Doerk, H.

Görler, T.

Jenko, F.

Nordman, H.

Oberparleiter, M.

Told, D.

English

MPG.PuRe

Interaction between turbulence and neoclassical effects in globalgyrokinetic simulations with GENEM. Oberparleiter1, H. Doerk2, T. Görler2, F. Jenko3, H. Nordman1, D. Told31Chalmers University of Technology, Gothenburg, Sweden2Max Planck Institute for Plasma Physics, Garching, Germany3University of California, Los Angeles, USAIntroductionThe steep radial gradients of the temperature and the pressure cause a tokamak plasma to bein a state of turbulence and this phenomenon provides the dominant channel for the transport ofparticles, heat and momentum. Collisions and the toroidal geometry of the magnetic guide field,however, provide an additional channel, neoclassical transport, which can become relevant if theturbulence becomes weak or suppressed[1].While both neoclassical and turbulent transport have been studied extensively and mainlyseparately in the last decades, their possible interactions leave a number of open questions. In par-ticular, regions with steep gradients such as transport barriers may enable synergies between thetwo as the separation of the ion gyroradius scale and the gradient length scale does not hold there.0.2 0.4 0.6 0.8x/a0.50.00.51.01.52.02.53.03.5a/LTa/Ln0.0 0.2 0.4 0.6 0.8 1.00.51.01.52.02.53.03.5qstdinvflat0.0 0.2 0.4 0.6 0.8 1.0x/a1.00.50.00.51.01.52.02.53.03.5ŝstdinvflat Figure 1: Gradient profiles, safety factorand magnetic shear profilesBy means of the gyrokinetic code GENE[2, 3] we investigatea potential interaction mechanism between ion-temperature-gradient (ITG) turbulence and neoclassical physics mainlyvia modifications of the zonal flow pattern by the long-rangeradial electric field connected to neoclassical effects.Role of q in gradient-driven simulationsIn prior work we found that in radially global fixed-gradient simulations of ITG turbulence the turbulent heatflux can be increased by 20-30% for ρ∗ > 1/300 in the pres-ence of neoclassical effects[4]. As expected the interactionvanishes when approaching the local limit. Here we demon-strate how the shape of the safety factor profile modifies theinteraction for a system with ρ∗(x/a = 0.5) = 1/150. Thetemperature and density gradient profiles have the peakedshape shown in Fig. 1 and the magnetic flux surfaces arecircular and concentric. Electrons are treated as adiabatic and ion-ion collisions are modelledwith a linearised Landau-Boltzmann operator.43rd EPS Conference on Plasma Physics P2.0450.2 0.4 0.6 0.8x/a202468101214Q/QgBQturb (wo. NC)Qturb (w. NC)QNC (w. NC)Chang-Hinton(a) Monotonic q0.2 0.4 0.6 0.8x/a505101520Q/QgBQturb (wo. NC)Qturb (w. NC)QNC (w. NC)Chang-Hinton(b) Flat q0.2 0.4 0.6 0.8x/a202468101214Q/QgBQturb (wo. NC)Qturb (w. NC)QNC (w. NC)Chang-Hinton(c) Inverse shear qFigure 2: Time-averaged radial heat flux profiles in simulations with and without neoclassical effects for different qprofiles0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9x/a0.30.20.10.00.10.20.30.4〈 ω E×B〉 /(c s/a)wo. NCw. NCγloc(a) Monotonic q0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9x/a0.30.20.10.00.10.20.30.4〈 ω E×B〉 /(c s/a)wo. NCw. NCγloc(b) Flat q0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9x/a0.20.10.00.10.20.30.4〈 ω E×B〉 /(c s/a)wo. NCw. NCγloc(c) Inverse shear qFigure 3: Time- and flux-surface-averaged E ×B shearing rate in simulations with and without neoclassical effectsfor different q profiles and local linear growth rates for comparison.We study the described system with three different safety factor profiles q(x): a monotonicone, one where constant q = 1.6 is set, so there is no magnetic shear, and one where a region ofinverse (i.e. negative) magnetic shear occurs for x/a < 0.6 (Fig. 1). The time-averaged radial heatfluxes for all three scenarios are plotted in Fig. 2. If included in the simulation, the neoclassicalflux is in good agreement with the well-established Chang-Hinton prediction[5] and due to itsproportionality to q2 increases to a significant fraction of the total transport at x/a < 0.5 in theinverse-shear case. The turbulent radial heat flux – both in cases with and without neoclassicaleffects – is larger by a factor of ∼ 1.6 for the flat q profile than in the two other scenarios. This isconsistent with local results on a maximum of the linear ITG growth rate at ŝ ∼ 0.5[6].If we compare the turbulent flux between the simulations with and without neoclassical effectsfor each of the three different q-profiles, an interesting trend can be observed: While the systemincluding neoclassical effects exhibits a systematically higher (ca. 20%) heat flux comparedto the purely turbulent one for the monotonic q, the flux is equal within the uncertainty forx/a . 