kazuo, TAMURA Naokir
KOSTRIOUKOV Yu. Artem, PETERSON J. Byron, SUDO Shigeru
and LHD Experimental Group
National Institute for Fusion Science, Toki 509-5292, Japant The Graduate University

for Advanced Studies, Toki 509-5292, Japan(Received: 14 December 2001 I Accepted: 31 July 2002)

Abstract
In the Large Helical Device, the tracer encapsulated solid pellet (TESPEL) injection has succeededto induce electron temperature perturbations. The TESPEL decreases electron temperature locally. A
small electron temperature perturbation (cold pulse) then propagates inwardly and thus it is separated
from the cooling source. The electron heat diffusivity obtained from the cold pulse propagation was thesame ol'der as the electron heat diffusivity, which was estimated from the power balance analysis.

Keywords:
transient response, TESPEL, cold pulse, temperature perturbation, ECE

1. Introduction

the temperature gradient may be a result of turbulence

The perturbative transport analysis, in which thedynamic resp()nse of the plasma to a perturbation isconsidered, can obtain the local transport coefficient.
The value obtained from transient analysis, however, isoften different from the one obtained from the steadystate (power-balance) analysis in a Tokamak [1]. The

driven by electron and/or ion gradients. Thereby thedifference in turbulence between Tokamaks and helicalsystems may explain the discrepancy between thetransient analysis and the steady-state analysis observedin Tokamaks but not in small-middle sized helicalsystems. The LHD can produce the net-current freetransient analysis usually gives a larger value. A
dependence of the transport coefficient on thetemperature gradient is one of the candidates used toexplain this enhancement of the transport coefficient.

plasmas with a wide range of gradient. Thus, the resultsfrom the LHD experiments are very important forunderstanding the transport mechanism common to all
toroidal plasmas. In this paper, the first result of theSuch a dependence on the temperature gradient leads totransient analysis in LHD using the cold pulse

power degradation of energy confinement. In small-propagation is presented and its validity is discussed.

middle sized helical systems, the power degradation has
been observed, however, such an enhancement of

To induce electron temperature perturbations in
LHD, tracer encapsulated solid pellets (TESPEL) areinjected. The cold pulses thereby are generated in theedge region of LHD. The local heat diffusivity istransport coefficient has not been observed [2]. Thereby,

it is hoped that perturbative transport analysis in thelarge helical device (LHD) will clarify whether theestimated from the propagation feature of the cold pulse.

As regards diagnostics, good temporal and spatialtransient transport coefficient is enhanced in a helicalplasma. The dopendence of the transport coefficient on@2002 by The Japan Society of Plasma
Science and Nuclear Fusion Research409

Inagaki S. et aL, Transient Response of Electron Temperature to Abrupt Plasma Edge Cooling on LHD

0.15 s. The time evolutions of stored energy, line
averaged electron density, local electron temperature
and ablation light during typical TESPEL injection areshown in Fig. 1. The change in the stored energy is lessthan 3Vo and the total input power is constant andthereby the global confinement is not affected byTESPEL injection. After TESPEL ablation, the line

resolutions are prerequisite. The electron temperature
measurement by electron cyclotron emission (ECE) suits
these requirements (time resolution is 0.01ms and spatial

resolution is about 0.02 m). A 32-channel heterodyne

radiometer is used to track the small electron
temperature perturbations. The 2nd harmonic of the Xmode is optically thick in this experiment. Eachradiometer channel is calibrated relative to Thomsonscattering measurement on similar NBI plasmas.

averaged density increases about 107o. This increase isconsistent with the contribution from the total electrons

brought to the plasma by the TESPEL. The TESPELs
typically penetrate into the radial region of rla - 0.6,

