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Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

  • Peter J. Catto (a1), Istvan Pusztai (a2) and Sergei I. Krasheninnikov (a3)
  • Please note a correction has been issued for this article.

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.

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Corresponding author

Email address for correspondence: catto@psfc.mit.edu

References

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Balbus, S. A. & Hawley, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376, 214222.
Blandford, R. D. & Payne, D. G. 1982 Hydromagnetic flows from accretion discs and the production of radio jets. Mon. Not. R. Astron. Soc. 199, 883903.
Braginskii, S. I. 1958 Transport phenomena in a completely ionized two-temperature plasma. Sov. Phys. JETP 6, 358369; (1957 Zh. Eksp. Teor. Fiz. 33, 459).
Braginskii, S. I. 1965 Transport processes in a plasma. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 1, pp. 205309. Consultants Bureau.
Catto, P. J., Bernstein, I. B. & Tessarotto, M. 1987 Ion transport in toroidally rotating tokamak plasmas. Phys. Fluids 30, 27842795.
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.
Chandrasekhar, S. 1956 Axisymmetric magnetic fields and fluid motions. Astrophys. J. 124, 232243.
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.
Helander, P. 2014 Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77, 087001-35.
Hinton, F. L. & Wong, S. K. 1985 Neoclassical ion transport in rotating axisymmetric plasmas. Phys. Fluids 28, 30823098.
Krasheninnikov, S. I., Catto, P. J. & Hazeltine, R. D. 1999 Magnetic dipole equilibrium solution at finite plasma pressure. Phys. Rev. Lett. 82, 26892692.
Krasheninnikov, S. I. & Catto, P. J. 1999 Equilibrium of a gravitating plasma in a dipolar magnetic field. Phys. Lett. A 260, 502506.
Krasheninnikov, S. I., Catto, P. J. & Hazeltine, R. D. 2000 Plasma equilibria in dipolar magnetic configurations. Phys. Plasmas 7, 18311838.
Krasheninnikov, S. I. & Catto, P. J. 2015 Axisymmetric plasma equilibrium in gravitational and magnetic fields. Fizika Plazmy 41, 11031107 [Plasma Phys. Rep. 41, 1023–1027 (2015)].
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.
Lovelace, R. V. E., Mehanian, C., Mobarry, C. M. & Sulkanen, M. E. 1986 Theory of axisymmetric magnetohydrodynamic flows: disks. Astrophys. J. Suppl. 62, 137.
McClements, K. G. & Thyagaraya, A. 2001 Azimuthally symmetric magnetohydrodynamic and two-fluid equilibria with arbitrary flows. Mon. Not. R. Astron. Soc. 323, 733742.
Ogilvie, G. I. 1997 The equilibrium of a differentially rotating disc containing a poloidal magnetic field. Mon. Not. R. Astron. Soc. 288, 6377.
Prasanna, A. R., Tripathy, S. C. & Das, A. C. 1989 Equilibrium structure for a plasma magnetosphere around compact objects. J. Astrophys. Astron. 10, 2134.
Shafranov, V. D. 1957 Magnetohydrodynamical equilibrium configurations. J. Expl Theoret. Phys. 33, 710722 [Sov. Phys. JETP 6, 545–554 (1958)].
Shafranov, V. D. 1966 Plasma equilibrium in a magnetic field. In Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 2, pp. 103151. Consultants Bureau.
Throumoulopoulos, G. N. & Tasso, H. 2001 Axisymmetric equilibria of a gravitating plasma with incompressible flows. Geophys. Astrophys. Fluid Dyn. 94, 249262.
Velikhov, E. P. 1959 Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Sov. Phys. JETP 36, 995998.
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A correction has been issued for this article: