Equilibrium of a gravitating plasma in a dipolar magnetic field

Krasheninnikov, S. I.; Catto, Peter J.

doi:10.1016/s0375-9601(99)00554-x

Cited by 10 publications

(14 citation statements)

References 2 publications

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“…We expect it will prove useful for future studies of the full Grad–Shafranov equation (2.12). Indeed, the self-similar technique can be extended to retain self-gravity (Krasheninnikov & Catto 1999, Krasheninnikov et al. 2000) so other interesting solutions are likely to exist.…”

Section: Discussion and Summarymentioning

confidence: 99%

Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

2015

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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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Section: Discussion and Summarymentioning

confidence: 99%

Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

2015

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“…The plasma equilibria in gravitational and magnetic fields considered by Krasheninnikov and Catto [4,8], where within the framework of separable solutions (6) for the case where the whole space was topologically connected by the magnetic field lines. Here, however, we follow [9] and consider equilibria with open magnetic field lines and topologically disconnected regions of the magnetic flux surfaces where plasma occupies just one of these regions (recall Fig.…”

Section: Solutions Of the Governing Equationmentioning

confidence: 99%

“…Here, we consider the case of plasma equilibria in gravitational and open magnetic fields corresponding to negative . In [4,8], only were considered for and the whole space was topologically connected by the magnetic field lines. The simplest symmetric ( ) case with topologically disconnected magnetic flux surfaces and open magnetic field lines can be found for .…”

Section: Solutions Of the Governing Equationmentioning

confidence: 99%

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Axisymmetric plasma equilibrium in gravitational and magnetic fields

Krasheninnikov

Catto

2015

Plasma Phys. Rep.

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Abstract-Plasma equilibria in gravitational and open-ended magnetic fields are considered for the case of topologically disconnected regions of the magnetic flux surfaces where plasma occupies just one of these regions. Special dependences of the plasma temperature and density on the magnetic flux are used which allow the solution of the Grad-Shafranov equation in a separable form permitting analytic treatment. It is found that plasma pressure tends to play the dominant role in the setting the shape of magnetic field equilibrium, while a strong gravitational force localizes the plasma density to a thin disc centered at the equatorial plane.

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“…78,79 A comparison of the properties of compressible and incompressible MHD oscillations in toroidal plasmas has been made by Wahlberg. Analytic solutions of the nonlinear GS equation for a plasma with vanishing poloidal current at either low or high pressure plasma confined by a dipolar magnetic field were obtained recently by Krash-eninnikov et al 96 Their studies were then extended to equilibria with purely toroidal flow, 97 gravitating magnetic dipolar plasmas without flow, 98 and plasmas with anisotropic pressure 99,100 ͑see references therein, too͒. 81 MHD equilibria with mass flow in an axisymmetric tokamak were constructed by Cheremnykh 82 assuming the adiabatic law as the equation of state.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear periodic solutions for isothermal magnetostatic atmospheres

2008

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Magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential A, known as the Grad-Shafranov equation. Specifying the arbitrary functions in the latter equation, one obtains three types of nonlinear elliptic equations ͑a Liouville equation, a sinh Poisson equation, and a generalization of those with a sum of exponentials͒. Analytical solutions are obtained using the tanh method; this is elaborated in the Appendix. The solutions are adequate to describe an isothermal atmosphere in a uniform gravitational field showing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium.

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Equilibrium of a gravitating plasma in a dipolar magnetic field

Cited by 10 publications

References 2 publications

Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

Axisymmetric global gravitational equilibrium for magnetized, rotating hot plasma

Axisymmetric plasma equilibrium in gravitational and magnetic fields

Nonlinear periodic solutions for isothermal magnetostatic atmospheres

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