Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-06-10T20:42:33.884Z Has data issue: false hasContentIssue false
  • English
  • Français

Poloidal impurity asymmetries, flow and neoclassical transport in pedestals in the plateau and banana regimes

Published online by Cambridge University Press:  27 July 2023

Rachel Bielajew  and
Peter J. Catto Open the ORCID record for Peter J. Catto [Opens in a new window]
Rachel Bielajew
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Peter J. Catto*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
† Email address for correspondence: catto@psfc.mit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Charge exchange recombination spectroscopy (CXRS) measures the radial electric field in the pedestal by measuring the impurity density, temperature and flow. Combined outboard and inboard CXRS measurements allow poloidal variations that arise due to the poloidal variation of the magnetic field to be determined. At present, impurity neoclassical pedestal models avoid the complications of treating finite poloidal gyroradius effects by assuming the impurity charge number is large compared with the main ion charge number. These models are extended slightly by retaining the impurity radial pressure gradient to demonstrate that no substantial effect occurs due to impurity diamagnetic effects. More importantly, the neoclassical model is significantly extended to obtain a more comprehensive treatment of the main ions in the plateau and banana regimes. A parallel impurity momentum equation is derived that is consistent with previous results in the banana regime and reduces to the proper large aspect ratio form required in the plateau regime. The implications for interpreting the CXRS measurements are discussed by writing all results in terms of the gradient drive and poloidal flow.

