A. Fukuyama

K. Itoh

M. Yagi

S.-I. Itoh

National Institute for Fusion Science (NIFS-Repository)

§33. Magnetic Turbulence and Anomalous Transport S.-1. ltoh, M. Yagi (Kyushu Univ.), K. ltoh, A. Fukuyama (Okayama Univ.) Self -sustained theory of plasma transport has provided an analysis of the anomalous transport due to magnetic braiding [1]. Self-consistent determination of magnetic turbulence and anomalous transport is performed [2]. The factors M and Ms are introduced to denote the enhancement of transport due to magnetic braiding. The coefficient Jmi I me M is introduced as the ratio between X~ and X~ [1]. We here assume that the collisionality is low, i.e., v << 11 and v << 'tdec, (11: transit time of particles, Lajvth, Lac : auto-correlation length of magnetic filed line in the presence of stochasticity, 'tdec : decorrelation time of plasma due to the crossfield diffusion). The transport coefficient due to the magnetic stochasticity is given as X-::::: (vthDM~dec/"tt if "tdec s "tt and X= vthDM if "tctec > "tt, where DM is the diffusion coefficient of the magnetic field line. The suppression factor Ms is the ratio 't;/'tdec· The decorrelation time is given by ?dec= 1 I X~ k:. The auto-correlation length of the magnetic field line is given by Br I B-::::: L~c1k~ 1 and has the relation DM = (B/B)2Lac· Using these relations, one has X~"' ("taec Vthe /"tfV Ap)k~2(~cl and x~= 1 /i~ec k;. We have In another word, Ms:::: 1 holds for electrons. For ions the decorrelation time is given by i _ ~ 1 e f "i l/"Mk"2 'tctec- V ~ M 'tctec or 'tctec = Xi ~ r· The ratio is found to be given by the suppression factor M, (2) The factor M and the diffusion coefficient DM are not independent and they should be determined consistent with theM-mode turbulence. The renormalization of turbulence gives the relations for electrons, e "M 't dec v the 1 1\ M A X ~ - - *"" B and X· ::<I> for ions. Notice e e V k r I 'tt A r the relations Br = (k 8 /k .l)4 sk~ki (~!~) and "M "M Jmi I me M = Xe IXi . After some algebra, the suppression factor M and thermal transport coefficients in case of the braided magnetic field are obtai ned as (3) Xi,... g-1(1 + G~lt 1 a2[)2 ~~e (4) Xe '""'Xi· J a ~imi /me (5) which shows an order-of-magnitude enhancement compared to the electrostatic limit. The factor M turns out to be much smaller than unity for the parameter of experimental interest. This result could be compared to the theory based on the scale-invariance method , in which the relation xoc a 282(vthe/qR) was derived for the case of braided magnetic field [3]. It agrees with Eq.(4). 1) S.-1. ltoh, et al., Phys. Rev. Lett. 76 ( 1996) 920. 2) S.-1. ltoh, et al., Research Report FURKU 95-13 ( 1995). 3) J. W. Connor, Plasma Phys. Contr. Fusion 35 ( 1993) 757. 171 

Magnetic Turbulence and Anomalous Transport

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