J. Plasma Fusion Res. SERIES, Vol.2 (1999) 81-84

Particle and Heat Transports in the Scrape-Off Layerof JFT-2M Tokamak
TSUSHIMA Akira, UEHARA Kazuyar and AMEMIYA Hiroshi2
Yokohama National University, Yokohama 240-8501, JapanlJapan Atomic Energy Research Institute, Naka 319-1195, Japan
2The Institute of Physical and Chemical Research, Wako 351-0198,
Japan(Received: 8 December 1998 / Accepted: 6 May 1999)

Abstract
In the scrape-off layer of the JFT-2M tokamak, ion temperature was measured by means of twotypes of double probes. Plasma density and electron temperature were measured by means of Langmuireprobes. The results show that they decayed exponentially with radius having different decay lengths.
Using these values, particle and thermal diffusivities for ion and electron are obtained from a model
averaged along a magnetic field.

Keywords:
scrape-off layer, tokamak, transport, diffusivity, thermal diffusivity, ion temperature, probe measurement

1. lntrodustion

2. Probe Measurements

The importance of the scrape-off layer of tokamak
plasma has been recognized in relation to improved
confinement modes []. The probe method has been
widely used to measure the plasma in the scrape-off

To obtain the profile of the ion temperature, twotypes of double probes were used. One was a rotating
cylindrical probe. This double probe uses the shadowing
effect of one electrode on the other electrode, where theion temperature is evaluated on the basis of a Monte
Carlo calculation of ion orbits to the two electrodes [3].
The other was an asymmetric cylindrical double probelayer, although the probe measurement has somedifficulties to be adapted under strong magnetic field
t2t.

consisting of two electrodes with different cylindricallengths whose axes are made parallel to the magneticfield. In the latter double probe, the probe current isevaluated from an analytical form, which depends on theion temperature, the magnetic field and the length of thecylinder [4].
The profiles of the plasma density and the electron
temperature were obtained by use of Lagmuire probes.

In the JFT-2M tokamak, a rotating double probe [3]and an asymmetric cylindrical double probe [4] havebeen used to measure ion temperature. For plasma
density and electron temperature, Langmuire probes
have been used [5]. Since only a few profiles of ion
temperature of the scrape-off layer have been measured,
reliable ion thermal diffusivity in the scrape-off layer
has not been obtained yet. Here, we present particle and

The plasma density was evaluated from the ion

thermal diffusivities for ion and electron on the basis of
the probe measurements using a model, which isextended from our previous model [6].

saturation current and the electron temperature wasevaluated from the probe characteristics with biasaround a floating potential.

C o rre sp ondin g autho r' s e - mail : das gupta @ plas ma. s aha. e rne t. in81

@1999 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchTsushima A. et al., Pafticle and Heat Transports in the Scrape-Off Layer of JFT-2M Tokamak

Figure I shows the result of these measurements ofthe scrape-off layer of the ohmic discharge of the JFT2M tokamak with an upper single null divertor, where
the major radius is R = 1.3m, the separatrx radius on theequatorial plane is r - 0.29m (the ellipticity is r : 1.3r,="^nl-i,JI

and the triangularity is d=0.41), the ioroidal magnetic'u'\'field is 'B1 = 1.25T, the toroidal current is10-'o-1.14x10-t4,"r,.(?)l'),/t: l90kA and the safety factor at the scrape-off layer

for a hydrogen plasma in the case of T"l I S 8 with anis q = 4.O.

ionization energy 1 in eV (1 = 13.60) [7].
Now, if we put Drj = Dr(r)(0) exp (-xl).prrir) and3. Transport Model
The ion and electron diffusivities are derived

assume that d is very high, we have the approximation

rl'=- D|'+ -'Dr|"tL"

from the particle continuity equation averaged along
a magnetic field line with a length of L = 2nqR^lri t"t@R)Td|- ''" n(' -'+:=nA_drL

dx

Further, assuming that E1= C[T"(O)l(eL")) exp (-xl,1,r.), we havep ,.r_ /?Dr(.)(l _ C).

