Bourdelle, C.

Citrin, J.

Felici, F.

Ho, A.

Sauter, O.

Teplukhina, A.A.

Van De Plassche, K.

English

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 Real-Time multichannel tokamak plasma profile simulationsusing the RAPTOR code and the QLKNN first-principletransport modelCitation for published version (APA):Felici, F., Citrin, J., Van De Plassche, K., Teplukhina, A. A., Ho, A., Bourdelle, C., & Sauter, O. (2018). Real-Time multichannel tokamak plasma profile simulations using the RAPTOR code and the QLKNN first-principletransport model. In S. Coda, S. Weber, J. Berndt, C. Michaut, G. Lapenta, & M. Mantsinen (Eds.), 45th EPSConference on Plasma Physics, EPS 2018 (pp. 1256-1259). European Physical Society (EPS).Document status and date:Published: 01/01/2018Document Version:Typeset version in publisher’s lay-out, without final page, issue and volume numbersPlease check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 05. Oct. 2023Real-time multichannel tokamak plasma profile simulations using theRAPTOR code and the QLKNN first-principle transport modelF. Felici1, J. Citrin2, K. van de Plassche2, A.A. Teplukhina1, A. Ho2, C. Bourdelle3, O. Sauter1,JET contributors∗, and the EUROfusion MST1 team†1Swiss Plasma Center (SPC), École Polytechnique Fédérale de Lausanne (EPFL), Station 13,CH-1015, Lausanne, Switzerland 2DIFFER, Eindhoven, The Netherlands. 3CEA-IRFM,France.IntroductionReal-time capable yet accurate simulators for the plasma (1D) profile evolution in a toka-mak are important for discharge preparation and optimization, controller validation, as well asreal-time profile reconstruction and control. The RAPTOR code, a transport code capable ofsimulating the plasma profile time-evolution in real-time, has been used for this purpose onTCV, AUG and RFX [1, 2, 3]. The code has recently undergone improvements and upgradesto improve its physics fidelity, while maintaining the real-time capabilities. In this work wepresent the recent addition of ion temperature and particle transport equations in RAPTOR, aswell as the use of first-principle-based QLKNN code, a neural-network emulation of the quasi-linear gyrokinetic code QuaLiKiz [4], to provide accurate transport coefficients. As a result, forthe first time, real-time-capable coupled simulations of the kinetic profiles Te, Ti and ne and qprofile have been obtained that agree well with experimental data for JET.The RAPTOR code and its recent upgradesIn order to be fast enough for routine use for control purposes, the RAPTOR code circum-vents common bottlenecks in tokamak transport simulations. For example, the Grad-Shafranovequilibrium is not self-consistently evolved, but geometric properties of the equilibrium aretaken from pre-computed equilibria. Similarly, deposition profiles from auxiliary heating andcurrent drive sources are implemented as parametrizations of results from heavier codes, andtransport coefficients are calculated using ad-hoc, analytical transport models. First versions ofthe RAPTOR code, aimed primarily at predicting the time-evolution of the q profile, solvedonly the poloidal flux diffusion and electron energy transport equations. In order to extend thepredictive capabilities of the code, the ion energy transport equation was added, as well as thepossibility to take into account a time-varying geometry [5]. Most recently, particle transportequations for ions, electrons and impurity species have been implemented as well. The particle∗See the author list of X. Litaudon et al 2017 Nucl. Fusion 57 102001†See the author list of H. Meyer et al 2017 Nucl. Fusion 57 10201445th EPS Conference on Plasma Physics P4.1091transport equation for a generic species s is implemented in RAPTOR as:1V ′ρ̂(∂∂ t∣∣∣∣ρ̂− Φ̇b2Φb∂∂ ρ̂ρ̂)[(V ′ρ̂)ns]+1V ′ρ̂∂∂ ρ̂Γs = Ss (1)withΓs =−g1V ′ρ̂Ds∂ns∂ ρ̂+g0Vsns (2)Here, ns(ρ, t) is the particle density of the species of interest, Γs is the particle flux, ρ̂ is thenormalized toroidal flux, Φb is the toroidal flux enclosed by the last closed flux surface, V ′ =∂V/∂ ρ̂ , g0 = 〈|∇V |〉 and g1 = 〈|∇V |2〉 depend on the magnetic equilibrium geometry and areexternally prescribed.To test the correctness of the implementation, a 4-channel RAPTOR simulation (ψ , Te, Ti, ne)was compared to a CRONOS simulation using the same QLKNN-4Dkin transport model (dis-cussed below). The results agree well, with small differences that can be explained by differingdetails of the numerics, treatment of boundary conditions, and smoothing in the two cases [6].Profile simulations using the QLKNN transport modelIn recent years, tokamak transport coefficient estimates that agree well with experimentalresults have been obtained from physics-based codes such as QuaLiKiz. QuaLiKiz solves thequasilinear gyrokinetic equation to calculate the linear stability of modes in the the plasma thatdrive turbulent fluxes, and uses a nonlinear saturation rule to calculate the dependence betweenthese linear growth rates and the resulting fluxes once the turbulent modes have reached satura-tion [4]. As such, QuaLiKiz is already several orders of magnitude faster than local nonlineardelta-f gyrokinetic codes, while providing comparable accuracy, typically returning the valuesof turbulent flux (or transport coefficients) in 10CPUs per radial position per time step. A fur-ther speed-up can be obtained by creating a surrogate model, or emulation, of the input-outputbehaviour or QuaLiKiz via neural-networks. Since the neural network is an analytic function,the resulting QLK-NN transport model takes only ∼1CPUms per radial position per time step,a speedup of 4 orders of magnitude compared to full QuaLiKiz. Crucially, also the Jacobiansof the outputs with respect to the input parameters can be returned, which is useful for implicitPDE transport solvers (allowing large simulation time steps) and for control and