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Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

Part of: Focus on Fusion

Published online by Cambridge University Press:  23 April 2018

E. G. Highcock Open the ORCID record for E. G. Highcock [Opens in a new window] ,
N. R. Mandell Open the ORCID record for N. R. Mandell [Opens in a new window] ,
M. Barnes Open the ORCID record for M. Barnes [Opens in a new window]  and
W. Dorland Open the ORCID record for W. Dorland [Opens in a new window]
E. G. Highcock*
Affiliation:
Department of Physics, Chalmers University of Technology, Fysikgården 1, 41258 Gothenburg, Sweden Rudolph Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, OX14 3DB, UK
N. R. Mandell
Affiliation:
Department of Astrophysical Sciences, Princeton University, Princeton NJ, 08540, USA
M. Barnes
Affiliation:
Rudolph Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK
W. Dorland
Affiliation:
Department of Physics, University of Maryland, College Park, MD, 20742, USA
*
†Email address for correspondence: [email protected]
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Abstract

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A twofold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.

Keywords

fusion plasmaplasma confinementplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 2 , April 2018 , 905840208
Copyright
© Cambridge University Press 2018 

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References

Abel, I. G. & Cowley, S. C. 2013 Multiscale gyrokinetics for rotating tokamak plasmas: II. Reduced models for electron dynamics. New J. Phys. 15, 023041.Google Scholar
Abel, I. G., Plunk, G. G., Wang, E., Barnes, M., Cowley, S. C., Dorland, W. & Schekochihin, A. A. 2013 Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows. Rep. Progr. Phys. 76 (11), 116201.Google Scholar
Abramson, D., Peachey, T. & Lewis, A. 2006 Model optimization and parameter estimation with Nimrod / O. In Proceedings of the 6th Intl Conf. on Computational Science (ICCS’06), vol. 1, pp. 720–727.Google Scholar
Barnes, M., Abel, I. G., Dorland, W., Görler, T., Hammett, G. W. & Jenko, F. 2010 Direct multiscale coupling of a transport code to gyrokinetic turbulence codes. Phys. Plasmas 17 (5), 056109.Google Scholar
Barnes, M., Parra, F. I., Highcock, E. G., Schekochihin, A., Cowley, S. C. & Roach, C. M. 2011a Turbulent transport in tokamak plasmas with rotational shear. Phys. Rev. Lett. 106 (17), 1–4.Google Scholar
Barnes, M., Parra, F. I. & Schekochihin, A. A. 2011b Critically balanced ion temperature gradient turbulence in fusion plasmas. Phys. Rev. Lett. 107 (11), 115003.Google Scholar
Beer, M. A., Cowley, S. C. & Hammett, G. W. 1995 Field-aligned coordinates for nonlinear simulations of tokamak turbulence. Phys. Plasmas 2 (7), 2687–2700.Google Scholar
Beer, M. A. & Hammett, G. W. 1996 Toroidal gyrofluid equations for simulations of tokamak turbulence. Phys. Plasmas 3 (11), 4046.CrossRefGoogle Scholar
Beer, M. & Hammett, G. 1998 The dynamics of small-scale turbulence-driven flows. In Varenna Proc., pp. 1–11.Google Scholar
Bourdelle, C., Citrin, J., Baiocchi, B., Casati, A., Cottier, P., Garbet, X. & Imbeaux, F. 2016 Core turbulent transport in tokamak plasmas: bridging theory and experiment with QuaLiKiz. Plasma Phys. Control. Fusion 58 (1), 014036.Google Scholar
