A. Ishizawa

H. Sugama

N. Nakajima

S. Maeyama

T.-H. Watanabe

National Institute for Fusion Science (NIFS-Repository)

In recent years, one of the main issues in theoreticalstudies on turbulent transport and zonal ﬂows in helicalsystems, such as the Large Helical Device (LHD), is thezonal ﬂow response enhancement by improvement of col-lisionless orbits of helical ripple trapped particles. It hasbeen pointed out that the long-time response functionof zonal ﬂows is ampliﬁed by an equilibrium scale radialelectric ﬁeld1), Er, which is spontaneously generated bythe ambipolar particle diﬀusion of the neoclassical trans-port and drives a poloidal E × B rotation. The zonalﬂow enhancement by the radial electric ﬁeld is conﬁrmedby the gyrokinetic simulation2) which is extended so asto incorporate ﬁeld-line-label dependence of the conﬁne-ment ﬁeld strength. Application of the poloidally globalmodel to the ITG turbulence, however, causes a diﬃ-culty associated with mixture of diﬀerent scale lengthsfor equilibrium and turbulence. To overcome this issue,we have devised a multi-scale simulation model, named“flux-tube bundle” model, for turbulence and zonal ﬂowsin helical plasmas with the poloidal E ×B rotation3).The zonal ﬂow response to a given source term iscalculated by means of the linear gyrokinetic simula-tion using the ﬂux-tube bundle model. Time-history ofthe zonal ﬂow potential is plotted in Fig. 1, where Mpmeans the poloidal Mach number, Mp = |ωθ|R0q0/vti =(R0q0/r0)|cEr/B0vti|. Eight ﬂux tubes are set in theﬂux-tube bundle model for a range of −pi/M ≤ α ≤+pi/M with M = 10 for the LHD conﬁguration, whereα means the ﬁeld line label α = ζ − qθ and q is thesafety factor. The residual zonal ﬂow level after the ini-tial damping of the geodesic acoustic mode (GAM) isenhanced by Er, which is consistent with the previoussimulaitons2). As the ﬁnite collision term is introducedhere, the residual zonal ﬂow level decays in a longer time.Nonlinear simulations of the ITG turbulence usingthe ﬂux-tube bundle model have also been carried outwhere the eight ﬂux tubes are employed. In case with-out the poloidal rotation (Mp = 0), turbulence and zonalﬂows in each ﬂux tube develop independently. The to-tal average of the heat ﬂux agrees with that of the singleﬂux tube case, because the ITG mode in LHD plasma haslittle dependence on the ﬁeld line label α. In case withthe poloidal rotation, a collective phenomenon amongﬂux tubes arises when zonal ﬂows developed in the ITGturbulence. Because of the zonal ﬂow response enhance-ment by Er, the zonal ﬂow amplitudes in the ﬂux tubescontinue to grow after the initial saturation of the insta-bility growth as seen in Fig. 2. For Mp = 0.3, the powerof zonal ﬂow potential averaged over ﬂux tubes is abouttwo times higher than that for Mp = 0.Multi-scale simulations for turbulence and zonalﬂows in poloidally-rotating helical plasmas have demon-strated strong zonal ﬂow generation by turbulence,which implies that turbulent transport processes in non-axisymmetric systems are coupled to the neoclassicaltransport through the macroscopic E × B ﬂows deter-mined by the ambipolarty condition for neoclassical par-ticle ﬂuxes.-0.2-0.1 0 0.1 0.2 0.3 0  10  20  30  40  50  60  70  80Re(φkx,0)Time (Ln/vti)kx ρi = 0.117; α = 0Mp = 0Mp = 0.3Fig. 1: Zonal ﬂow response calculated by means ofthe ﬂux-tube bundle model with and without poloidalrotation, where Mp denotes the poloidal Mach numberof the E ×B ﬂow4). 0 2 4 6 8 10 12 14 0  50  100  150  200  250  300  350  400Σ kx |φ kx,ky=0|2  (α-averaged)Time (Ln/vti)Mp = 0.0Mp = 0.3Fig. 2: Time-history of zonal ﬂow potential driven bythe ITG turbulence in a helical system with and withoutthe poloidal E ×B rotation4).1) Sugama, H. and Watanabe, T.-H.: Phys. Plasmas 16(2009) 056101.2) Watanabe, T.-H., Sugama, H., and Nunami, M.:Nucl. Fusion 51 (2011) 123003.3) Watanabe, T.-H., Sugama, H., Nunami, M., andNakata, M.: J. Phys.: Conf. Ser. bf 399 (2012)012020.4) Watanabe, T.