Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-24T02:44:34.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Electromagnetic zonal flow residual responses

Part of: Focus on Fusion

Published online by Cambridge University Press:  03 July 2017

Peter J. Catto ,
Felix I. Parra  and
István Pusztai
Peter J. Catto*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Felix I. Parra
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK Culham Centre for Fusion Energy, Abingdon OX14 3DB, UK
István Pusztai
Affiliation:
Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.

Keywords

fusion plasmamagnetized plasmasplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 4 , August 2017 , 905830402
Check for updates
Copyright
© Cambridge University Press 2017 

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

Belli, E. A.2006 Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence. PhD thesis, Princeton University.Google Scholar
Biglari, H., Diamond, P. H. & Terry, P. W. 1990 Influence of sheared poloidal rotation on edge turbulence. Phys. Fluids B 2 (1), 1–4.Google Scholar
Catto, P. J. 1978 Linearized gyro-kinetics. Plasma Phys. 20 (7), 719.CrossRefGoogle 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), 969–983.Google Scholar
Dimits, A. M., Williams, T. J., Byers, J. A. & Cohen, B. I. 1996 Scalings of ion-temperature-gradient-driven anomalous transport in tokamaks. Phys. Rev. Lett. 77, 71–74.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 2007 Table of Integrals, Series, and Products, 7th edn. Elsevier/Academic, 182, 186, 187, and 615–616.Google Scholar
Helander, P. & Sigmar, D. J. 2005 Collisional Transport in Magnetized Plasmas. pp. 126–127. Cambridge University Press.Google Scholar
Hinton, F. L. & Rosenbluth, M. N. 1999 Dynamics of axisymmetric $E\times B$ and poloidal flows in tokamaks. Plasma Phys. Control. Fusion 41 (3A), A653–A662.Google Scholar
Jenko, F., Dorland, W., Kotschenreuther, M. & Rogers, B. N. 2000 Electron temperature gradient driven turbulence. Phys. Plasmas 7 (5), 1904–1910.Google Scholar
Kagan, G. & Catto, P. J. 2008 Arbitrary poloidal gyroradius effects in tokamak pedestals and transport barriers. Plasma Phys. Control. Fusion 50 (8), 085010.CrossRefGoogle Scholar
Kagan, G. & Catto, P. J. 2009 Zonal flow in a tokamak pedestal). Phys. Plasmas 16 (5), 056105.Google Scholar
Monreal, P., Calvo, I., Sánchez, E., Parra, F. I., Bustos, A., Könies, A., Kleiber, R. & Görler, T. 2016 Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths. Plasma Phys. Control. Fusion 58 (4), 045018.Google Scholar
Rosenbluth, M. N. & Hinton, F. L. 1998 Poloidal flow driven by ion-temperature-gradient turbulence in tokamaks. Phys. Rev. Lett. 80, 724–727.CrossRefGoogle Scholar
Shafranov, V. D. 1966 Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 2, p. 103. Consultants Bureau.Google Scholar
Sugama, H. & Watanabe, T.-H. 2005 Dynamics of zonal flows in helical systems. Phys. Rev. Lett. 94, 115001.CrossRefGoogle ScholarPubMed
Terry, P. W. 2000 Suppression of turbulence and transport by sheared flow. Rev. Mod. Phys. 72, 109–165.CrossRefGoogle Scholar
Terry, P. W., Pueschel, M. J., Carmody, D. & Nevins, W. M. 2013 The effect of magnetic flutter on residual flow. Phys. Plasmas 20 (11), 112502.Google Scholar
Winsor, N., Johnson, J. L. & Dawson, J. M. 1968 Geodesic acoustic waves in hydromagnetic systems. Phys. Fluids 11 (11), 2448–2450.Google Scholar
Xiao, Y. & Catto, P. J. 2006a Plasma shaping effects on the collisionless residual zonal flow level. Phys. Plasmas 13 (8), 082307.Google Scholar
Xiao, Y. & Catto, P. J. 2006b Short wavelength effects on the collisionless neoclassical polarization and residual zonal flow level. Phys. Plasmas 13 (10), 102311.Google Scholar
Xiao, Y., Catto, P. J. & Dorland, W. 2007a Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual. Phys. Plasmas 14 (5), 055910-6.CrossRefGoogle Scholar
Xiao, Y., Catto, P. J. & Molvig, K. 2007b Collisional damping for ion temperature gradient mode driven zonal flow. Phys. Plasmas 14 (3), 032302.Google Scholar