Budny, R. V. 2009 Comparisons of predicted plasma performance in ITER H-mode plasmas with various mixes of external heating. Nucl. Fusion 49 (8), 85008.CrossRefGoogle Scholar
Burrell, K. H. 1997 Effects of ExB velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices. Phys. Plasmas 4 (5), 1499–1518.Google Scholar
Chang, C. S. & Hinton, F. L. 1982 Effect of impurity particles on the finite-aspect ratio neoclassical ion thermal conductivity in a tokamak. Phys. Fluids 25 (1493), 3314.Google Scholar
Chen, C., Wicks, R., Horbury, T. & Schekochihin, A. 2010 Interpreting power anisotropy measurements in plasma turbulence. Astrophys. J. Lett. 711 (2), L79.CrossRefGoogle Scholar
Citrin, J., Breton, S., Felici, F., Imbeaux, F., Aniel, T., Artaud, J. F., Baiocchi, B., Bourdelle, C., Camenen, Y. & Garcia, J. 2015a Real-time capable first principle based modelling of tokamak turbulent transport. Nucl. Fusion 55 (9), 92001.Google Scholar
Citrin, J., Garcia, J., Görler, T., Jenko, F., Mantica, P., Told, D., Bourdelle, C., Hatch, D. R., Hogeweij, G. M. D., Johnson, T. et al. 2015b Electromagnetic stabilization of tokamak microturbulence in a high- $\unicode[STIX]{x1D6FD}$ regime. Plasma Phys. Control. Fusion 57 (1), 014032.Google Scholar
Citrin, J., Jenko, F., Mantica, P., Told, D., Bourdelle, C., Dumont, R., Garcia, J., Haverkort, J., Hogeweij, G., Johnson, T. et al. 2014 Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment. Nucl. Fusion 54 (2), 023008.Google Scholar
Colyer, G. J., Schekochihin, A. A., Parra, F. I., Roach, C. M., Barnes, M. A., Ghim, Y. C. & Dorland, W. 2017 Collisionality scaling of the electron heat flux in ETG turbulence. Plasma Phys. Control. Fusion 59 (5), 055002.Google Scholar
Dimits, A. M., Bateman, G., Beer, M. A., Cohen, B. I., Dorland, W., Hammett, G. W., Kim, C., Kinsey, J. E., Kotschenreuther, M., Kritz, A. H. et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7 (3), 969.Google Scholar
Dorland, W. & Hammett, G. W. 1993 Gyrofluid turbulence models with kinetic effects. Phys. Fluids B 5, 812–835.Google Scholar
Dorland, W., Jenko, F., Kotschenreuther, M. & Rogers, B. N. 2000 Electron temperature gradient turbulence. Phys. Rev. Lett. 85 (26 Pt 1), 5579–5582.CrossRefGoogle ScholarPubMed
Doyle, E. J., Houlberg, W. A., Kamada, Y., Mukhovatov, V., Osborne, T. H., Polevoi, A., Bateman, G., Connor, J. W., Cordey, J. G., Fujita, T. et al. & ITPA Transport Physics Topical Group, ITPA Confinement Database, Modelling Topical Group & ITPA Pedestal Edge Topical Group, Physics 2007 Chapter 2: Plasma confinement and transport. Nucl. Fusion 47 (6), S18.Google Scholar
Esteco, M.2018 modeFrontier Home Page. http://www.esteco.com/modefrontier.Google Scholar
Federici, G., Kemp, R., Ward, D., Bachmann, C., Franke, T., Gonzalez, S., Lowry, C., Gadomska, M., Harman, J., Meszaros, B. et al. 2014 Overview of EU DEMO design and R&D activities. Fusion Engng Des. 89 (7–8), 882–889.Google Scholar
Frieman, E. A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25 (3), 502.Google Scholar
Galambos, J., Perkins, L., Haney, S. & Mandrekas, J. 1995 Commercial tokamak reactor potential with advanced tokamak operation. Nucl. Fusion 35 (5), 551–573.CrossRefGoogle Scholar
Glasstone, S. & Lovberg, R. H. 1960 Controlled Thermonuclear Reactions. D. Van Noatrand Company.Google Scholar
Hammett, G. W. & Perkins, F. W. 1990 Fluid moment models for Landau damping with application to the ion-temperature-gradient instability. Phys. Rev. Lett. 64 (25), 3019–3022.Google Scholar