0.4 with the flat and inverse shear q-profiles. In the latter case also the difference at x & 0.4is only around 10%.Since ITG turbulence typically saturates due to ~E ×~B shear generated by zonal flows, we studythe radial profiles of the shear pattern ω~E×~B(x) for the three different q profiles. As can be seen43rd EPS Conference on Plasma Physics P2.045in Fig. 3, the presence of the additional long-range radial electric field in the simulations withneoclassical effects modifies the time averaged shear. For monotonic q (Fig. 3a) the presence ofneoclassical effects aligns a region of very low ~E ×~B shear with the maximum of the local lineargrowth rate at x/a ∼ 0.47, which possibly explains the increase in transport. The scenario withinverse magnetic shear (Fig. 3c) on the other hand generates very similar average ω~E×~B - onlywith different sign - in the region with maximal growth rate. With the flat q profile (Fig. 3b) thepicture is not as clear. The maximal linear growth rate, however, occurs farther out at x/a ∼ 0.58.Flux-driven simulations0.3 0.4 0.5 0.6 0.7 0.8x/a01234567a/LT w/o collT w/o colla/LT w/o NCT w/o NCa/LT w/ NCT w/ NC(a) Temperature and logarithmic gradient0.3 0.4 0.5 0.6 0.7 0.8x/a0.50.00.51.01.52.02.53.03.54.0Q/QgBw/o collw/o NCw/ NCgrad(b) Radial heat flux, dashed: Qnc,solid:QturbFigure 4: Time averaged profiles for flux-driven simulations. The gradient-driven caseuses the temperature profile of "w/ NC"For simulations with fixed power input a model sys-tem with ρ∗ = 1/150 heated by a power source with agaussian profile at x = 0−0.4 is studied. We compare acollisionless simulation, a collisional case without neo-classical effects and a simulation with comprehensivecollisional physics (including neoclassical transport). Inaddition, the evolved temperature profiles from the lastcase are used for a gradient-driven simulation. As canbe seen in Fig 4a, including collisions and neoclassicaleffects leads to lower average temperature and gradient.Since the system is quite close to marginality, this canbe explained by the collisional Dimits shift softening[7].The system with NC effects establishes a higher gradi-ent than its collisional counterpart which means that theneoclassical channel has notable impact. The gradient-driven simulation on the other hand generates a higherheat flux, which implies that there is a considerabledifference in the dynamics for the two heating schemes.If we compare the probability density functions of the radial turbulent flux in Fig. 5, cleartendencies arise: First, transport in the collisional simulations is occurring on considerablyhigher levels compared to their collisionless counterpart. This is consistent with our previousargument on the softening of the Dimits shift. Secondly, while the difference between thesimulations without and with neoclassical effects is not as drastic, the latter has a reduced levelof high transport with Qturb > 4QgB of the former. In presence of the neoclassical transportchannel (which does not have a critical threshold) the build-up of energy is obstructed leadingto less bursty behaviour of the system. Besides the higher average transport the gradient-driven43rd EPS Conference on Plasma Physics P2.045simulation also exhibits a wider distribution. Hence, it is strongly fluctuating and we can confirmthat the non-localized heating scheme has a notably large impact on the system.Conclusions0 1 2 3 4 5 6 7Qturb/QgB0.00.20.40.60.81.0w/o coll.w/o NCw/ NCgrad-drivenFigure 5: Probability density distributions forturbulent heat flux at x/a = 0.4−0.75In this work, previous studies of the interaction ofneoclassical effects and ITG turbulence in gyrokineticsimulations[4] were expanded. In gradient-driven sim-ulations it was found that the difference in turbulenttransport between a system including or excluding neo-classical effects changes from on average 20% to below10% depending on the shape of the safety factor profile.This has interesting implications for studies of inter-nal transport barriers where the magnetic shear is oftennegative.For a system with fixed power input it was demonstrated that the presence of collisions andwith them neoclassical physics has a profound effect on the average gradients and heat fluxes aswell as the temporal distribution of the heat flux which implies different intermittent behaviour. Inaddition, a gradient-driven simulation based on the evolved profiles reveals remarkably differentheat fluxes, which suggest further investigation.AcknowledgementsThis work has been carried out within the framework of the EUROfusion Consortium and hasreceived funding from the Euratom research and training programme 2014-2018 under grantagreement No 633053. The views and opinions expressed herein do not necessarily reflect thoseof the European Commission. The simulations in this work were carried out using the HELIOSsupercomputer system at the Computational Simulation Centre of International Fusion EnergyResearch Centre (IFERC-CSC), Aomori, Japan, the HYDRA supercomputer at the Max PlanckComputing and Data Facility (MPCDF), Garching, Germany as well as resources provided bythe Swedish National Infrastructure for Computing(SNIC) at PDC Centre for High PerformanceComputing (PDC-HPC).References[1] R. C. Wolf. In: Plasma Phys. Control. Fusion 45.1 (Jan. 2003).[2] F. Jenko, W. Dorland, and G. W. Hammett. In: Phys. Plasmas 8.9 (2001).[3] T. Görler, X. Lapillonne, et al. In: J. Comput. Phys. 230.18 (2011). URL: http://genecode.org.[4] M. Oberparleiter, F. Jenko, et al. In: Phys Plasmas 23.4 (Apr. 2016).[5] C. S. Chang and F. L. Hinton. In: Phys. Fluids 25.9 (1982).[6] J. Q. Dong, W. Horton, and J. Y. Kim. In: Phys. Fluids B-Plasma 4.7 (1992).[7] Z. Lin, T. S. Hahm, et al. In: Phys. Rev. Lett. 83 (18 Nov. 1999).43rd EPS Conference on Plasma Physics P2.045

Interaction between turbulence and neoclassical effects in global gyrokinetic simulations with GENE

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Interaction between turbulence and neoclassical effects in global gyrokinetic simulations with GENE

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