(1)

An

The ion and electron thermal diffusivities are thus

with the perpendicular particle flux

obtained as follows:car,,,-rrt,'(- dn * .-eE t ,Q)
dxTj

Dr(') 10;=where the plus sign for ion (j = i) and the minus sign forD,,",(o)=Lfl--electron (j = e). If the ion sound velocity is written as c.
= c,(0) exp (-xl)."), then c,(0) = { 1r"1q a ryqy,??r"(O)lL -ao(3)011)011, + lllp,')'D-,t'' (o)(4)t-candand),pru = ),on,4toll/eror T, _T:

I2lT"(O) + 4(0)l I_T:'€\c't I,
Icsince all the measured plasma quantities decay
exponentially, such as n = n(0) exp (-xlL^),7 = {(0)exp (-x/L7). The coefficient d of the right-hand-side ofeq. (1) is due to the existence of neutral particles

dQ;j'Q,ir't? - 4) u'"'l; * i =tlenELuit'- ir?,-I

density at the limiter edge (.r = 0)

_ nTi Fic(0)+ | | ),/^,ow"(0)/(Ll")-(5)

dolho'

derived from the conservation equation of heat averaged
along a magnetic field= no(0)Si(0) and, llLo - llLo + llL7.. The neutralt0) 21tR(l- ao

The ion and electron thermal diffusivities are(ionization) and we put d= a(0) exp (-xl),"), with a(0)no (0) =,x(0)"(0)/L(6)with the perpendicular heat flux

7'
"our+! nT.ul:' .
Qli'=- nyi:'!
dx 2 J-is deduced by assuming that all the neutrals recombinedon the limiter flow back into the scrape-off layer. Here,l,nour and l.rour mean the decay lengths of the plasma
density and the ion sound velocity out of the limiteredge (x > 0). The decay length of :ggq3l
ryrticle is ,l.o =tl8T"/(rcm),v,(O)/[z(0)S,(0)]withv"(0)where Q is=-a)

and the parallel heat flux

Q,li'=A:nT,c",wherethe neutral temperature being equal to the limiter

temperature (: 0.3eV). Note that Lo < 0 because theneutral density increases with -r. The ionization rate in
m3 /s is approximated by

Ai=2,82

and^' T,(O)4(0)I
2 l2nm,+ 4@)l

A-=2+1''l'(8)TsushimaA. etal., Particle andHeatTransportsintheScrape-Off Layerof JFI-2MTokamakr (e) A. c,(0) T-. eEr(O) v L(0)are used. The second term of the right-hand-side of eq.

"(6) is due to heat exchange between ion and electronL4(o)and. [' - 19] v,"i(o)+8"(o)'vr''=4.11x l0 14 J-+,I ttol;

A -u"" Tf,''

with the charge state Z and the mass number A.ur. of anion (v7"iin s-r, n in m-3 and T" in eV). The third term of
the right-hand-side of eq. (6) is due to the existence of_ r"pi_''ro)'4n.
l+ . +Ar,. +)Ao;,'J(tz)\^,neutral particles and we put A = B3(0) exl (xl ),p,) with0r = no(Si + Sg, and 0" = noSr [312 + IlT"(0)]. Since
the cross-section in m2 for charge exchange by protons(i) A,c.(o) c 40) Dj"(o)'nDt L
tr, Tr{o'1 1,in atomic hydrogen is approximated byfogy= 3.95 x 10-

re- 5.90 x ro-228,

nr

\r
-^
t+-+l+-l-8,' Ln
Lr, ,to'," l.

