TGLF transport model predictions have been assessed in the vicinity of a theoretical high β burning plasma spherical tokamak at Q=10. Linear micro-stability calculations from TGLF have been compared on a surface at mid-radius with the gyrokinetic code GS2. Differences between TGLF and GS2 spectra can be characterised by the RMS difference in growth rates, σγ. We find considerable improvement in the quality of TGLF growth rate spectrum can be achieved by increasing the number of parallel basis functions and by tuning the TGLF parameter used in the model for trapped particles, θtrap

Dickinson, David

Koechl, F.

Patel, Bhavin

Roach, Colin

Staebler, Gary

Wilson, Howard Read

English

White Rose Research Online

This is a repository copy of Optimising TGLF for a Q=10 Burning Spherical Tokamak.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/159700/Version: Accepted VersionProceedings Paper:Patel, Bhavin, Dickinson, David orcid.org/0000-0002-0868-211X, Koechl, F. et al. (3 more authors) (2019) Optimising TGLF for a Q=10 Burning Spherical Tokamak. In: 46th EPS Conference on Plasma Physics, EPS 2019. 46th EPS Conference on Plasma Physics, EPS 2019, 08-12 Jul 2019 European Physical Society (EPS) , ITA . eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Optimising TGLF for a Q=10 Burning Spherical TokamakBhavin Patel1,2, D. Dickinson1, F. Koechl2, C. Roach2, G. Staebler3, and H. Wilson1,21York Plasma Institute, Department of Physics, University of York, YO10 5DD, UK2Culham Centre for Fusion Energy, Abingdon, Oxfordshire, OX13 3DB, UK3General Atomics (GA), P.O. Box 85608, San Diego, CA, 92121, USAAbstractTGLF transport model predictions have been assessed in the vicinity of a the-oretical high β burning plasma spherical tokamak at Q=10. Linear micro-stabilitycalculations from TGLF have been compared on a surface at mid-radius with thegyrokinetic code GS2. Differences between TGLF and GS2 spectra can be charac-terised by the RMS difference in growth rates, σγ . We find considerable improve-ment in the quality of TGLF growth rate spectrum can be achieved by increasingthe number of parallel basis functions and by tuning the TGLF parameter used inthe model for trapped particles, θtrap.1 IntroductionThe fusion performance of a Burning Spherical Tokamak (BurST) will be criticallydependant on the quality of confinement, and the plasma will be in a regime where no othermachine has operated. While it is possible to extrapolate the confinement using existingglobal scaling laws (e.g. H98 [1] and HPetty08 [2]), obtaining higher fidelity predictionsrequires using physics based models like TGLF [3, 4]. However, TGLF remains largelyuntested in the extreme parameters space of BurST. This work sets out to address this.A candidate Q=10 design has been proposed based on a confinement assumption, usingthe fixed boundary equilibrium solver SCENE and the NUBEAM code [5]. The neutralbeam configuration was chosen to generate a current profile suitable for non-inductiveoperation. The temperature and density profiles, including the pedestal height wereprescribed, consistent with the Q=10 requirement. This equilibrium is used to exploreTGLF predictions for the core plasma. The pedestal region requires its own separatestudy and is not examined here.TGLF solves the linear Gyro-Landau fluid equations and uses the eigenmodes to calcu-late the quasi-linear fluxes of energy and particles. A model for the saturated fluctuationintensity has been created by comparisons to non-linear simulations with GYRO, allowingfor estimation of absolute fluxes.JINTRAC [6], a integrated modelling suite has been used to model the heat transportin BurST and predict the temperature profiles. The neoclassical transport has beencalculated using NCLASS [7], and the anomalous transport with TGLF.Starting with the target SCENE equilibrium, the electron and ion temperature profiles1were evolved until a steady state solution was reached with TGLF’s default settings. Thefusion power falls from Pfus = 1.1GW → 350MW . Increasing the number of TGLFparallel basis functions used to fit the eigenmode to 8 reduces the transport and providestemperatures profiles consistent with Pfus = 1.3GW . This highlights that TGLF predic-tions for BurST are highly sensitive to TGLF’s tuning parameters, which motivates ourgoal to verify TGLF via direct comparisons with the local gyrokinetic code GS2 [8], witha view to improve TGLF predictions in the burning ST regime.2 TGLF default settingsThe default parameters for TGLF include to ignore the pressure component to thecurvature drift and use 4 basis functions to fit the eigenmode. Furthermore, TGLF hasa tunable parameter called θtrap setting a boundary to divide the treatment of trappedparticles as either resonant or Landau averaging, which directly impacts the trappedelectron drive. To consistently calculate this boundary the parallel wavenumber is needed,yet it is not known before the calculation. The choice of θtrap is effectively a guess at k||.