Highcock, E. G., Barnes, M., Parra, F. I., Schekochihin, A. A., Roach, C. M. & Cowley, S. C. 2011 Transport bifurcation induced by sheared toroidal flow in tokamak plasmas. Phys. Plasmas 18 (10), 102304.Google Scholar
Highcock, E. G., Barnes, M., Schekochihin, A. A., Parra, F. I., Roach, C. M. & Cowley, S. C. 2010 Transport bifurcation in a rotating tokamak plasma. Phys. Rev. Lett. 105 (21), 215003.Google Scholar
Highcock, E. G., Schekochihin, A. A., Cowley, S. C., Barnes, M., Parra, F. I., Roach, C. M. & Dorland, W. 2012 Zero-turbulence manifold in a toroidal plasma. Phys. Rev. Lett. 109 (26), 265001.Google Scholar
Howes, G. G., TenBarge, J. M., Dorland, W., Quataert, E., Schekochihin, A. A., Numata, R. & Tatsuno, T. 2011 Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Phys. Rev. Lett. 107 (3), 035004.Google Scholar
Jardin, S. C., Kessel, C. E., Mau, T. K., Miller, R. L., Najmabadi, F., Chan, V. S., Chu, M. S., Lahaye, R., Lao, L. L., Petrie, T. W. et al. 2006 Physics basis for the advanced tokamak fusion power plant, ARIES-AT. Fusion Engng Des. 80 (1–4), 25–62.CrossRefGoogle Scholar
Kawamori, E. 2013 Experimental verification of entropy cascade in two-dimensional electrostatic turbulence in magnetized plasma. Phys. Rev. Lett. 110 (9), 095001.CrossRefGoogle ScholarPubMed
Kinsey, J. E., Staebler, G. M., Candy, J., Waltz, R. E. & Budny, R. V. 2011 ITER predictions using the GYRO verified and experimentally validated trapped gyro-Landau fluid transport model. Nucl. Fusion 51 (8), 083001.Google Scholar
Kotschenreuther, M., Rewoldt, G. & Tang, W. M. 1995 Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities. Comput. Phys. Commun. 88 (2–3), 128–140.CrossRefGoogle Scholar
Lewis, A.2004 Parallel optimisation algorithms for continuous, non-linear numerical simulations. PhD thesis, Griffith University, Brisbane, Australia.Google Scholar
Luce, T., Challis, C., Ide, S., Joffrin, E., Kamada, Y., Politzer, P., Schweinzer, J., Sips, A. C. C., Stober, J., Giruzzi, G. et al. 2014 Development of advanced inductive scenarios for ITER. Nucl. Fusion 54 (1), 013015.Google Scholar
Lütjens, H., Bondeson, A. & Sauter, O. 1996 The CHEASE code for toroidal MHD equilibria. Comput. Phys. Commun. 97, 219–260.Google Scholar
Maggi, C. F., Groebner, R. J., Oyama, N., Sartori, R., Horton, L. D., Sips, A. C., Suttrop, W., Leonard, A., Luce, T. C., Wade, M. R. et al. 2007 Characteristics of the H-mode pedestal in improved confinement scenarios in ASDEX upgrade, DIII-D, JET and JT-60U. Nucl. Fusion 47 (7), 535–551.Google Scholar
Mandell, N. & Dorland, W. 2014 Hybrid gyrokinetic/gyrofluid simulation of ITG turbulence. In Bull. Am. Phys. Soc., vol. 59. Abstract CP8.039.Google Scholar
Mandell, N., Dorland, W. & Landreman, M. 2018 Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics. J. Plasma Phys. 84 (1), 905840108.Google Scholar
Manousopoulos, P. & Michalopoulos, M. 2009 Comparison of non-linear optimization algorithms for yield curve estimation. Eur. J. Oper. Res. 192 (2), 594–602.Google Scholar
Marinoni, A., Brunner, S., Camenen, Y., Coda, S., Graves, J. P., Lapillonne, X., Pochelon, A., Sauter, O. & Villard, L. 2009 The effect of plasma triangularity on turbulent transport: modeling TCV experiments by linear and non-linear gyrokinetic simulations. Plasma Phys. Control. Fusion 51 (5), 055016.Google Scholar
