J. Plasma Fusion Res. SERIES, Vol. 3 (2000) 431435

The Study on the Neoclassical Transport Analysis
using ECE Measured Temperature Profiles in the
LHD Long Pulse Plasma
SASAO Hajime*, WATANABE Kiyomasar, INAGAKI Shigerur. NAGAYAMA Yoshior. PETER. C. de Vriesr.

TANAKA Kenjir, TOKUZAWA Tokihikor, KAWAHATA Kazuor, NARIHARA Kazutor, YAMADA lchihiror,
IDA Katsumir, KADO Shinichirour, KUBO Shinr, KoMoRI Akior, YAMADA Hiroshir,
KANEKO Osamul, MOTOJIMA Osamur and LHD Exp. Group I and 2Department of Fusion Science, The Graduate University for Advanced Studies, Toki-shi, JapanlNational Institutefor Fusion Science, 322-6 Oroshi-cho, Toki-shi, 509-5292, Japan(Received: 18 January 2000 / Accepted: 19 April 2000)

Abstract
The purpose of this paper is to show the change of the neoclassical transport and the radial electricfield in the long pulse LHD plasmas by using the experimental ECE data. The neoclassical heat flux,
which the neo-classical theory predicts, changes due to the change of the radial electric field. The
increase of H ions injected by Neutral Beam Injection (NBI) in He discharge produce effect on theelectric field. There is the threshold of H quantity on the change of the electric field polarity.

Keywords:
ECE, neoclassical transport theory, radial electric field

the plasma from the inboard to outboard sides. The

1. lntroduction
In long pulse NBI helium discharge, the density ofelectron cyclotron wave, which is emitted from the torus
inner electron cyclotron resonance region, is absorbed in
the outboard resonance region. Therefore, it is difficult
to measure the electron temperature of the torus region
from the outside ports with the ECE diagnostics. Wehydrogen increases with the extension of the dischargetime. For example, in the case of 10 keV and I MW

NBI discharge, the quantity of the injected H is about 2x l0l8 m-2 s-r in 30 m-3 devices. In He plasmas, it isinstalled an antenna at the inner torus port of the LHD
in order to measure the emission of the electron
cyclotron wave that propagates to the center of torus.
The ECE inner antenna is designed with gaussian beam
optics and is based on the concept of the constant phase,
proposed by S. Kubo et al. [l]. This concept indicatesthat the surface of the antenna is decided by thefollowing condition; the sum of the microwave phases
calculated from two points, which are the start point andthe end point of the wave trace, is constant on thepossible that this increment of H affects the transport ofions and electrons, which leads to the change of radial

electric field polarity according to the ambipolar
condition. In this paper, we apply the ECE data to study
the change of the neoclassical transport and the radial
electric field in the long pulse LHD plasmas.

2. The EGE Diagnostics
The LHD has two electron cyclotron resonanceregions in the equatorial plane because magnetic fieldstrength does not change monotonically when traversing@2000 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author's e-mail: hsasao@ ms.ntfs.ac.ip431

Sasao H. et al., The Study on the Neoclassical Transport Analysis using ECE Measured Temperature Profiles in the LHD Long Pulse Plasma

the ion temperature I and the electron density n". The
electron and ion neoclassical thermal conductivity X;or*, X"_,on-*, in non-aximmetric magnetic configuration
are given by,antenna surface.

In this study, the electron temperature profile ismeasured with a 32ch-heterodyne radiorieter. It covers

the fundamental harmonic of O-mode emission in thefrequency range of 64-86 GHz in the case of Bo = 2.75
T operation [2]. The ECE electron temperature iscalibrated with the data obtained bv the Thomson

X,oon-*=-Qi' I n,Y T, ,(5)

X"_non_*=-Qi'ln"YT".

(6)

scattering measurement.

4. The Experimental Results
4.1 Neoclassical transport in long pulse

3. Neoclassical Transport and the Radial
Electric Field
The neoclassical radial electric field in theplasmas

In order to study the behavior of the neoclassicaltransport, we analyze a typical example og a long pulse
discharge. The discharge starts by ECH and it has been

heliotron/torsatron plasmas is decided by the ambipolar
condition:

I z"ry=g,

sustained by NBI for 35 s on2.75 T operation.

