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Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

Part of: PLA Tribute to V D Shafranov: 1929-2014

Published online by Cambridge University Press:  20 November 2015

Peter J. Catto ,
Istvan Pusztai  and
Sergei I. Krasheninnikov
Peter J. Catto*
Affiliation:
Plasma Science and Fusion Center, MIT, Cambridge, MA 02139, USA
Istvan Pusztai
Affiliation:
Department of Applied Physics, Chalmers University of Technology, Gothenburg 41296, Sweden
Sergei I. Krasheninnikov
Affiliation:
Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: catto@psfc.mit.edu
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Abstract

We present analytic solutions for three-dimensional magnetized axisymmetric equilibria confining rotating hot plasma in a gravitational field. Our up–down symmetric solution to the full Grad–Shafranov equation can exhibit equatorial plane localization of the plasma density and current, resulting in disk equilibria for the plasma density. For very weak magnetic fields and high plasma pressure, we find strongly rotating thin plasma disk gravitational equilibria that satisfy strict Keplerian motion provided the gravitational energy is much larger than the plasma pressure, which must be large compared to the magnetic energy of the poloidal magnetic field. When the rotational energy exceeds the gravitational energy and it is larger than the plasma pressure, diffuse disk equilibrium solutions continue to exist provided the poloidal magnetic energy remains small. For stronger magnetic fields and lower plasma pressure and rotation, we can also find gravitational equilibria with strong localization to the equatorial plane. However, a toroidal magnetic field is almost always necessary to numerically verify these equilibria are valid solutions in the presence of gravity for the cases considered in Catto & Krasheninnikov (J. Plasma Phys., vol. 81, 2015, 105810301). In all cases both analytic and numerical results are presented.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 515810603
Copyright
© Cambridge University Press 2015 

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