-H. et al.: 24th IAEA Fusion EnergyConference 2012, San Diego, USA (IAEA, Vienna,2012) TH/8-1.Electromagnetic simulation codes for studyingmicro-turbulence in magnetically confined plasmas, suchas GKV+/EM solving the gyrokinetic equations for ionsand electrons and GKV+/EMH solving the hybrid modelof gyrokinetic ion and fluid electron equations, are newlydeveloped. These codes are applied to the linear andnonlinear analyses of micro-instabilities of finite betaplasmas in the Cyclone base case tokamak and in a modelconfiguration of standard LHD 1).Accuracy of the hybrid model is confirmed throughcomparison with linear and nonlinear simulation resultsfor the tokamak and the LHD plasmas obtained by thefull gyrokinetic code. The comparison in the linear anal-ysis confirms good agreement in the growth rates andreal frequencies of KBMs in high-beta regime. In non-linear simulations the hybrid code can run with aboutfour times faster speed than that of the full gyrokineticcode. The hybrid code is especially useful for nonlinearanalysis of LHD for which full gyrokinetic simulation isdifficult because of large computational cost.The nonlinear simulation of KBM turbulence in theCBC with β = 2% and ηe = 0 shows that the ion heat(particle) transport coefficient given by electrostatic per-turbations is about 0.6 (0.5) vTiρ2i /Ln. The magneticperturbation of KBM turbulence has small pinch effectson the ion heat and particle transport, which is in con-trast with Rechester-Rosenbluth model. The electronheat flux is about 0.4 TivTiρ2i /L2n (-0.3 TivTiρ2i /L2n) forηe = 0.2 ( ηe = 0). The analysis of beta scaling of thesefluxes and a comparison between the kinetic simulationresults and our previous fluid simulation results will bemade in our future work. Turbulent fluctuation of KBMsatisfies the entropy balance equation, and the entropy(or free energy) is transferred from ions to electrons.Although it has been shown that the zonal flow pro-duced by KBM is weak compared to ITG with the adi-abatic electron, it is valuable to study the productionof zonal structure in KBM turbulence. By using theentropy balance relation it is shown that the entropytransfer to the zonal component from magnetic (elec-trostatic) nonlinearity is positive (negative). It is no-ticed that the magnetic (electrostatic) nonlinearity cor-responds to the Maxwell (Reynolds) stress in the fluidlimit. This zonal structure production is in contrast withthe production (reduction) of zonal flow by the Reynolds(Maxwell) stress in two-fluid simulations 2).Linear analysis of KBM in the model configurationof standard LHD plasmas by means of the full kineticcode shows that the ITG mode is stabilized around β =0.8% and the critical value of KBM onset is about β =1.5% for ηi = 3, ηe = 0 and sˆ = −0.85. When ηe = 3,the growth rate of ITG is suppressed with beta but it isnot stabilized completely and KBM appears in β > 1%.One of the significant feature of KBM in the standardLHD is that the most unstable mode has a finite radialwavenumber. This is in contrast to ITG in the LHD andmicro-instabilities in tokamaks, where the most unstablemode has vanishing radial wavenumber, which is thenset by the magnetic shear length scale.The first nonlinear simulation of turbulence in thefinite beta LHD plasma is demonstrated, and the earlystage of nonlinear saturation of KBM with β = 2%,ηi = 3 and ηe = 0 is obtained. The magnetic perturba-tion of KBM causes small ion heat and particle pinches.After the KBM growth is saturated, small ky modes growand the system does not reach a steady state. Thesesmall ky modes are linearly unstable, and the zonal flowis too weak to regulate these modes. This is a possibleexplanation of the difficulty in finding a steady state inthe standard LHD with the magnetic hill component inthe magnetic drift term. In contrast the ITG has stableregion in small kyρi and also produces strong zonal flow.Other possible explanations of the difficulty are the lackof numerical resolution and the model configuration usedin the present study. Electromagnetic gyrokinetic simu-lations of LHD plasmas with higher resolution and witha realistic magnetic configuration remain in our futurework.Fig. 1: Color contours of electrostatic potential φ andparallel component of vector potential A‖ on z = 0 att = 80.4Ln/vTi.1) Ishizawa, A., Maeyama, S., Watanabe, T.-H.,Sugama, H., and Nakajima, N., Nuclear Fusion 53,(2013) 053007.2) Ishizawa, A. and Nakajima, N., Nuclear Fusion 47,(2007) 1540.387§11. Gyrokinetic Turbulence Simulations of High-beta Tokamak and Helical Plasmas with Full-kinetic and Hybrid ModelsIshizawa, A., Maeyama, S., Watanabe, T.-H.,  Sugama, H., Nakajima, N.

Gyrokinetic Turbulence Simulations of High-beta Tokamak and Helical Plasmas with Full-kinetic and Hybrid Models

https://nifs-repository.repo.nii.ac.jp/?action=repository_action_common_download&item_id=5278&item_no=1&attribute_id=25&file_no=1

Gyrokinetic Turbulence Simulations of High-beta Tokamak and Helical Plasmas with Full-kinetic and Hybrid Models

Abstract

Similar works

Full text

Available Versions

National Institute for Fusion Science (NIFS-Repository)