A. Ishizawa

H. Sugama

N. Nakajima

S. Maeyama

T.-H. Watanabe

National Institute for Fusion Science (NIFS-Repository)

A saturation mechanism for microturbulence in aregime of weak zonal ﬂow generation is investigated bymeans of electromagnetic gyrokinetic simulations. Thestudy identiﬁes a new saturation process of the kineticballooning mode (KBM) turbulence originating from thespatial structure of the KBM instabilities in a ﬁnite-betaLarge Helical Device (LHD) plasma. Speciﬁcally, themost unstable KBM in LHD has an inclined mode struc-ture with respect to the mid-plane of a torus, i.e. it hasa ﬁnite radial wave-number in ﬂux tube coordinates, incontrast to KBMs in tokamaks as well as ion-temperaturegradient (ITG) modes in tokamaks and helical systems.The simulations reveal that the growth of KBMs in LHDis saturated by nonlinear interactions of oppositely in-clined convection cells through mutual shearing as wellas by the zonal ﬂow. The saturation mechanism is quan-titatively investigated by analysis of the nonlinear en-tropy transfer that shows not only the mutual shearingbut also a self-interaction with an elongated mode struc-ture along the magnetic ﬁeld line 1).Electromagnetic turbulence in ﬁnite-beta Large He-lical Device (LHD) plasmas is studied by means of gy-rokinetic simulations. The study shows common featuresto those found in gyrokinetic simulations of ﬁnite betatokamaks such as the stabilization of ITG modes, thedestabilization of KBMs, and weak zonal ﬂows in KBMturbulence 2). The turbulent transport due to the ITGin LHD plasmas with β = 0.2% is regulated by zonalﬂows, even in the presence of electromagnetic perturba-tions. The contribution of convective part to the energyﬂux is comparable with that of the turbulent diﬀusiveheat ﬂux part, because of the ﬁnite density gradient ofthe model conﬁguration of LHD. For a small density gra-dient that is often observed in LHD, the contribution ofthe convective part can be diﬀerent from the results ob-tained here. In addition, magnetic perturbations havesmall pinch eﬀects on the energy and the particle ﬂuxes.A new mechanism of saturation process of KBMturbulence in LHD is presented by analysis of nonlin-ear entropy transfer. The analysis has revealed thatthe growth of KBM is saturated by nonlinear interac-tions of oppositely inclined convection cells with mutualshearing as well as by the zonal ﬂow (Fig. 1). It is ex-pected that the KBMs have inclined mode structure andare saturated through the new mechanism, when parti-cle trapping by helical ripples is signiﬁcant, because thebounce-average of magnetic drift velocity has ﬁnite ra-dial component in the bounce-average of magnetic driftfrequency to destabilize Fourier modes with ﬁnite radialwavenumber. The new mechanism may also cause satu-ration of turbulence in ﬁnite-beta tokamaks in the pres-ence of three-dimensionality such as toroidal ripples andresonant magnetic perturbation (RMP). In the steadystate the amplitudes of energy and particle ﬂuxes due toKBM at β = 1.7% are similar to those caused by theITG turbulence at β = 0.2%, even though the amplitudeof the KBM turbulence is larger than that of the ITGturbulence. The spectrum of electrostatic potential forthe KBM turbulence is sharply peaked compared withthat for the ITG turbulence (Fig. 2).-1 -0.5  0  0.5  1 0 0.1 0.2 0.3 0.4 0.5 0.6-0.1-0.05 0 0.05 0.1(0.31,0.12) (-0.93,0.12) (-0.62,0) (0, 0.23) (-0.31,0.12) (-0.31,0.35) k (-0.62,0.46) x r i k y r i Linear growth rateZF ZF KBM KBM KBM ZF ZF ZF KBM KBM KBM KBM KBM KBM Fig. 1: Diagrams of nonlinear entropy transfer for theKBM turbulence with a color map of the linear growthrate of the KBM in the Fourier space (kx, ky): blue ar-rows show the transfer of the entropy/free-energy fromKBM to linearly stable modes through zonal ﬂow shearand red arrows show the transfer through KBM/inclined-mode shear. Black points represent the locations ofFourier modes, and ZF→ and KBM→ show the scatterby the zonal ﬂow shear and KBM/inclined-mode shear,respectively. 0.001 0.01 0.1 1 10 100 0  0.2  0.4  0.6  0.8  1  1.2  1.4<|φ k|2>ky ρiLHD standard: SpectrumKBM β=1.7%ITG β=0.2%Fig. 2: Spectrum of electrostatic potential �|φk|2�. Thespectrum for the KBM turbulence is sharply peaked ata low wavenumber compared with that for the ITG tur-bulence.1) A. Ishizawa, T.-H. Watanabe, et.al., Physics of Plas-mas 21, 055905 (2014).2) A. Ishizawa, S. Maeyama, et.al., Nuclear Fusion 53,053007 (2013).232§3. New Saturation Mechanism of Turbulence in Finite-beta Helical PlasmasIshizawa, A., Watanabe, T.-H. (Nagoya Univ.), Sugama, H., Maeyama, S. (JAEA), Nakajima, N.

New Saturation Mechanism of Turbulence in Finite-beta Helical Plasmas

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