θtrap = 0.7, by default, as this value minimised the fractional error between TGLF andGKS [9] growth rates for DIII-D like equilibria [10]. In an ST the trapped particle fractionis much larger than for a conventional device like DIII-D, so θtrap was re-optimised forBurST. This work examines a mid flux surface r/a = 0.5.3 Simplified geometryUsing the SCENE equilibrium the local Miller parameters, like elongation and trian-gularity, were determined. Before exploring this challenging equilibrium, a simplifiedFigure 1: Linear growth rates (left) and frequencies (right) of the mode calculated by GS2 and TGLF fora R/a = 3.0, β = 0 equilibrium. Qualitative agreement can be seen between the two, with the change infrequency, indicating switching to a new branch occurring at the similar kyρs.2Figure 2: Linear growth rates calculated by GS2 and TGLF for a R/a = 1.9, β = 0 equilibrium. Withdefault TGLF settings (left) and optimised settings (right). Increasing the number of basis functions andsetting θtrap = 0.4 results in the lowest σγ .version was examined where β = 0, β′ = 0 and the aspect ratio was artificially increasedfrom R/a = 1.9 → 3.0. The linear growth rate spectra from the two codes for theseelectrostatic modes are shown in Figure 1.With default TGLF input parameters, the linear growth rates from TGLF exceed thegrowth rates predicted by GS2, with the RMS fractional difference σγ = 58%. Increasingthe number of TGLF basis functions to 8 reduces the difference to σγ = 45%.We have also considered an equilibrium with a consistent aspect ratio of R/a = 1.9, atβ = 0. The results are shown in Table 1 where σγ is examined in three regions, kyρs < 1(low), 1 < kyρs < 10 (mid) and kyρs > 10 (high). Again, increasing the number of basisfunctions from 4 to 8 reduced σγ, this time from 77% to 55%. If θtrap is set to 0.4, thenthis is further reduced down to 29%. Figure 2 shows the linear growth rates. It can alsobe seen that around ky = 10, for the modified settings, TGLF and GS2 diverge quite abit as it appears TGLF picks up a different mode, raising σγ to 38%.By increasing the number of basis functions further from 8 to 16, the agreement inthe low and mid regions can be improved further. Curiously, however, TGLF the high4 basis 8 basis 8 basis 8 basis 8 basis 8 basisθtrap = 0.7 θtrap = 0.7 θtrap = 0.6 θtrap = 0.5 θtrap = 0.4 θtrap = 0.3σlowγ (%) 56 60 44 32 30 40σmidγ (%) 86 58 48 29 12 58σhighγ (%) 80 50 36 43 38 48σtotalγ (%) 77 55 43 36 29 50Table 1: Differences in the growth rates for 3 different regions in ky (low, mid and high - see text) forR/a = 1.9. Increasing the number of basis function reduced σγ . Reducing θtrap reduced the differencesin the low to mid ky regions. Colours correspond to σγ > 50% , 30% < σγ < 50% & σγ < 30%3ky modes are stable when using 16 basis functions, but again are unstable with 32 basisfunctions. This discrepancy should be examined. The difference in σγ between 8 and 32was not significant and the increased number of basis functions would be computationallyexpensive in a transport solver. 8 basis functions appears to be a good balance of accuracyand speed. Another option is to have the number of basis functions depend on ky.4 ConclusionsThe TGLF linear electrostatic micro-instability predictions have been compared withlocal gyrokinetic calculations using GS2 for highly shaped equilibria at R/a = 3.0 andR/a = 1.9, where the other local parameters are taken from a SCENE equilibrium forBurST. We have explored the sensitivity of the TGLF results to the number of basisfunctions and the value of θtrap. For the local equilibrium with R/a = 3.0, the defaultTGLF settings resulted in a σγ = 58%. Increasing the number of basis functions to 8reduced this to σγ = 45%. Similarly at R/a = 1.9 increasing the number of basis functionsto 8 and reducing the value of θtrap = 0.4 dropped σγ from 77% to 29%. This indicatesthat the default TGLF parameters can be adjusted to improve the model’s descriptionof electrostatic micro-instabilities in STs. Note that the parameters found here may notbe suitable for all flux surfaces, and other surfaces must be studied to assess the optimalvalues. A more self-consistent approach, with a modest additional computational cost,may be to update θtrap using the k|| after a first iteration, and use this to recalculate theimpact on trapped particles. Future work will compare TGLF with local gyrokinetics forhigh β equilibria, where fluctuations in the magnetic field are more important; this willbe the regime necessary to optimise the efficiency of fusion power production.This work was supported by the Engineering and Physical Sciences Research Council[EP/L01663X/1]. This work has been carried out within the framework of the EURO-fusion Consortium and has received funding from the Euratom research and trainingprogramme 2014-2018 and 2019-2020 under grant agreement No 633053. The views andopinions expressed herein do not necessarily reflect those of the European Commission.References[1] ITER Physics Basis 1999 Nucl. Fusion 39 2137[2] C.C. Petty, Physics of Plasmas 15 080501,2008.[3] G.M. Staebler, J.E. Kinsey, and R.E. Waltz.,Phys. Plasmas, 14:055909, 2007.[4] G.M. Staebler and J.E. Kinsey., Phys. Plas-mas, 17:122309, 2010.[5] A. Pankin, et al., Computer Physics Commu-nications 159.3 157-184, 2014.[6] M. Romanelli, et al., Plasma and Fusion re-search 9, 3403023, 2014.[7] S. Breton et al. Phys. Plasmas 25, 012303,2018.[8] M. Barnes et al 2019, (June10) GS2 v8.0.2 (Version 8.0.2).http://doi.org/10.5281/zenodo.2645150[9] M. Kotschenreuther, Bull. Am. Phys. Soc. 371432, 1992.[10] G.M. Staebler, J.E. Kinsey and R.E. Waltz.,Phys. Plasmas, 12:102508, 2005.4

Optimising TGLF for a Q=10 Burning Spherical Tokamak

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Optimising TGLF for a Q=10 Burning Spherical Tokamak

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