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Sub-Alfvénic reduced magnetohydrodynamic equations for tokamaks

Part of: Focus on Fusion

Published online by Cambridge University Press:  27 June 2017

W. Sengupta Open the ORCID record for W. Sengupta [Opens in a new window] ,
A. B. Hassam  and
T. M. Antonsen Jr
W. Sengupta*
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA
A. B. Hassam
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA
T. M. Antonsen Jr
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA
*
†Email address for correspondence: wricksg@gmail.com
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Abstract

A reduced set of magnetohydrodynamic (MHD) equations is derived, applicable to large aspect ratio tokamaks and relevant for dynamics that is sub-Alfvénic with respect to ideal ballooning modes. This ordering optimally allows sound waves, Mercier modes, drift modes, geodesic-acoustic modes (GAM), zonal flows and shear Alfvén waves. Wavelengths long compared to the gyroradius but comparable to the minor radius of a typical tokamak are considered. With the inclusion of resistivity, tearing modes, resistive ballooning modes, Pfirsch–Schluter cells and the Stringer spin-up are also included. A major advantage is that the resulting system is two-dimensional in space, and the system incorporates self-consistent and dynamic Shafranov shifts. A limitation is that the system is valid only in radial domains where the tokamak safety factor, $q$, is close to rational. In the tokamak core, the system is well suited to study the sawtooth discharge in the presence of Mercier modes. The systematic ordering scheme and methodology developed are versatile enough to reduce the more general collisional two-fluid equations or possibly the Vlasov–Maxwell system in the MHD ordering.

Keywords

plasma confinementplasma dynamicsplasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 3 , June 2017 , 905830307
Copyright
© Cambridge University Press 2017 

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