2. Transient Analysis

which are estimated from TESPEL velocities andSmall perturbations of temperature, d?i(r,t), anddensity, 6n"(r1) are considered. The mass conservationand energy conservation equations for the electron
perturbations can be written as [3],0dz"
dr-v (otl )+ dso,ablation durations (-l ms). They provide cold electrons

and impurity ions and thus reduce the electrontemperature. The cold pulses resulting from the cooling(1a)

Idg = 3.6m I-=

q-06n.
1 dd'?"*i',,.". a,= -v (aa*f eaf

6sn,)+-n{&6r:="dr_LHD #24:!53

0.f 1.5
Ep1o5
0.5
rO
r-^ 0
j4(lc),

a6r"

6,>o 100

(lb)

,(td)

i'.T=+#1"", i; )'TESPEL(5-oI

rla=O-242__1.5

ff(l)ll.Y0.431 '-d+d#l0.552--"Fand heat source rue negligible, the equation (1) in a cylindrical geometry can be written in essential form:

aar.\FIR:2

where 65o is the perturbation of the particle source and655 is the perturbation of the heat source including thechange in radiation loss and electron-ion energy exchange loss. The scale length of the perturbations is assumed to be much smaller than the equilibrium scale
length in these equations. The convective term can beneglected if D < 7, 6nJn" < df/?i and the scale lengthof the temperature perturbation is less than that of density perturbation. If the perturbations of particle sourcee ddr. 1^(z.ET^ 200
5a,Oe"= - n"I=o.7u

0.5(2)
ECE

014

3. Experimental Results

1.95

The TESPELs are injected to NBI plasmas onLHD, which have the following parameters: NBI power- 2 MW, R"" = 3.5-3.6 m, Bu* = 2.75-2.95 T, minor
radius - 0.6 m, n. = 1-2x10re m-3, f"(0) - 2 keY, tB -2

2.05

2.1Time (s)Fig. 1 Typical time evolution of plasma perturbationsderived by the TESPEL injection.

4r0Inagaki S. et al., Transient Response of Electron Temperature to Abrupt Plasma Edge Cooling on LHDof plasma traveled inward on a time-scale of l0 ms asshown in Fig. 1. The relative 4 perturbation is 3-57o in
the region of interest (rla < 0.6). The time evolutions of
the radial profile of electron density and radiation loss
are shown in Fig. 2. A typical error of the local density
is estimated from the accuracy of the Abel inversion.
The local electron density increases in the ablation
rcgion (rla > 0.6) while it doesn't change in core region

4. Simulation Results
The perturbation equation is solved numericallyand compared with the experimental result to estimate

the heat diffusivity. For simplification, the heatdiffusivity is assumed to be homogeneous. The density
profile is flat in the core region and thereby eq. (2) isreduced to the simplest form:?z!! l,,4]).
'gt"=
dt -3^rdr\'
0r l'

within the accuracy of the Abel inversion. This suggeststhat the densitl,perturbation is less than the temperature
perturbation in the region of rla < 0.6. Moreover, thetypical particle diffusivity - 0.1 m2ls, which is obtained
from gas-puff modulation experiments, is much smaller
than the typical heat diffusivity - l-3 m2ls [4], and(3)The eq. (3) is solved by using experimental data at
rla = 0.552 as a time dependent boundary. The heatdiffusivity is determined to minimize the sum of squaresof the difference between the simulation result and theexperimental result. The best fit is obtained when I is
3.3 m2ls and the simulation result is shown in Fig. 3.
The experimental result is also shown in Fig. 3. The
simulation is in good agreement with the experimental

therefore the convection is neglected. The radiation loss

is also unaffected in the region of interest (rla < 0.6).
The perturbation of particle source and heat source are
therefore negligible in this region. Hence eq. (4) is usedin the transient analysis.

Exp.

-LHD fl124353

t'" (")
1.5

I

r(=3'3""-X=4.0-4.0(/a)-LHD#243s3--1r-------1----f_N \\\Eelo- ----BeforelnJectionco--' -'- 2.00 s

AT

2.01 s-9 lo

0.5-t-2.02s

Io!