Keywords

fusion plasmaplasma confinementplasma flows
Type
Research Article
Information
Journal of Plasma Physics , Volume 89 , Issue 4 , August 2023 , 905890411
Check for updates
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brau, K., Suckewer, S. & Wong, S.K. 1983 Vertical poloidal asymmetries of low-Z element radiation in the PDX divertor. Nucl. Fusion 23, 1657–1668.CrossRefGoogle Scholar
Churchill, R.M., Lipschultz, B., Theiler, C. & Alcator C-Mod Team. 2013 In-out impurity density asymmetry in the pedestal region of Alcator C-Mod. Nucl. Fusion 53, 122002.CrossRefGoogle Scholar
Churchill, R.M., Theiler, C., Lipschultz, B., Hutchinson, I.H., Reinke, M.L., Whyte, D., Hughes, J.W., Catto, P., Landreman, M., Ernst, D., Chang, C.S., Hager, R., Hubbard, A., Ennever, P., Walk, J.R. & Alcator C-Mod Team. 2015 Poloidal asymmetries in edge transport barrier. Phys. Plasmas 22, 056104.CrossRefGoogle Scholar
Cruz-Zabala, D.J., Viezzer, E., Plank, U., Mcdermott, R.M., Cavedon, M., Fable, E., Dux, R., Cano-Megias, P., Pütterich, T., Jansen van Vuuren, A., Garcia-Munoz, M., Garcia Lopez, J. & ASDEX Upgrade Team. 2022 In-out charge exchange measurements and 3D modelling of diagnostic thermal neutrals to study edge poloidal impurity asymmetries. Plasma Phys. Control. Fusion 64, 045021.CrossRefGoogle Scholar
Durst, R.D. 1992 Vertical asymmetries in soft x-ray emissivity in COMPASS-C. Nucl. Fusion 32, 2238–2242.CrossRefGoogle Scholar
Espinosa, S. & Catto, P.J. 2017 a Pedestal radial flux measuring method to prevent impurity accumulation. Phys. Plasmas 24, 055904.CrossRefGoogle Scholar
Espinosa, S. & Catto, P.J. 2017 b Radial impurity flux measuring method with plasma heating in general geometry. Plasma Phys. Control. Fusion 59, 105001.CrossRefGoogle Scholar
Espinosa, S. & Catto, P.J. 2018 Theoretical explanation of I-mode impurity removal and energy confinement. Plasma Phys. Control. Fusion 60, 094001.CrossRefGoogle Scholar
Espinosa, S. & Catto, P.J. 2019 Non-linear neoclassical model for poloidal asymmetries in tokamak pedestals: diamagnetic and radial effects included. arXiv:1911.06365.Google Scholar
Fülöp, T. & Helander, P. 1999 Nonlinear neoclassical transport in a rotating impure plasma with large gradients. Phys. Plasmas 6, 3066–3075.CrossRefGoogle Scholar
Fülöp, T. & Helander, P. 2001 Nonlinear neoclassical transport in toroidal edge plasmas. Phys. Plasmas 8, 3305–3313.CrossRefGoogle Scholar
Helander, P. 1998 Bifurcated neoclassical particle transport. Phys. Plasmas 11, 3999–4004.CrossRefGoogle Scholar
Hinton, F.L. & Hazeltine, R.D. 1976 Theory of plasma transport in toroidal confinement systems. Rev. Mod. Phys. 48, 239–308.CrossRefGoogle Scholar
Landreman, M., Fülöp, T. & Guszejnov, D. 2011 Impurity flows and plateau-regime poloidal density variation in a tokamak pedestal. Phys. Plasmas 18, 092507.CrossRefGoogle Scholar
Maget, P., Frank, J., Nicolas, T., Agullo, O., Garbet, X. & Lütjens, H. 2020 a Natural poloidal asymmetry and neoclassical transport of impurities in tokamak plasmas. Plasma Phys. Control. Fusion 62, 025001.CrossRefGoogle Scholar
Maget, P., Manas, P., Frank, J., Nicolas, T., Agullo, O. & Garbet, X. 2020 b An analytic model for the collisional transport and poloidal asymmetry distribution of impurities in tokamak plasmas. Plasma Phys. Control. Fusion 62, 105001.CrossRefGoogle Scholar
Marr, K.D., Lipschultz, B., Catto, P.J., Mcdermott, R.M., Reinke, M.L. & Simakov, A.N. 2010 Comparison of neoclassical predictions with measured flows and evaluation of a poloidal impurity density asymmetry. Plasma Phys. Control. Fusion 52, 055010.CrossRefGoogle Scholar
Mcdermott, R.M., Lipschultz, B., Hughes, J.W., Catto, P.J., Hubbard, A.E., Hutchinson, I.H., Granetz, R.S., Greenwald, M., Labombard, B., Marr, K., Reinke, M.L., Rice, J.E., Whyte, D. & Alcator C-Mod Team. 2009 Edge radial electric field structure and its connections to H-mode confinement in Alcator C-Mod plasmas. Phys. Plasmas 16, 056103.CrossRefGoogle Scholar
