K. Itoh

N. Kasuya

Y. Takase

National Institute for Fusion Science (NIFS-Repository)

Kasuya, N. (Sch. Science, Univ. Tokyo)Itoh, K.Takase, Y. (Sch. Frontier Sciences, Univ. Tokyo)§ 14. Asymmetrical Bifurcation of the RadialElectric Field Structure Induced byElectrode Biasing in TokamaksThe transition from the L-mode to the H-mode is abifurcation phenomenon. The radial electric fieldstructure distinguishes the L/H mode, and spatiallynon-constant structures are taken in the H-mode. Weextend the previous H-mode bifurcation model intokamaks to include the effect of electrode biasing. Theplasma nonlinear response is the origin of structuralbifurcation, and electrode biasing acts as an additionaldriving term for structure formation. It shows a uniqueasymmetric feature ben"een positive and negativebiasing.A model equation for the radial electric fieldstructure is a combination of Poisson's equation and thecharge conservation law,so 3V n .1-3T4o-60.5Fig.1 Phase diagram of the radial electric field structure.Sand T (TI T4) represent regions where asolitary solution and a spatially constant solutionexist, respectively. The shaded regions indicatewhere both solutions can exist and give hysteresis.In this figure only solitary solutions that have onepeak are considered.radial electric field transition can take place even thoughthe profiles of plasma parameters become steeper (whenlXal becomes larger). On the contrary for the negativebiasing case, the two nonlinear terms have opposite signsand increase the number of spatially constant solutionsfor adequate conditions depending on the ambipolarradial electric field, the distance between the electrodeand the limiter, and so on. Figure I shows a phasediagram in the X a - Vext space, where Vext is the appliedbiasing voltage. The threshold voltage for hard transitionis given by the boundaries of the shaded regions. Theboundaries neighboring Sand T give the forwardtransition threshold and the backward transition threshold,respectively. As the ambipolar radial electric fieldincreases, transitions still take place for positive biasing,but do not take place for negative biasing. When thedistance benveen the electrode and the limiter is large,the competition between the two nonlinear terms gives alarger number of solutions for adequate conditions.ReferenceI) Kasuya, N., et aI., Plasma Phys. Control. Fusion. 44(2002) A2872) Kasuya, N., et aI., Plasma Phys. Control. Fusion 45(2003) 183(1)a I-E =--(J. +J +J . -J ),'"I r \1SC r <'rblt ext·01 BoB1.where Jvisc is the current driven by shear viscosity, Jr isthe local current, Jorbit is the current driven by ion orbitlosses, J ext is the current driven into the electrode by theexternal circuit, is the vacuum susceptibility, and B1 isthe dielectric constant of a magnetized plasma. J\'isc termacts as a diffusion term due to anomalous shear viscosity.Various structures \"ith multiple peaks are obtainedfor the same boundary condition. I ) The model equationhas two nonlinear terms, Jr and Jorbit. Their balancingexplains the H-mode transition mechanism and anasymmetrical bifurcation feature with respect to theelectrode current term.2) The ambipolar radial electricfield (Xa) varies in accordance with the pressure gradient,and it affects the dependency of the radial current and cangive an asymmetric property as well. For the positivebiasing case, various solitary solutions can exist and a191

Asymmetrical Bifurcation of the Radial Electric Field Structure Induced by Electrode Biasing in Tokamaks

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