Biancalani, A.

Bottino, A.

Falessi, M.

Hayward-Schneider, T.

Lauber, P.

Mishchenko, A.

Vannini, F.

Villard, L.

Zonca, F.

English

MPG.PuRe

Interaction of Alfvénic modes and turbulence via the nonlinearmodification of the equilibrium profilesA. Biancalani1,2, A. Bottino2, M. V. Falessi3, T. Hayward-Schneider2, P. Lauber2, A. Mishchenko4,F. Vannini2, L. Villard5, F. Zonca3,61Léonard de Vinci Pôle Universitaire, Research Center, 92916 Paris La Défense, France2Max-Planck Institute for Plasma Physics, 85748 Garching, Germany3Center for Nonlinear Plasma Science and ENEA C. R. Frascati, 00044 Frascati, Italy4Max-Planck Institute for Plasma Physics, 17491 Greifswald, Germany5Swiss Plasma Center, EPFL, 1015 Lausanne, Switzerland6Institute for Fusion Theory and Simulation and Department of Physics, Zhejiang Univ.,Hangzhou, ChinaIntroduction and motivationA key step towards the achievement of controlled nuclear fusion in magnetic confinementdevices is the mitigation of turbulence. Turbulence is generated by the nonlinear interaction ofmicro-instabilities like ion-temperature-gradient (ITG) modes [1]. ITGs are dominantly elec-trostatic (ES) modes driven unstable by the gradients of plasma temperature. A population ofenergetic particles (EP) is present in tokamak plasmas due fusion reactions and external heatingmechanisms. EPs can drive electromagnetic (EM) oscillations like Alfvén Modes (AM) [2, 3]unstable.The study of the interaction of EPs, macroscopic AMs and microscopic ITG-turbulence is anumerically demanding problem due to its multi-scale character. Moreover, a kinetic treatmentis necessary to properly include wave-particle interactions. As the dynamics of interest is slowerthan gyrofrequencies, the gyrokinetic (GK) ordering is valid. Interaction of EPs and turbulencehas been observed in experiments [4, 5, 6, 7]; it has been investigated by means of analyticaltheory [8, 3, 9, 10]; it has been investigated by means of flux-tube numerical simulations [11,12, 13, 14, 15, 16]; recently, a first investigation by means of global EM numerical simulationshas been performed [17].AMs nonlinearly modify the equilibrium profiles [3, 18, 19, 20, 17]. Can we isolate andstudy numerically how this affects ITG turbulence? In this work, we investigate this problem,by means of the following simplified test. First, we run global selfconsistent EM simulationsof AMs and turbulence with ORB5 (similarly to Ref. [17]) to save the profiles modified by theAM. Secondly, we use the modified profiles, for ES simulations of ITG turbulence.48th EPS Conference on Plasma Physics P5b.117Model and equilibriumThe numerical tool used in this work is the multispieces EM GK particle-in-cell code ORB5 [21,22]. ORB5 is global, i.e. it resolves modes with structure comparable with the minor radius.Figure 1: Safety factor profileThus, it is appropriate for studying AMs with low toroidalmode number. A Krook operator is used as source forthe thermal species, slowly restoring the initial thermalplasma profiles (it is not applied to the EP species here).A magnetic equilibrium with circular concentric fluxsurfaces is considered. The geometry has a large aspectratio and gradients peaked at mid-radius for simplicity.We use a monotonic safety factor profile here (see Fig. 1),instead of the profile with reversed shear used in Ref. [17].The plasma density and temperature correspond to a value of normalized sound gyroradius ofρ∗ = ρs/a =√Te/mi/Ωi = 0.00571, and β = 8πn(Ti +Te)/B2 = 1 ·10−3.First part of the numerical experiment: study of the profiles modified by the AMIn the first part of this numerical experiment, we run selfconsistent nonlinear global EM simu-lations, with the goal of studying the modification of the equilibrium profiles. These simulationsare similar to those described in Ref. [17].In Fig. 2-left, the evolution of the radial electric field in time is depicted. In the first half of thesimulation, no EPs are present, and ITG modes grow in amplitude and form a saturated turbu-lence state. Both zonal (i.e. flux-surface-averaged) and non-zonal (the remaining part) electricfields are shown. EPs are switched on at t = 6 · 104 Ω−1i , driving AMs near the radius ρ = 0.4(blue lines in Fig. 2-left). Note that Ωi = 175.4cs/a, with cs =√Te/mi.The heat flux carried by the AM modifies the equilibrium profiles. As an example, one canFigure 2: On the left, radial electric field for a simulation with EPs (blue) and without EPs (red). Onthe right, modified ion temperature profile (red) compared with the unperturbed profile (black).48th EPS Conference on Plasma Physics P5b.117see the thermal ion temperature profile at t = 0 and t = 75000Ω−1i (normalized with the valueat ρ = 0.5). The modified profiles are saved, and used as input for ES ITG simulations.Second part of the numerical experiment: effect of the modified profiles on turbulenceIn the second part of this numerical experiment, we want to design a simple numerical testto isolate the indirect