Meneghini, O., Snyder, P. B., Smith, S. P., Candy, J., Staebler, G. M., Belli, E. A., Lao, L. L., Park, J. M., Green, D. L., Elwasif, W. et al. 2016 Integrated fusion simulation with self-consistent core-pedestal coupling. Phys. Plasmas 23 (4), 042507.Google Scholar
Merle, A., Sauter, O. & Yu Medvedev, S. 2017 Pedestal properties of H-modes with negative triangularity using the EPED-CH model. Plasma Phys. Control. Fusion 59 (10), 104001.Google Scholar
Mukhovatov, V., Shimomura, Y., Polevoi, A., Shimada, M., Sugihara, M., Bateman, G., Cordey, J. G., Kardaun, O., Pereverzev, G., Voitsekhovitch, I. et al. 2003 Comparison of ITER performance predicted by semi-empirical and theory-based transport models. Nucl. Fusion 43 (9), 942–948.Google Scholar
Parail, V., Albanese, R., Ambrosino, R., Artaud, J. F., Besseghir, K., Cavinato, M., Corrigan, G., Garcia, J., Garzotti, L., Gribov, Y. et al. 2013 Self-consistent simulation of plasma scenarios for ITER using a combination of 1.5D transport codes and free-boundary equilibrium codes. Nucl. Fusion 53 (11), 113002.Google Scholar
Parker, J. T., Highcock, E. G., Schekochihin, A. A. & Dellar, P. J. 2016 Suppression of phase mixing in drift-kinetic plasma turbulence. Phys. Plasmas 23 (7), 070703.Google Scholar
Pochelon, A., Angelino, P., Behn, R., Brunner, S., Coda, S., Kirneva, N., Medvedev, S., Reimerdes, H., Rossel, J., Sauter, O. et al. 2012 Recent TCV results – Innovative plasma shaping to improve plasma properties and insight. Plasma Fusion Res. 7 (SPL.ISS.1), 1–8.Google Scholar
Pochelon, A., Goodman, T., Henderson, M., Angioni, C., Behn, R., Coda, S., Hofmann, F., Hogge, J.-P., Kirneva, N., Martynov, A. et al. 1999 Energy confinement and MHD activity in shaped TCV plasmas with localized electron cyclotron heating. Nucl. Fusion 39 (11Y), 1807–1818.Google Scholar
Roach, C., Walters, M., Budny, R., Imbeaux, F., Fredian, T., Greenwald, M., Stillerman, J., Alexander, D., Carlsson, J., Cary, J. et al. 2008 The 2008 public release of the international multi-tokamak confinement profile database. Nucl. Fusion 48 (12), 125001.Google Scholar
Rogers, B. N., Dorland, W. & Kotschenreuther, M. 2000 Generation and stability of zonal flows in ion-temperature-gradient mode turbulence. Phys. Rev. Lett. 85 (25), 5336–5339.Google Scholar
Rosenbluth, M. & Hinton, F. 1998 Poloidal flow driven by ion-temperature-gradient turbulence in tokamaks. Phys. Rev. Lett. 80 (4), 724.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. & Tatsuno, T. 2009 Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. Ser. 182 (1), 310–377.CrossRefGoogle Scholar
Schekochihin, A. A., Parker, J. T., Highcock, E. G., Dellar, P. J., Dorland, W. & Hammett, G. W. 2016 Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence. J. Plasma Phys. 82 (02), 905820212.CrossRefGoogle Scholar
Simpson, T., Toropov, V., Balabanov, V. & Viana, F. 2008 Design and analysis of computer experiments in multidisciplinary design optimization: a review of how far we have come - or not. In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (September), pp. 1–22.Google Scholar
Snyder, P. & Hammett, G. 2001 A Landau fluid model for electromagnetic plasma microturbulence. Phys. Plasmas 8 (7), 3199–3216.CrossRefGoogle Scholar
Sorbom, B. N., Ball, J., Palmer, T. R., Mangiarotti, F. J., Sierchio, J. M., Bonoli, P., Kasten, C., Sutherland, D. A., Barnard, H. S., Haakonsen, C. B. et al. 2015 ARC: a compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets. Fusion Engng Des. 100, 378–405.Google Scholar