optimizationpurposes.Depending on the amount of inputs into QuaLiKiz that are varied during training of the neu-ral network, various versions of QLKNN are obtained. A proof-of-principle version, namedQLKNN-4D, uses four inputs: the normalised logarithmic ion temperature gradient R/LTi , the45th EPS Conference on Plasma Physics P4.1091ion to electron temperature ratio Ti/Te, the safety factor q, and magnetic shear s and returnsonly electron and ion heat diffusion coefficients [7]. More recently, this has been extended tothe QLKNN-4Dkin transport model featuring kinetic electrons and to returning also the par-ticle diffusion and pinch coefficients De and Ve. This model was trained in the regime whereturbulence drive is dominated by ITG modes and has proven successful in reproducing kineticprofiles from the well-studied JET 73342 discharge, while setting only the value of the pro-files at the top of the pedestal as a boundary condition. Comparisons of experimental data topredicted profiles, as well as comparison of fluxes obtained from QLKNN-4Dkin versus fullQuaLiKiz are presented in detail in [6]. In Figure 1 the main result is shown: the core profilesare well-approximated in the region 0.4< ρ < 0.85 with slight underestimation in the core. Thissimulation used a source profiles parametrization, as well as equilibrium data, from a previousCRONOS simulation. In the future, real-time capable heating and current drive source codessuch as RT-TORBEAM for Electron Cyclotron heating and current drive [8] and the RABBITcode for Neutral Beam deposition calculations [9] can be used. Adding the effect of sawteeth,radiation losses and ICRH heating improves the result further.0 0.5 100.511.522.533.544.5;NTe [keV]exp4Dkin w.o. ST,IC,RAD10D w.o. ST,IC,RAD4Dkin w . ST,IC,RAD0 0.5 100.511.522.533.544.5;NTi [keV]exp4Dkin w.o. ST,IC,RAD10D w.o. ST,IC,RAD4Dkin w . ST,IC,RAD0 0.5 1024681012;Nne [1019m -3]exp4Dkin w.o. ST,IC,RAD10D w.o. ST,IC,RAD4Dkin w . ST,IC,RADFigure 1: RAPTOR prediction of Te, Ti and ne profiles with QLKANN-4D (with and without includingsawteeth, radiation sinks and ICRH heating), as well as first predictions with QLKANN-10D.Time-varying simulations were also carried out in order to test the speed of the code towardsentire-discharge simulations. Using a simulation time step of 0.25s, which is comparable to theJET energy confinement time, one second of JET plasma could be simulated in less than 0.2s ona standard laptop with an i5 processor, showing the potential for accurate faster-than-real-timesimulations.We show here for the first time the most recent results using RAPTOR with an even moreadvanced version of the neural network transport model, QLKNN-10D [10]. This model istrained on an extended parameter space including further dependence on the electron temper-45th EPS Conference on Plasma Physics P4.1091ature gradient R/LTe , the density gradient R/Lne , local aspect ratio ε , normalised collisionalityν∗, effective charge Ze f f , and perpendicular flow shear ΓE ∼ ∂vtor∂ρ , and covers ITG/TEM/ETGturbulence regimes. In order to account for known limitations in the QuaLiKiz predictions athigh collisionality, the training range was purposely restricted to ν∗ < 0.05 and the inputs intothe transport model are clipped to that maximum. Results with this transport model are alsoshown in Figure 1 (green curve), showing that the simulation approaches the experimental mea-surements even more closely than the QLKNN-4Dkin results.Conclusions and OutlookMultichannel (ψ , Te, Ti, ne) core profile simulations using the fast RAPTOR transport modelwith the fast-yet-accurate physics-based QLKNN-4Dkin transport model has shown to be ableto reproduce core profiles from a JET discharge, with simulation times satisfying the require-ments for real-time simulations. First tests of the more complete transport model, QLKNN-10D, point towards further improvements of accuracy. Development and integration of real-time capable particle, heating and current drive source codes will reduce the dependency onparametrized actuator models. More tests of RAPTOR using this transport model are underwaytowards showing entire-discharge simulations for various shots in different scenarios on vari-ous tokamaks. Real-time implementations of multichannel simulations for plasma monotiring,profile estimation and control are foreseen on JET and MST1 devices in the near future.References[1] Felici, F. et al. 2012 Plasma Physics and Controlled Fusion 54 025002[2] Felici, F. et al. 2016 in 26th IAEA Fusion Energy Conference, Kyoto, Japan EX/P8–33[3] Piron, C. et al. 2016 in Proceedings of the 29th Symposium On Fusion Technology[4] Bourdelle, C. et al. 2016 Plasma Physics and Controlled Fusion 58 014036[5] Teplukhina, A.A. et al. 2017 Plasma Physics and Controlled Fusion 59 124004[6] Felici, F. et al. 2018 Nuclear Fusion To be published[7] Citrin, J. et al. 2015 Nuclear Fusion 55 092001[8] Poli, E. et al. 2018 Computer Physics Communications 225 36[9] Weiland, M. et al. 2018 Nuclear Fusion to be published[10] van de Plassche, K. et al. in This conference, P2.1086This work has been carried out within the framework of the EUROfusion Consortium and has received fundingfrom the Euratom research and training programme 2014-2018 under grant agreement No 633053. The viewsand opinions expressed herein do not necessarily reflect those of the European Commission. This project is alsosponsored in part by the Swiss National Science foundation.45th EPS Conference on Plasma Physics P4.1091

Real-Time multichannel tokamak plasma profile simulations using the RAPTOR code and the QLKNN first-principle transport model

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Real-Time multichannel tokamak plasma profile simulations using the RAPTOR code and the QLKNN first-principle transport model

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