interaction of the AMs with turbulence, by means of the profile modifi-cation. We are not interested here in the wave-wave interaction of AMs and ITGs. To this aim,we take the saved profiles from the EM simulations, and we use them to perform nonlinearglobal electrostatic simulations. These simulations have no AMs. We also have only one kineticspecies: thermal ions. No EPs are included here. Therefore, only ITG turbulence is present here(and zonal flows). The turbulence dynamics is measured with its heat fluxes. We find that theheat fluxes of the simulations with the modified profiles are about a factor 2 lower than theheat fluxes of the simulations with unperturbed profiles. This means that there is an effect ofturbulence reduction due to the fact that AMs flatten the equilibrium profiles around ρ = 0.4.Figure 3: Turbulence intensity (estimated by means of heat fluxes) in the ES simulation for the unper-turbed (blue) and modified profiles (red). Time evolution (left) and radial structure (right).Conclusions and next stepsIn this work, we have measured the modification of the equilibrium profiles due to AMswith EM simulations, and we have investigated the effect of the profile modification on ITGturbulence. The first part of the study is done by means of EM simulations (including AMson top of ITG turbulence), whereas the second part is done by means of nonlinear ES ITGsimulations. Turbulence is found to be reduced when the profiles modified by the AM are used,in comparison with simulations where the unperturbed profiles are used. This is a sign of anindirect reduction of turbulence by AMs.As next steps, we would like to measure the phase-space zonal structures [18], to characterizethe transport in simplified tests like this, and in selfconsistent simulations. Then, we will relax48th EPS Conference on Plasma Physics P5b.117some simplifications on the configuration, to be closer to experiments, like in Refs. [23, 24, 25].Finally, we want to study the effects on turbulence in self-consistent simulations, with linearlyunstable AMs (like in Ref. [17]) or marginally stable AMs (like in Ref. [16]), with ORB5.Acknowledgements: Discussions with D. Del Sarto, J.-N. Sama, Ö. Gürcan, P. Morel, B. Rettino, A.Di Siena, E. Poli, and X. Wang are gratefully acknowledged. This work has been carried out within theframework of the EUROfusion Consortium, funded by the European Union via the Euratom Researchand Training Programme (Grant Agreement No 101052200 - EUROfusion) within the framework ofthe TSVV-10 and ATEP projects. Views and opinions expressed are however those of the author(s)only and do not necessarily reflect those of the European Union or the European Commission. Neitherthe European Union nor the European Commission can be held responsible for them. This work wassupported in part by the Swiss National Science Foundation. Simulations were performed on the HPCMarconi and Marconi-100 supercomputers with the ORBFAST, OrbZONE and TSVV-10 projects.References[1] L. I. Rudakov, and R. Z. Sagdeev, Sov. Phys. Dokl. 6 498 (1965)[2] K. Appert, et al. Plasma Phys 24, 1147 (1982)[3] L. Chen, F. Zonca, Rev. Mod. Phys. 88, 015008 (2016)[4] G. Tardini, et al., Nucl. Fusion 47, 280 (2007)[5] W. W. Heidbrink, et al., Phys. Rev. Lett. 103, 175001 (2009)[6] M. Romanelli, A. Zocco, F. Crisanti, and JET Contributors, Plasma Phys. Control. Fusion 52, 045007 (2010)[7] A. Bock, et al., Nucl. Fusion 57 126041 (2017)[8] R. White, and H. Mynick, Phys. Fluids B 1, 980 (1989)[9] F. Zonca, et al., Plasma Phys. Control. Fusion 57 014024 (2015)[10] Z. Qiu, L. Chen, and F. Zonca, Nucl. Fusion 56, 106013 (2016)[11] C. Angioni, et al., Nucl. Fusion 49, 055013 (2009)[12] E. M. Bass and R. E. Waltz, Phys. Plasmas 17, 112319 (2010)[13] W. Zhang, V. Decyk, I. Holod, Y. Xiao, Z. Lin, and L. Chen Phys. Plasmas 17, 055902 (2010)[14] J. Citrin, et al, Phys. Rev. Lett. 111, 155001 (2013)[15] J. Garcia, et al., Nucl. Fusion 55 053007 (2015)[16] A. Di Siena, et al., 2019 Nucl. Fusion 59, 124001 (2019)[17] A. Biancalani, et al., Plasma Phys. Control. Fusion 63, 065009 (2021)[18] M. V. Falessi, and F. Zonca, Phys. Plasmas 26, 022305 (2019)[19] F. Zonca, L. Chen, M. V. Falessi and Z. Qiu, J. Phys. Conf. Ser. 1785, 012005 (2021)[20] M. V. Falessi, F. Zonca, Z. Qiu, and L. Chen, P5b.106, this conference.[21] A. Mishchenko, et al, Comp. Phys. Commun. 238, 194 (2019)[22] E. Lanti, et al, Comp. Phys. Commun. 251, 107072 (2020)[23] A. Mishchenko, et al., Plasma Phys. Control. Fusion 63, 084007 (2021)[24] T. Hayward-Schneider, et al, O4.111, this conference.[25] B. Rettino, et al, P1a.112, this conference.48th EPS Conference on Plasma Physics P5b.117

Interaction of Alfvénic modes and turbulence via the nonlinear modification of the equilibrium profiles

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Interaction of Alfvénic modes and turbulence via the nonlinear modification of the equilibrium profiles

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