Alfvén wings in nonuniform plasmas: analysis using curvilinear coordinates

Sallago, Patricia Alejandra; Platzeck, A. M.

doi:10.1017/s0022377802001733

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…An earlier paper on torsional Alfvén waves in circular cross section cylindrical magnetic tubes in a linear approximation is due to Spruit (1982) and an analysis of large amplitude torsional Alfvén waves in magnetic loops by using threedimensional (3D) MHD simulations is given by Miyagoshi et al (2001). Using an analytical method an exact solution of the MHD equations for large-amplitude Alfvén waves propagating in non-uniform background fields, varying with a rectilinear variable is found by Sallago and Platzeck (2000).…”

Section: Introductionmentioning

confidence: 99%

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Large-amplitude Alfvén waves in cylindrical magnetic tubes

Sallago¹,

Platzeck²

2006

J. Plasma Phys.

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The aim of this paper is to analyze the propagation of large-amplitude Alfvén waves in a perfectly conducting plasma in the magnetohydrodynamic approximation, for cylindrical magnetic tubes. In a similar way to that done in Sallago and Platzeck, instead of linearizing the magnetohydrodynamic equations and searching monochromatic waves, we impose the conditions that the perturbations propagate without distortion with a group velocity parallel to the background magnetic induction field, in the reference system in which the plasma is locally at rest, the perturbations are incompressible, there exists a relation between the velocity and induction magnetic field perturbations, and the total pressure remains constant. The solutions are similar to the case in which the background fields vary with a rectilinear variable. When the solution is searched using this methodology there is no singularity problem. If the background total pressure is not uniform and constant, it is not possible to find waves of large amplitude that propagate like Alfvén waves in cylindrical magnetic tubes.

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Section: Introductionmentioning

confidence: 99%

“…These are regions characterized by perturbed fields and intense electric currents. In a previous work (Sallago and Platzeck 2002) it was proved that Alfvén wings exist in plasmas with spatial dependence on r, ϕ, or a function η = η(r, ϕ) where r, ϕ are cylindrical coordinates.…”

Section: Introductionmentioning

confidence: 99%

Large-amplitude Alfvén waves in cylindrical magnetic tubes

Sallago¹,

Platzeck²

2006

J. Plasma Phys.

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“…They have analyzed the cases of the Io‐Jupiter system [ Goertz , 1980; Acuña et al , 1981; Wright , 1987; Wolf‐Gladrow et al , 1987; Hastings et al , 1988; Wright and Schwartz , 1990], the Europa and Callisto‐Jupiter system [ Neubauer , 1999], satellites moving through the Earth's ionosphere [ Drell et al , 1965; Dobrowolny and Veltri , 1986], and tethered probes [ Sanmartín and Estes , 1997]. The Alfvén wings problem, supposing simple Ohm's law, was studied by Neubauer [1980] using a nonlinear analytic model, by McKenzie [1991] using Green functions, and for nonuniform plasmas by Sallago and Platzeck [2000, 2002] using the methodology of stream functions. The aim of this paper is to analyze the influence of electronic pressure and Hall terms on the construction of Alfvén wings in a perfectly conducting plasma in the magnetohydrodynamic approximation.…”

Section: Introductionmentioning

confidence: 99%

Alfvén waves and wings in Hall magnetohydrodynamics

Sallago

Platzeck

2004

J. Geophys. Res.

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[1] The problem of a conducting body moving in a magnetized plasma when the electronic pressure and Hall terms in Ohm's law cannot be neglected is analyzed in the magnetohydrodynamic approximation. Since Alfvén wings are closely related to Alfvén waves, the influence of these terms in the propagation of Alfvénic perturbations of large amplitude is studied. Instead of linearizing the magnetohydrodynamic equations and searching monochromatic waves, the conditions that the group velocity be parallel to the background magnetic induction field, in the reference system in which the plasma is locally at rest, that the perturbation be incompressible, that the perturbations in velocity and the magnetic induction field be related, and that a magnitude connected to the pressure remain constant are imposed. It is shown that large-amplitude Alfvén waves can propagate in homogeneous plasmas if a ''polarization condition'' on the current density is fulfilled. The value of their group velocity is different from the value that it takes when simple Ohm's law is used. On the other hand, the methodology of stream functions is used for the analysis of Alfvén wings. Their existence, when the Hall term in Ohm's law is relevant, is proved, and the relations among the plasma pressure, induction magnetic field, velocity, and electric current density in the wing are found. The present results can be applied, as an approximation, to spacecraft or space tethers moving in a circular orbit if one can consider that the density and the magnetic induction field do not change as the source is orbiting and if the influence of partial ionization can be neglected.

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Stability of Alfvén wings in uniform plasmas

Sallago¹,

Platzeck²

2007

J. Plasma Phys.

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A conducting source moving uniformly through a magnetized plasma generates, among a variety of perturbations, Alfvén waves. An interesting characteristic of Alfvén waves is that they can build up structures in the plasma called Alfvén wings. These wings have been detected and measured in many solar system bodies, and their existence has also been theoretically proven. However, their stability remains to be studied. The aim of this paper is to analyze the stability of an Alfvén wing developed in a uniform background field, in the presence of an incompressible perturbation that has the same symmetry as the Alfvén wing, in the magnetohydrodynamic approximation. The study of the stability of a magnetohydrodynamic system is often performed by linearizing the equations and using either the normal modes method or the energy method. In spite of being applicable for many problems, both methods become algebraically complicated if the structure under analysis is a highly non-uniform one. Palumbo has developed an analytical method for the study of the stability of static structures with a symmetry in magnetized plasmas, in the presence of incompressible perturbations with the same symmetry as the structure (Palumbo 1998 Thesis, Universidad de Firenze, Italia). In the present paper we extend this method for Alfvén wings that are stationary structures, and conclude that in the presence of this kind of perturbation they are stable.

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Alfvén wings in nonuniform plasmas: analysis using curvilinear coordinates

Cited by 4 publications

References 7 publications

Large-amplitude Alfvén waves in cylindrical magnetic tubes

Large-amplitude Alfvén waves in cylindrical magnetic tubes

Alfvén waves and wings in Hall magnetohydrodynamics

Stability of Alfvén wings in uniform plasmas

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