H. Yamada

K.Y." Watanabe

S. "Sakakibara

"Sakakibara,  S.

Yamada,  H.

Watanabe,  K.Y."

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§16. Diamagnetic Flux Measurement in LHD Sakakibara, S., Yamada, H., Watanabe, K.Y. Since LHD experiments were started in 1998, plasma parameters have been improved with progress of heating power systems during every experimental campaign. The 3rd campaign experiments based on high power neutral beam heating enable us to obtain a plasma stored energy Wp of 0.88 MW. The plasma stored energy Wp can be estimated by measured diamagnetic flux L1<Pdia on MHD equilibrium condition. On the assumption that plasmas are confined by non-shifted circular averaged magnetic surfaces in the large-aspect-ratio limit, the plasma stored energy is given by (1) where <Po and Eave are a toroidal flux and an averaged toroidal field strength inside plasma, respectively, and Vp is a plasma volume. This formula is well used in various magnetic confinement devices. In LHD, since there is a relatively large Shafranov shift and it may lead to the reduction of Vp, the relation between Wp and L1<Pdia must be obtained in consideration of non-linear change in the magnetic configuration for accurate estimation. Here, the pressure profile and Vp dependences of L1<l>dia are investigated by using the 3-D magnetic analysis code DIAGNO [1], which uses the solution of MHD equilibrium calculated by using the VMEC [2]. Figure 1 (a) shows the changes in Vp and Eave as a function of L1<Pdia in currentless plasmas with different pressure profiles. Here, three kinds of pressure profiles are assumed. The Vp decreases with L1<l>dia because a model that the shift of LCFS is limited at a specific position is applied here, and Vp in the peaked case reaches about 22.2 m3 when L1<l>dia is 0.036 Weber. The Shafranov shift in the peaked case is larger than that in the broaden one and it leads to more large reduction of Vp at the same L1<l>dia' On the other hand, the Eave increases with L1<l>dia in any profile. The shift of plasma boundary to low-field side leads to the decrease in Bave, while the deterioration of Vp scrapes the magnetic hill in the peripheral region and increases Bave. This suggests that an increment of Eave is caused by the reduction of magnetic hill rather than the Shafranov shift itself. The change in Wp as a function of L1<l>dia is shown in Fig. l (b). The Wp linearly change as a function of L1<l>dia and the difference of Wp between peaked and broad profiles at the same L1<l>dia is within 5 %. In addition, Wp given by formula (1) is well consistent with 3-D calculation results within 6 %. These calculation results suggest that an estimation of Wp yielded by the diamagnetic flux measurement does not depend on any pressure profile and Vp. And this simple model also gives good approximation in LHD, although it is assumed that the plasma has non-shifted circular averaged magnetic surfaces 20 in the large-aspect-ratio limit. If Ip exists, observed toroidal flux may include two components due to Ip besides the diamagnetic flllX. One is the paramagnetic flux which is produced by a plasma current flowing along the helical self-transformed magnetic field line, and the other is paramagnetic or diamagnetic flux due to the interaction of the helical field produced by helical coils with the toroidal current. The later component depends on the current density profile and rotational transform in addition to the absolute value of I p, and especially, the deficiency of experimental information on the current profile gives an ambiguity for measurements. In experiments, Ip has maximum value of 60kA in low-density plasmas and decreases with density [3]. ell g a. > 20 15 10 5 0 2 P = PO(1-pUl)(1-pal) --a1=2, a2=2 • ·0· ·a1=8, a2=8 -0-a 1 =8, a2:::2 (b) .. ,.' ..... .......... ~ : : R ' =3.6m B =3T ax ' t , , i j • /Q, : . ~~ .. 1<r~1 :/ " • 900/"-,v<". ,--'- {>.-a-1 =-2,-a2~=-2 ----, : /' 0 a1:::8,a2=8 • ~, '. 0 a1=8,a2=2 Y : • a1=8, a2=2, 100 kA ., .. ' ' • a1=8, a2=2, -100kA ." ...... -<f3>12 = -/',<S)6;a/<S)o O~~· •• ~~~~~-L~~~~~~~l o 2 3 4 ':\<D (10-2 Weber) 2.8 tlJ DI 2.7 < (I) 3 2.6 Fig. 1. Changes in (a): Vp, Rax and (b) : Wp as a function of L1<l>T in plasmas with different pressure profiles and plasma currents. If there is no plasma current, L1<l> dia = L1<PT· Reference [1] Gardner, H.J., Nucl. Fusion 30 (1990) 1417. [2] Hirshman, S.P. et ai" Phys. Fluids 29 (1986) 2951. [3] Sakakibara, S. et ai" Proc. ITC-I0 (submitted) 

Diamagnetic Flux Measurement in LHD

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