Pedersen, T.S., Granetz, R.S., Marmar, E.S., Mossessian, D., Hughes, J.W., Hutchinson, I.H., Terry, J. & Rice, J.E. 2002 Measurements of large poloidal variations of impurity density in the Alcator C-Mod H-mode barrier region. Phys. Plasmas 9, 4188–4192.CrossRefGoogle Scholar
Pusztai, I. & Catto, P.J. 2010 Neoclassical plateau regime transport in a tokamak pedestal. Plasma Phys. Control. Fusion 52, 075016.CrossRefGoogle Scholar
Pütterich, T., Viezzer, E., Dux, R., Mcdermott, R. M. & ASDEX Upgrade Team. 2012 Poloidal asymmetry of parallel rotation measured in ASDEX upgrade. Nucl. Fusion 52, 083013.CrossRefGoogle Scholar
Rice, J.E., Terry, J.L., Marmar, E.S. & Bombarda, F. 1997 X ray observations of up-down impurity density asymmetries in Alcator C-Mod plasmas. Nucl. Fusion 37, 241–249.CrossRefGoogle Scholar
Rosenbluth, M.N., Hazeltine, R.D. & Hinton, F.L. 1972 Plasma transport in toroidal confinement systems. Phys. Fluids 15, 116–140.CrossRefGoogle Scholar
Ryter, F., Fischer, R., Fuchs, J.C., Happel, T., Mcdermott, R.M., Viezzer, E., Wolfrum, E., Barrera Orte, L., Bernert, M., Burckhart, A., da Graça, S., Kurzan, B., Mccarthy, P., Pütterich, T., Suttrop, W., Willensdorfer, M. & ASDEX Upgrade Team. 2017 I-mode studies at ASDEX upgrade: L-I and I-H transitions, pedestal and confinement properties. Nucl. Fusion 57, 016004.CrossRefGoogle Scholar
Terry, J.L., Marmar, E.S., Chen, K.I. & Moos, H.W. 1977 Observation of poloidal asymmetry in impurity-ion emission due to ∇B drifts. Phys. Rev. Lett. 39, 1615–1618.CrossRefGoogle Scholar
Theiler, C., Churchill, R.M., Lipschultz, B., Landreman, M., Ernst, D.R., Hughes, J.W., Catto, P.J., Parra, F.I., Hutchinson, I.H., Reinke, M.L., Hubbard, A.E., Marmar, E.S., Terry, J.T., Walk, J.R. & Alcator C-Mod Team 2014 Inboard and outboard radial electric field wells in the H- and I-mode pedestal of Alcator C-Mod and poloidal variations of impurity temperature. Nucl. Fusion 54, 083017.CrossRefGoogle Scholar
Trinczek, S., Parra, F.I., Catto, P.J., Calvo, I. & Landreman, M. 2023 Neoclassical transport in strong gradient regions of large aspect ratio tokamaks. J. Plasma Phys. 89, 905890304.CrossRefGoogle Scholar
Viezzer, E., Cavedon, M., Fable, E., Laggner, F.M., Mcdermott, R.M., Galdon-Quiroga, J., Dunne, M.G., Kappatou, A., Angioni, C., Cano-Megias, P., Cruz-Zabala, D.J., Dux, R., Püterich, T., Ryter, F., Wolfrum, E., ASDEX Upgrade Team & Eurofusion MST1 Team. 2018 Ion heat transport dynamics during edge localized mode cycles at ASDEX upgrade. Nucl. Fusion 58, 026031.CrossRefGoogle Scholar
Viezzer, E., Fable, E., Cavedon, M., Angioni, C., Dux, R., Laggner, F.M., Bernert, M., Burckhart, A., Mcdermott, R.M., Püterich, T., Ryter, F., Willensdorfer, M., Wolfrum, E., ASDEX Upgrade Team & Eurofusion MST1 Team. 2017 Investigation of inter-ELM ion heat transport in the H-mode pedestal of ASDEX upgrade plasmas. Nucl. Fusion 57, 022020.CrossRefGoogle Scholar
Viezzer, E., Pütterich, T., Conway, G.D., Dux, R., Happel, T., Fuchs, J.C., Mcdermott, R.M., Ryter, F., Sieglin, B., Suttrop, W., Willensdorfer, M., Wolfrum, E. & ASDEX Upgrade Team. 2013 a High-accuracy characterization of the edge radial electric field at ASDEX upgrade. Nucl. Fusion 53, 053005.CrossRefGoogle Scholar
Viezzer, E., Pütterich, T., Fable, E., Bergmann, A., Dux, R., Mcdermott, R.M., Churchill, R.M., Dunne, M.G. & ASDEX Upgrade Team. 2013 b Rotation and density asymmetries in the presence of large poloidal impurity flows in the edge pedestal. Plasma Phys. Control. Fusion 55, 124037.CrossRefGoogle Scholar
Wade, M.R., Houlberg, W.A. & Baylor, L.R. 2000 Experimental confirmation of impurity convection driven by the ion-temperature gradient in toroidal plasmas. Phys. Rev. Lett. 84, 282–285.CrossRefGoogle ScholarPubMed
Wagner, F., et al. 1982 Regime of improved confinement and high beta in neutral-beam-heated divertor discharges of the ASDEX Tokamak. Phys. Rev. Lett. 49, 1408–1412.CrossRefGoogle Scholar
Whyte, D.G., et al. 2010 I-mode: an H-mode energy confinement regime with L-mode particle transport in Alcator C-Mod. Nucl. Fusion 50, 105005.CrossRefGoogle Scholar