(1)

Figure I shows the time evolution of Wo,7", Ti, n".
I is measured witha charge exchange spectrscopy [4], and n, is measured
with a far-infrared laser interferometer [5]. The electron
density profiles are constructed by Abel inversion
method. Wo is estimated by the Diamagnetic flux
measurement. ECH is supplied for first I s. Two NB areinjected, but one NB injection is terminated at f = 5 s.
The He gas is puffed until t =17 s. I and Z, remain at ahigh level, and then they decrease after / = 5 s.

where Zo, | f;o are the atomic number and the radial

T" is measured with a ECE system.

particle flux of species a in the non-axisymetricmagnetic configuration. Shaing et al. gave the formulaof the particle flux f l' and the heat flux QI' I3l.

|"= -4o:\'' u:)"' aiG,E.) ,tto,, ,'r" n" [- d, ,t,, e-, i ,(x)'"JoQ)
Q.=-e? etn'' v'0. n,T"I d.rx5t2 e-' i"t*y 4l!.D .
oze, E,)'

*Jo

(3)

e300

g
So

where,- . _dn.ldt -#Z.e E.+(x-:? .) dT-ldt"A"\x,L,)="noT"Z'na*=Lr^,v2 lTo , io= v,*l(eo*t''),vdo=-Tol(ZoerB), af,- o?n+ a|+ otlo+ tttl
Here a)r7,, ap, asb and al, are the angular frequency inthe region of the l/v collisional regime, the helical ripple

plateau regime, the resonant superbanana, andcollisionless detrapping regime respectively. 16o, I arta
thermal velocity and the collisionality. To, mo, no\ €1, t6
and I are the temperature, the mass and density ofspecies a, the toroidal ripple, helical ripple and themagnetic field.
In our study, He, H and electron are considered aso'oJ

P =O.5
P =o.8gtr

plasma species. Then, the ambipolar condition is written

sas,

Z"lf, +Zr"fff"+ZHlff =O .

(4\Fig. 1 The time evolution of W, T", I and n.. Threesolid lines indicate the time evolution of Wo, T.
and n, at p = 0.2.

In order to estimate the electric field E,, we solve eq. (4)with the experimental data; the electron temperature I",
432

Sasao H. et dl., The Study on the Neoclassical Transport Analysis using ECE Measured Temperature Profiles in the LHD Inng Pulse Plasmae\XttoI.c)

0.1

I1

\t= 10.5 s

0.01
100otrAq)c3(b) The electron thermal conductiritv

10t=4.5st =10.5 sHe lOWo

1t=22.5 s,aIX{0.1\0.013020t=4.5sltt=10.5s{)(c) The Neo Clssical {10a0-1010.2

0.4

0.60.8po.2

0.4

p0.60.8Fig. 3 (a) the ion thermal conductivity, (b) the electron

thermal conductivity and (c) the radial electricfield.

Fig. 2 The profiles of 4, Ti and n"at f = 4.5 s, t= 10.5 s
and f= 22.5 s.

t12J_i 4 =Z.Z5T\ =3.6mHe 1007a(a) X-.on'"* and X"-non-u* at P = 0.8

Afterward, they increase gradually. On the other hand,n" is constant before r = 5 s and it increases until t = 8 s,then it decreases. We analyze the radial electric field of
this discharge at t = 4.5 s when Z" starts to decrease(case (1)), at / = 10.5 s when T" and n" are constant (case0.1(2)), and at22.5 s when n, is decreasing (case (3)). The
profiles of 7,, Ti and n" are shown in Fig. 2. The lines inFig. 2 are the fitting curves. We apply the fitting data to
the caluculation of the electric field and the thermalconductivity.
The neoclassical thermal conductivity profile ofnon-axisymetric plasmas and electric field profile are0.pt.-tJ-sa (h) tr}
II '"'. "'1ii.

tr-_ p =o.z-- p, =o.s_____0.8)1.

