A. Ishizawa

M. Nakata

M. Yagi

N. Miyato

S. Maeyama

T.-H. Watanabe

Y. Idomura

National Institute for Fusion Science (NIFS-Repository)

The kinetic ballooning mode (KBM) turbulence inTokamak plasma is investigated by electromagnetic gy-rokinetic simulations. From the entropy balance analy-sis, it is revealed that the ﬁeld-particle interactions trans-fer a signiﬁcant fraction of the ion entropy produced bythe instability to electrons. Then, the produced ion en-tropy balances to the sum of the ion and electron dissi-pations at the saturation of the KBM instability growth,in contrast to ITG turbulence where ion entropy produc-tion mostly balances to ion dissipation 1, 2).In the next generation fusion devices, such as JT-60SA and DEMO, high-β operations are planned to makethe design of a nuclear fusion reactor more realistic andattractive (where β ≡ µ0nT/B2 is the normalized plasmapressure). A ﬁnite β eﬀect introduces coupling of driftand Alfve´n waves in magnetized plasma, and changesthe nature of plasma turbulence from electrostatic toelectromagnetic, where stabilization of the ion temper-ature gradient modes (ITG) and destabilization of thekinetic ballooning modes (KBM) are observed as β in-creases. Since the ﬁnite β eﬀect may have large impactson turbulent transport levels, understanding of the elec-tromagnetic turbulence is critically important for high-βoperations.We have carried out KBM turbulence simulationsby means of the ﬂux-tube gyrokinetic code GKV. Plasmaparameters are set to be the so-called Cyclone base caseparameters without the electron temperature gradient(R/Ln = 2.2, R/LTi = 6.82, R/LTe = 0, Ti/Te = 1, q =1.4, sˆ = 0.78, r/R = 0.18 and β = 2%). We haveanalyzed the saturation mechanism of KBM instabilitygrowth from the viewpoints of the entropy balance equa-tion. The equation describes the time evolution of theperturbed gyrocenter entropy Ssk for ions and electrons(s = i, e) and electromagnetic ﬁeld energyWk in the per-pendicular wave number space k,dSskdt= Θsk +Dsk + Isk + Esk +Rsk, (1)dWkdt= −∑sRsk, (2)where, Θsk, Dsk and Isk denote the entropy produc-tion due to the particle and heat transport, the col-lisional dissipation and the nonlinear transfer, respec-tively. The parallel streaming term Esk represents theentropy transfer between diﬀerent radial wave numbercomponents due to the periodic boundary condition forLow-kion perturb.Entropy ProductionDissipationField-particle interaction  nonlinearity(& parallel twisting)   nonlinearity(with twisted modes)Low-kelectron perturb.High-kion perturb.High-kelectron perturb.DissipationDissipationDissipationFig. 1: Schematic picture of the entropy transfer at thesaturation mechanism of KBM instability growth.twisting mode structures in the sheared magnetic geom-etry. The ﬁeld-particle interaction term Rsk correspondsto the energy exchange among the ion entropy, electronentropy and ﬁeld energy. In a steady state (d/dt ∼ 0),the entropy production, transfer and dissipation are sta-tistically balanced, Θsk + Dsk + Isk + Esk + Rsk = 0,and the ﬁeld-particle interactions stand for the entropytransfer among particle species,∑sRsk = 0.The saturation mechanism of KBM instabilitygrowth is summarized as a schematic picture in Fig.1. The low-wave-number ion entropy is produced bythe particle and heat transport Θik. They are trans-fered to the same wave-number modes of electron ﬂuctu-ations via the ﬁeld-particle interactions Rik = −Rek < 0.Rapid parallel advection of electrons leads to elongatedmode structures along ﬁeld lines, which in turn enhancesthe twisted modes in the sheared magnetic ﬁelds Eek.Then, the nonlinear mode coupling Isk with the domi-nant unstable mode and its twisted modes transfers thelow-wave-number ion and electron entropy to wide wave-number-space range. Finally, the total ion entropy pro-duction balances to the total ion and electron dissipa-tions Dsk.The importance of the entropy transfer betweenions and electrons via the ﬁeld-particle interactions isidentiﬁed. This is in contrast to ITG turbulence wherethe ion entropy production mostly balances to the iondissipation. In addition, it is revealed that the KBM in-stability growth is saturated through the coupling of thedominant and its twisted modes, rather than the zonalﬂow shearing.1) S. Maeyama, A. Ishizawa, T.-H. Watanabe, M.Nakata, N. Miyato, Y. Idomura, Plasma Fusion Res.9, 1203020 (2014).2) S. Maeyama, A. Ishizawa, T.-H. Watanabe, M.Nakata, N. Miyato, M. Yagi, Y. Idomura, Phys. Plas-mas 21, 052301 (2014).385§13. Kinetic Ballooning Mode Turbulence Simulation based on Electromagnetic GyrokineticsMaeyama, S. (JAEA),  Ishizawa, A.,  Watanabe, T.-H. (Nagoya Univ.),  Nakata, M., Miyato, N., Yagi, M., Idomura, Y. (JAEA)

Kinetic Ballooning Mode Turbulence Simulation based on Electromagnetic Gyrokinetics

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