K." Narihara

N. "Ohyabu

Y. Nagayama

Y. Narushima

National Institute for Fusion Science (NIFS-Repository)

§24. Bifurcation of Equilibria with and without a Large Island in the LHD Ohyabu, N., Narushima, Y., Nagayama, Y., N arihara, K. Figurel shows how the island width (n/m~ll1) changes when externally imposed resonant field and hence w" (the width of the vacuum island in terms of p) increase. When w" is below 0.17, an island structure is undetectably small in the observed Te-profile. Uncertainty in the profile measurement means that the width must be below 0.04. Plasma dynamics suppresses the island width from 0.17 down to below 0.04, proving existence of a surprisingly strong suppression mechanism. When Wex exceeds a critical value (w,;) of 0.17, plasma suddenly can not suppress the island any more and the island grows and becomes 0.22, even larger than the vacuum island. It is a rapid bifurcation of the equilibrium with and without a large magnetic island. Figure 2 shows density dependence of the island suppression with fixed input power (P). The widths are taken in the discharges with gradual increasing phase ofthe density (dnJdt - 2xlO'9m-'s'). The external perturbation field (and hence w,,) is fixed during each discharge. When the perturbation field is high ( ... : w,,~0.15S), no suppression of the island is seen at any density. For the case with Wex = 0.144 (0), strong island suppression occurs suddenly when the density exceeds a critical value of2x 1 OI9m-3, exhibiting a sharp transition from an equilibrium with a large island to non-island equilibrium. This critical value of the density decreases when the external perturbation field becomes weak (see the cases with -$-: w,,~0.132, .: O.IIS). The other dependences of the width are: (I) When P is increased with fixed 0, island suppression becomes stronger and hence wcx" increases, (2) For fixed P and 0, wcx" increases with decreasing B. For physics understanding of the mechanism, it may be more appropriate to use dimensionless parameters such as ~, v.., p. at the surface with ,12" ~L In the standard LHD operational regime, the shape of the temperature profile is nearly independent of plasma conditions and the temperature (T) at any location ex; -035p043B d h h d' . I n' . an t us t e ImenSIOn ess parameters approximately scales as: ~ oc nO.65 pO.43B-I, v· oc nl.7 p-O.86S-2, p. oc n-O. 17 pO.22B-o.5• We find that higher power, higher density and lower magnetic field leads to stronger island suppression. This dependence means that higher f3 leads to stronger suppression and hence larger we/. In Fig.3, we combine data with various magnetic field (B) and plot wex•2 as a function of beta. The critical width (we/) is found to almost proportional to Jjj. The f3-value is that of the bulk plasma. For low density regime (n<L5xlO19m-'), w,; tends to become higher than predicted value by the aboveJjj scaling. In this regime, however, the beam beta is not small, probably contributing island suppression. 28 0.25 J 0.2 0.15 ;00 0.1 Vacuum Island Width K • 0.05 Island Width (p=o. 58% p la,ma) L O~~~-Y~~~~~~ o 0.05 O. 1 W O. 15 O. 2 .. Fig. 1 When w" (vacuum island width) is increased by increasing external resonant field, the island width is nearly zero and suddenly increases for Wex > 0.17. " O. 25 r:o--,-..,....,...-....--.... ~",,"-"-T''';.;'";.;~::;., • .,,<{l.IIS .1, Ell .,,<{l.131 : _ ... 0.2 o w ... ~.I« ... j. i ; .... ~ ' .. ~' 158 1.,;········· •.. ~ ......•... : ~ : .. ~ 0.15 .............• i ............• 1 •. 0. ......• ,............ ,'. • ············r··· .. o j 0P . 0.1 0.05 .. ).... . ....... ~..... . ...... ~.... .. ·····f··· . !)li .......•••••• : •••.•••..••............ , .••••••••••.• -!-.•.• ·······i··· O~~ __ ~~~~~~~ 0.5 1. 5 2 1.5 3 3.5 n (xl019m-3) Fig.2 Island width as a function of density for various wex. 5,--,~~--~--~--~ .,04-<1&''''''''''''1>01, 4 3 o o ~ o o _0 00 o o o OL-~~~--~--~~~ o 0.2 0.4 0.6 0.8 ~(%) at the island Fig. 3 The critical island width (w,,'), below which the island is suppressed is plotted as a function of f3-value at the island. 

Bifurcation of Equilibria with and without a Large Island in the LHD

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