K. Itoh

N. Kasuya

Y. Takase

National Institute for Fusion Science (NIFS-Repository)

§ 13. Selection Ru Ie for the Radial ElectricField Structure Formed by BiasedElectrodes in Tokamak PlasmasKasuya, N. (Sch. Science, Univ. Tokyo)Itoh, K.Takase, Y. (Sch. Frontier Sciences, Univ. Tokyo)The transition from L-mode to H-mode ischaracterized by a sudden change of the radial electricfield (Er) structure in tokamaks. Imposing a radial electricfield at the plasma edge can also lead to an improvedconfinement state. In TEXTOR biasing experiments thespatial profile of the radial electric field measured at theplasma edge changed from a flat one before transition toa peaked one after transition. 1) We have obtained variousEr structures between an electrode and a limiter. Astability analysis of these Er structures is carried out anda selection rule for a structure after the transitioninduced by electrode biasing is clarified.A model equation for the radial electric fieldstructure is a combination of Poisson's equation and thecharge conservation law,a I-;-, Er =---(Jvisc +Jr + Jorbit -Jext ) , (1)l' &0&1-where Jvisc is the current driven by shear viscosity, Jr isthe local current, Jorbit is the current driven by ion orbitlosses, Jext is the current driven into the electrode by theexternal circuit, co is the vacuum susceptibility, and &-1 isthe dielectric constant of a magnetized plasma. NonlinearEr dependencies of the local current and orbit loss currentare the origins of structural bifurcation. Here the orbitloss current is neglected for simplicity.The radial electric field equation Eq. (1) is anonlinear differential equation and is solved with theboundary condition 8Er/8r = O. In stationary state,spatially constant solutions (L-mode) and solitarysolutions with at least one peak (H-mode) are obtained.2) The electrode is part of an electric circuit, and theelectrode current must satisfy the circuit relationship.190A stability of the solutions is evaluated by thelinear growth rate of perturbations. Both stable andunstable regions exist in stationary solutions, and theseboundary points give critical points of transition fromone state to the other. While the applied voltage increasesfrom zero, the Er structure is a spatially constant one atlow applied voltage, but when it comes to point B in Fig.1, a certain perturbation can grow so that the structurebecomes unstable. The perturbation p= 1, where thenumber p corresponds to the mode number ofperturbation, becomes unstable first in this situation. Thispoint is given by the intersection of branch T2 and branchS1. Time evolution of the Er structure is calculated by Eq.(1), and the structure acquires one peak. When theperturbation p=2 grows, the structure acquires two peaks,and similarly for p=3, but p= 1 mode becomes unstablebefore other modes become unstable, so branch S1 istaken after the transition. Other branches are notaccessible in the quasistatic process. This result agreeswith experiments in which only a single-peaked structureis observed. If the structure with multiple peaks isattained, it can stay on that state because this structurecan be stable with an appropriate applied voltage.120:: 80Q,l100100::UQ,l"'C 40c.::Q,l0.5 1 1.5Applied Voltage [kV]Fig.l Relationship between the applied voltage and theelectrode current. Tl and T2 are spatially constantbranches and S1 are solitary solution brancheswith peaks, respectively. A, B, AI, Bl, etc.denote transition points. Solid lines are stable anddotted lines are unstable on each branch.Reference1) Weynants, R. R., et aI., Nucl. Fusion 32 (1992) 8372) Kasuya, N., et aI., Plasma Phys. Control. Fusion. 44(2002) A287

Selection Rule for the Radial Electric Field Structure Formed by Biased Electrodes in Tokamak Plasmas

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