Irl

shown in Fig, 3. Xt_,on-^, X"_non-o, and E, are estimatedwith experimental data of 7", Ti and n". We can find inFig. 3 (a) that Xi_non.* becomes small in the periphery ofplasma at t = 4.5 s though the decrement of Xi_non.^ is10

not found at / = 10.5 s and at t = 22.5 s. On the other
hand, the decrease in X"_,on-* at the periphery doesn't
appear in Fig. 3 (b). The reason is the following. At t =4.5 s, the large positive electric field is predicted and theplasma is in the electron root as shown in Fig. 3 (c).
In Figs. 4, the time evolution of X;_non-*, X"_non-*

15

20

25time (sec)Fig. 4 (a) The time evolution o X1non.",, X"_non.", and (b)E,.

and E, at P = 0.8 is shown. Here, we interpolated Ti data

and take an average of I" and n" for 3.0 sec which

linearly between measurement points of Z; time seriesZ;

corresponds to the accumulation time of433

Sasao H. et al., T\e Study on the Neoclassical Transport Analysis using ECE Measured Temperature Profiles in the LHD Long Pulse Plasmameasurement. The conductivity of ions is quite smaller

than that of electrons before t = 5 s. Afterwitd, X;_a6n-6
increases, then both of Xi_no,-*andXe_non-; decrease andthey hold the constant value. Figure 4 (b) shows thetime evolution of Er at p = 0.8. The positive E. changes*100X10(a) Ion,=-;:-;i#1T]rll-]]:]T;t-"'-I\r-- He80%H20% \ t'.
-._-..He50%H50% \_-_'.---Hln%Ix

to be negative at t = 5 s. Until t = 5 s, the electron root

0.1

0.01

plasmas is predicted artd X,_non-^ has a small value in the*

periphery. And X"_oon-o, after t = 5 s becomes smaller
than the value before / = 5 s because of the small
negative electric field which corresponds to the ion root

1x
A

plasma.

X"l4.2 The effect of the H injection
We study the effects of the H injection on Xi_non-o"and X"_non.* at t = 4.5 s. Figures 5 show the profile ofpFig. 5 (a) The profile of the ion thermal conductivity and(b) the profile of the electron thermal conductivity.

Xi-,o,-* and X"_no,-* for different ratios of He and H. We
find that Xi_,on-o, becomes large when the ratio of H
increases. On the contrary, a large difference is notfound about X"_non-o,. The dependence of the atomic
number Z and, atomic mass number A on the flux of ionsin the l/v region is written as,#ll?/s p = 0.8 He plasma+4-An.An^-o'"Z,l, = -7.Do'"i * Z,(2,' v.,t \ 2,''ctr'drnz,t A:,, ,*+al<-a)

HoEo

H2o%
H30Vo

H40%
H50%
Ht00%

where yrr is collision frequency between ions. When on
the contraty, the flux of electrons is written as,r"=-Da; * o;ir* *t;;,(8)pwherc 2"6 is the effective charge. The ratio of ion andelectron flux is written as,fl"= Z,l,ll"n7-s A'' Z*Fig.6 The profile of the neoclassical E.

(9)antenna to estimate the temperature in the long pulse
discharge. We summarize the preceding argument as

In the case of H and He, the ratio is, fls/fIp" - 16. Here,
we assume 2"6 is same between H plasmas and He
plasmas. It is expected that the diffusion of ionsbecomes large when H is injected, the negative E, isgenerated and as a result, the ion conductivity becomeslarge. In fig. 6, the profile of E, is shown when thedifferent ratio of He and H at t = 4.5 s is assumed.
When the ratio of H increases, the positive E, tums to benegative in the periphery. The sign of E, suddenly
changes when the ratio increases from 307o to 4O Vo as
shown in Fig. 6.

follows,l.

In the NBI (H ions were injected into He plasma)long pulse discharge of LHD, the decrement of theneoclassical conductivity of ions is observed in theperiphery.

2. The above picture is significantly sensitive to theamount of H. It is predicted that the H injection inHe discharge produces significant effect on theelectric field and the polarity changes on thethreshold of H quantity.

5. Summary

Acknowledgment
We would like to thank the members of LHD

In order to study the behavior of the neoclassicalthermal conductivity and the radial electric field, weapplied the ECE experimental data with the innerexperimental group I and group 2 in National Institutefor Fusion Science, for their work in maintaining and434

Sasao H. et al., T\e Study on the Neoclassical Transport Analysis using ECE Measured Temperature Profiles in the LHD Long Pulse Plasma

t3l K.C. Shaing, Phys. Fluids 27, 1567 (1984).
t4l K. Ida and S. Hidekuma, Rev. Sci. Instrum. 60,867

operating LHD.

(l989).

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