A. Fukuyama

K. Itoh

M. Yagi

S.-I. Itoh

National Institute for Fusion Science (NIFS-Repository)

§23. Self-sustained Turbulence and H-mode Confinement in Toroidal Plasmas Itoh, S.-I., Yagi, M. (Kyushu U.) Itoh, K Fukuyama, A. (Okayama U.) The equation for the dressed test mode for the nonlinear ballooning mode turbulence in the presence of the radial electric field has been derived [ 1] as d2 pI dt1 2 + (aA I K){1- ( 112 + a-s) rt 2} p - MA[l + 3 (s -a) 211 2] p + L1p = 0 L 1p = w E1[KF- 1 d3pldY]3 - A(l+MIK)F2dpldY]] In this equation, normalization is: rIa ~r, A 2 ~ 2 ~ t I 'tAP~ t, X 'tAp I a ~ X, f..l't Ap I a ~ f.l, 2 ~ 4 " ~ 'tAp I f.lo<J ca ~ 1 /a, A 'tAp I f.loa ~II., yt Ap ~ 'Y· We employ the notation 'tAp = aJ f.lomini IB P' "44 ~22 ~22 A = 11.n q , K = xn q , M = J.ln q , F = 1 + ( Sfl - a sin 11) 2, s = r ( dq I dr) I q, C%1 = 'tAp(dEr I dr) (srB)- 1 and a=- q2R~'. Other notation is standard. The eigenfunction is written as n= I where the function un is explicitly given as un = Hn(Y) exp (- y214) and Hn(Y) is the n-th order Hermite function. The odd and even parity modes are mixed by the operator L 1 when roE1 -:t 0. The normalized eigenvalue is calculated by 1 00 1 Q = 2 + n~1 n(O I L11 n) (n I L11 0). (In the previous work [ 1], only neighbouring terms were kept.) The turbulent transport coefficient is given as A XL XH = 1 + 0 (t~ 1 wC1 { 6(s- a)2 }-1 G 1 = 8 a (1 + 2a - 2s) 2 + 1 + 2( a _ s) x[{Io- (s- a)2) + 2 (1 +6 (s- a)2)}2 8 4a l_{l- 5(s- a)2 _ 2 (s- a)2 } 2 J] +2 4 a +8 204 The contour lines of XH are illustrated in Fig.1 on the a- roE 1 plane. The correction appears in the numerical coefficient G1. The cross-field momentum flux can be calculated by the relation Normalized momentum flux is given as Pe.r = J.lHC%1, and the normalized velocity gradient is expressed by wE1. Figure 2 illustrates Pe as a function of wE1. Viscosity is calculated ,r and is close to X H. It is shown that the radial momentum flux is a decreasing function of the velocity shear in the high rotation shear limit. This indicates that, for a fixed momentum flux, two solutions of the rotation shear are available. This provides a basis for the bifurcation in the radial electric field structure in the H-mode modelling. 1.5 ,..- -.........----.,....---.,..---....---, I i S 1 ~- I i1 I ~~ : it I il ' 0.5 it • il ' l! ', ! • ' l 0 ~~ \ 1. ! ~ "A-lo-s !x= w-6 x- I -0.5 L_ __ l__ ___ L._ .. ______ L, _____ J. ____ ! 0 0.4 0.8 1.2 1 .6 2 a Fig.1 Contour plot of the normalized thermal conductivity as a function of (a, ~1). 0 <%t Fig.2 Anomalous cross-field momentum flux P e r as a function of the velocity gradient ~1 . Reference [ 1] ltoh S-I, Itoh K, Fukuyama A and Y agi M 1994 Phys. Rev. Lett. 72 1200 

Self-sustained Turbulence and H-mode Confinement in Toroidal Plasmas

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