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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.

Information

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

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References

Balbus, S. A. & Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376, 214–222.CrossRefGoogle Scholar
Blandford, R. D. & Payne, D. G. 1982 Hydromagnetic flows from accretion discs and the production of radio jets. Mon. Not. R. Astron. Soc. 199, 883–903.Google Scholar
Braginskii, S. I. 1958 Transport phenomena in a completely ionized two-temperature plasma. Sov. Phys. JETP 6, 358–369; (1957 Zh. Eksp. Teor. Fiz. 33, 459).Google Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 1, pp. 205–309. Consultants Bureau.Google Scholar
Catto, P. J., Bernstein, I. B. & Tessarotto, M. 1987 Ion transport in toroidally rotating tokamak plasmas. Phys. Fluids 30, 2784–2795.CrossRefGoogle Scholar
Catto, P. J. & Krasheninnikov, S. I. 2015 A rotating and magnetized three-dimensional hot plasma equilibrium in a gravitating field. J. Plasma Phys. 81, 105810301.Google Scholar
Chandrasekhar, S. 1956 Axisymmetric magnetic fields and fluid motions. Astrophys. J. 124, 232–243.Google Scholar
Grad, H. & Rubin, H. 1958 Hydromagnetic equilibria and force-free fields. In Proceedings of the 2nd UN Conference on the Peaceful Uses of Atomic Energy, vol. 31, p. 190. IAEA.Google Scholar
Helander, P. 2014 Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77, 087001-35.CrossRefGoogle ScholarPubMed
Hinton, F. L. & Wong, S. K. 1985 Neoclassical ion transport in rotating axisymmetric plasmas. Phys. Fluids 28, 3082–3098.Google Scholar
Krasheninnikov, S. I., Catto, P. J. & Hazeltine, R. D. 1999 Magnetic dipole equilibrium solution at finite plasma pressure. Phys. Rev. Lett. 82, 2689–2692.Google Scholar
Krasheninnikov, S. I. & Catto, P. J. 1999 Equilibrium of a gravitating plasma in a dipolar magnetic field. Phys. Lett. A 260, 502–506.Google Scholar
Krasheninnikov, S. I., Catto, P. J. & Hazeltine, R. D. 2000 Plasma equilibria in dipolar magnetic configurations. Phys. Plasmas 7, 1831–1838.CrossRefGoogle Scholar
Krasheninnikov, S. I. & Catto, P. J. 2015 Axisymmetric plasma equilibrium in gravitational and magnetic fields. Fizika Plazmy 41, 1103–1107 [Plasma Phys. Rep. 41, 1023–1027 (2015)].Google Scholar
Kunz, M. W., Schekochihin, A. A., Chen, C. H. K., Abel, I. G. & Cowley, S. C. 2015 Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas. J. Plasma Phys. 81, 325810501.CrossRefGoogle Scholar
Lovelace, R. V. E., Mehanian, C., Mobarry, C. M. & Sulkanen, M. E. 1986 Theory of axisymmetric magnetohydrodynamic flows: disks. Astrophys. J. Suppl. 62, 1–37.CrossRefGoogle Scholar
McClements, K. G. & Thyagaraya, A. 2001 Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows. Mon. Not. R. Astron. Soc. 323, 733–742.Google Scholar
Ogilvie, G. I. 1997 The equilibrium of a differentially rotating disc containing a poloidal magnetic field. Mon. Not. R. Astron. Soc. 288, 63–77.CrossRefGoogle Scholar
Prasanna, A. R., Tripathy, S. C. & Das, A. C. 1989 Equilibrium structure for a plasma magnetosphere around compact objects. J. Astrophys. Astron. 10, 21–34.Google Scholar
Shafranov, V. D. 1957 Magnetohydrodynamical equilibrium configurations. J. Expl Theoret. Phys. 33, 710–722 [Sov. Phys. JETP 6, 545–554 (1958)].Google Scholar
Shafranov, V. D. 1966 Plasma equilibrium in a magnetic field. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 2, pp. 103–151. Consultants Bureau.Google Scholar
Throumoulopoulos, G. N. & Tasso, H. 2001 Axisymmetric equilibria of a gravitating plasma with incompressible flows. Geophys. Astrophys. Fluid Dyn. 94, 249–262.Google Scholar
Velikhov, E. P. 1959 Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Sov. Phys. JETP 36, 995–998.Google Scholar