D,"'(o) /\n,for T' - 100eV. Then, we have fi(0) = no(0) [Sr(0) +scx(0)1, 0"(0) = no(0)sr(0), ll Lp"- ll L6 + ll )a. andAp, Ao(13)Jr (e) A.c.(o) . c DJ'tlo)

ILAnAn{(0)+0.78/rp) 1-r.
o.78/7Io)-I ttol;s",= (6.18 x 1o-15 - 1.84 x t0-"r; fi4(0)-I rrorl=l:1r,"'(0)+P,0)+ll-

for an ion energy of 50 < Ei ( 200eV [8], the rate of thecharge exchange in m3/s is approximated byll=-t ffi]v,"'(o)+f"(o)I4(0)+0.78/ryO) 2)"r;_ B-

p,:'(o)._Lj,
An f+.+\^, Ar, Ao','' J'Assuming ,(r(j) = 1(j)(0) exp (-xl ),rr1iy), we finally(14)

obtain the ion and electron thermal diffusivities asfollows:rlne)=.J],,F oi''(9)

Lrrr,=t.

(lo)r {i) A,c,(0) I - C 4(0) Dr"(O)

' D2
l- nr

\whereFr(')=4ix'(0) -I

ffi (t :r-+)1",.,,

eE'(0) vr(0)40)+.[t -ffi]y."i(o)+p,(o)_u,,;;:0,(+.+:*),^^
1,1,Ti(g) In

fr-1.-L)\ lr, Ar. tr"'-).[(* ]+)

andF Do'L

F,{Ufi-u,or#(+. ,t.-t),(1 1)

and83(ls)Tsushima A. et al., Particle and Heat Transports in the Scrape-Off Layer of JFT-2M Tokamak

1020.[(+ ]+)

1hffi(+ z'.+')1" '(0)u)

10r

n l0r

re

^pj''(ot/r r r*t l^nAD*, \^n101

O^.1* p,to)7^-8,-;:z::l*+'

10r

cai,.

(16))'

It is worth noting that C is a value, with which all thec)transport coefficients are positive.

c,)l-{=4. Gonclusion

c6t-'r(DUsing the model in the previous section with theplasma density n:6.0 x 1016m-3, the ion temperature I: 80eV, the electron temperature T"- 6eY at the limiteredge (.r = 0) and their decay lengths Ln= 0.014m, Ar,=0.13m, ie = 0.053m between the separatrix and thelimiter edge (x < 0) from Fig. 1, we obtain the iongtr(DF0.35
Radius (m)0.3

diffusivity Drtt) - 9.7^z'1s, the electron diffusivity Dr(")- 0.6-0.7m21s, the ion thermal diffusivity LLo = 2.32.5mzls and the electron thermal diffusivity )(t@ 2.O=
2.7m2/s, ror I c l< o.z o.

Fig. 1 The profiles of the plasma density, the ion

lr.l< sov/-.

temperature and the electron temperature

In summary, the estimated ion and electron

measured at the scrape-off layer of the ohmic

diffusivities are about twice the Bohm diffusivity D" -discharge plasma of the JFT-2M tokamak with anupper single null divertor. where major radius is B
= 1.3m. the toroidal magnetic field is Br= 1.25T,
the toroidal current is /r - 190kA and the safety
factor at the scrape-off layer is q - 4.0. Theseparatrix is located at the radius r - 0.29m andthe limiter edge is located at the radius r -0.35m.

eT"l(168) = 0.29m2/s and the estimated ion and electron
thermal diffusivities are about eight times larger thanDB.

[]

References
F. Wagner and U. Stroh, Plasma Phys. Control.

Fusion 35, l32l (1993).
t2l G.F. Matthews, Plasma Phys. Control. Fusion 36,1595 (1994).

t3j K. Htjthker, W. Bieger, H.J. Belitz and H.
Amemiya, Rev. Sci. Instrum. 61, ll4 (1990).
t4l H. Amemiya and K. Uehara, Rev. Sci. Instrum. 65,2607 (1994\.

t5l K. Uehara, T. Kawakami, H. Amemiya, K.
Hdthker, A. Cosler, W. Bieger, Nucl. Fusion 38,(1998) to be published.

t5l K. Uehara, A. Tsushima and H. Amemiya, Czec!r'.
J. Phys. to be published.

[7] K.L. Bell, H.B. Gilbody, J.G. Hughes, A.E.
Kingston and F.J. Smith, cLM-R216 (1982).

t8l A.C. Riviere, Nucl. Fusion ll, (1971) 363 (1971).
84