0F(b)

uO

0.01

rrr

FBefor€ lnjection
2.01sm-2.02s=ae o.oo5

II

0L0-IiAffected byTESPEL

0.2 0.4

0.6

0.8

0

rla

0.01

o.o2 0.03 0.04
t-t (s)oFig. 2 Radial profiles of (a) electron density and (b)Fig. 3 Time evolution of electron temperature measured
with heterodyne radiometer. The TESPEL is in-radiation power density.

jected at t = fo. The simulation results are also
shown.

4tr

Inagaki S. et al., Transient Response of Electron Temperature to Abrupt Plasma Edge Cooling on LHD

5. Discussion

6The Tokamak like power degradation has beenobserved in LHD [5]. And thus the enhancement of theTransient Response
atransport coefficient determined from transient analysis
is expected. However an enhancement of heat diffusivity
has not been observed in the cold pulse experiments on4€,3LHD. In W7-AS, the same value for the electron

X= 4.0-4.0(rla)><4diffusivity was found from power balance and transientanalysis [2]. Instead of a local model, the global modelof y is employed to interpret the observed power
degradation in W7-AS [2]. Unfortunately the firstz
Power Balance

00.2 0.4 0.6

0.8

experiments of cold pulse have been carried out under alow heating power and therefore the experimental data
are insufficient to compare with theoretical models in1rlaFig. 4 Comparison between the transient analysis andthe power balance analysis.

LHD. In the near future it is expected that further
experimental work will be carried out.

6. Summary
To understand the transport in magneticallyresult. The transient analysis should be compared withthe power balance analysis to see whether the transienttransport coefficient is enhanced in LHD. The radial
profile of electron heat diffusivity, which is determinedfrom the power balance analysis, is shown in Fig. 4. The
equilibrium T" and n" profiles just before the TESPEL
injection are used and the beam power deposition profile
is calculated numerically in the power balance analysis.
The difference in magnitude of 7 between the transient
analysis and the power balance analysis is small in theregion of 0.552 < rla < 0.242. The power balance 7 iswritten as X = 44(rla) in the region of 0.552 a rla 3O.242 and the simulation using this model of 7 is also
shown in Fig. 3 to compare the transient analysis withthe power balance analysis more directly. The simulation result does not differ greatly from the experimentalresult. However, the homogenous model is better thanthe power balance model as shown in Fig. 3. This may
suggest that the transient analysis gives the radial profileof 7 different from the power balance analysis in theLHD. The heat diffusivity from transient analysis may
depend on the employed model of y. A more suitablemodel is left to future work. It must be emphasized stillthat the agreement between the magnitude of ; from thetransient analysis and the power balance analysis indicates that the propagation of cold pulse can be explainedby the heat diffusive nature.

confined thermonuclear plasmas, the transient transport
analysis is important as well as the steady-state transport
analysis. In the Large Helical Device, the TESPEL isinjected to induce electron temperature perturbations.
The TESPEL typically affects the radial region of rla >0.6. The cold pulse resulting from the cooling of theedge plasma propagates inwardly in the region of rla >
0.6, while the electron density and other parameters are
essentially unaffected in this region. The cold pulse is
separated from the cooling source and radiating source,and hence the simple model is used to simulate theelectron temperature perturbations. The electron heatdiffusivity obtained from the simulation method is thesame order as the electron heat diffusivity, which isestimated from the power balance analysis.

References

lll K.W. Gentle, Phys. Fluids 31, 1105 (1988).
l2l L. Giannone et al., Nucl. Fusion 32, 1985 (1992).
[3] N.J. Lopes Cardozo, Plasma Phys. Control Fusion
37,799 (1995).

t4l K. Tanaka et al., J. Plasma Fusion Res. Series 4,421 (200t\.
[5] H. Yamada et al., Phys. Rev. Lett. 84, 1216 (2000).

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