Staebler, G. M. & John, H. E. S. 2006 Predicted toroidal rotation enhancement of fusion power production in ITER. Nucl. Fusion 46 (8), L6–L8.CrossRefGoogle Scholar
Staebler, G. M., Kinsey, J. E. & Waltz, R. E. 2007 A theory-based transport model with comprehensive physics. Phys. Plasmas 14 (5), 055909.Google Scholar
Stork, D., Agostini, P., Boutard, J. L., Buckthorpe, D., Diegele, E., Dudarev, S. L., English, C., Federici, G., Gilbert, M. R., Gonzalez, S. et al. 2014 Materials R&D for a timely DEMO: key findings and recommendations of the EU Roadmap Materials Assessment Group. Fusion Engng Des. 89 (7–8), 1586–1594.Google Scholar
Sugama, H. & Horton, W. 1998 Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows. Phys. Plasmas 5 (7), 2560.Google Scholar
Synakowski, E. J. 1999 Formation and structure of internal and edge transport barriers. Plasma Phys. Control. Fusion 40 (5), 581–596.Google Scholar
Tatsuno, T., Dorland, W., Schekochihin, A. A., Plunk, G. G., Barnes, M., Cowley, S. C. & Howes, G. G. 2009 Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence. Phys. Rev. Lett. 103 (1), 2–5.Google Scholar
Tatsuno, T., Plunk, G., Barnes, M., Dorland, W., Howes, G. & Numata, R. 2012 Freely decaying turbulence in two-dimensional electrostatic gyrokinetics. Phys. Plasmas 19 (12), 122305.Google Scholar
Uckan, N. 1990 ITER Physics Design Guidelines: 1989, ITER Documentation Series, vol. 10. IAEA.Google Scholar
Wagner, F., Fussmann, G., Grave, T., Keilhacker, M., Kornherr, M., Lackner, K., McCormick, K., Müller, E. R., Stäbler, A., Becker, G. et al. 1984 Development of an Edge Transport Barrier at the H-Mode Transition of ASDEX. Phys. Rev. Lett. 53 (15), 1453–1456.Google Scholar
Weisen, H., Alberti, S., Berry, S., Behn, R., Blanchard, P., Bosshard, P., Bühlmann, F., Chavan, R., Coda, S., Deschenaux, C. et al. 1999 Effect of plasma shape on confinement and MHD behaviour in TCV. Plasma Phys. Control. Fusion 39 (12B), B135–B144.Google Scholar
Wenninger, R., Arbeiter, F., Aubert, J., Aho-Mantila, L., Albanese, R., Ambrosino, R., Angioni, C., Artaud, J.-F., Bernert, M., Fable, E. et al. 2015 Advances in the physics basis for the European DEMO design. Nucl. Fusion 55, 063003.Google Scholar
White, A. E., Howard, N. T., Greenwald, M., Reinke, M. L., Sung, C., Baek, S., Barnes, M., Candy, J., Dominguez, A., Ernst, D. et al. 2013 Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulations. Phys. Plasmas 20 (5), 056106.Google Scholar
van Wyk, F., Highcock, E. G., Schekochihin, A. A., Roach, C. M., Field, A. R. & Dorland, W. 2016 Transition to subcritical turbulence in a tokamak plasma. J. Plasma Phys. 82 (6), 905820609.Google Scholar
Xanthopoulos, P., Mynick, H. E., Helander, P., Turkin, Y., Plunk, G. G., Jenko, F., Görler, T., Told, D., Bird, T. & Proll, J. H. 2014 Controlling turbulence in present and future stellarators. Phys. Rev. Lett. 113 (15), 1–4.Google Scholar
Xiao, Y., Catto, P. J. & Dorland, W. 2007 Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual. Phys. Plasmas 14 (5), 055910.Google Scholar
Zohm, H., Angioni, C., Fable, E., Federici, G., Gantenbein, G., Hartmann, T., Lackner, K., Poli, E., Porte, L., Sauter, O. et al. 2013 On the physics guidelines for a tokamak DEMO. Nucl. Fusion 53 (7), 073019.Google Scholar