Abstract. The problem of a source moving in a plasma with background fields varying in one direction, in the magnetohydrodynamic approximation, is analyzed. The variation of the background fields is assumed to be perpendicular to the background velocity and induction magnetic fields. Since Alfv6n wings are closely related to Alfv6n waves, the existence of Alfvenic perturbations, in this case, is searched. Instead of linearizing the MHD 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, the perturbation be incompressible, and the total pressure remain constant, are imposed. Two modes of propagation are found. Since it is possible to define an invariant direction, the methodology of stream functions is used for the analysis of Alfv6n wings. Their existence, when the variation of the background fields satisfies some conditions, is proved, and the relations among the density, pressure, magnetic field, plasma velocity, and electric current density in the wing are found. Physical situations in which these results can be applied, with such a particular spatial dependence of the background fields, are restricted. However, as an approximation, it can be applied to spacecraft or space tethers moving in a circular orbit, if one takes into account that the density and the induction magnetic field change with the altitude. The method can be extended to cases in which the background fields vary in a more general way.

[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.

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.

The results of a previous work, which describes in the magnetohydrodynamic approximation Alfvén wings in nonuniform plasmas, are extended in order to consider more general variations of the background fields. As mathematical tools we use general curvilinear coordinates and stream functions. We prove the possibility of existence of Alfvén wings when the background fields have cylindrical or helical symmetry. For the former, the wings are cylinders, and for the latter, they have helicoidal form; this last includes the case of uniform background fields. We also obtain the relations among the different physical magnitudes in the wing.

A conducting source moving uniformly through a magnetized plasma generates, among a variety of perturbations,Alfvén waves. Alfvén waves can build up structures in the plasma called Alfvén wings. The wings have been detec-ted and measured in many solar system bodies, and their existence have been theoretically proved also. Under certainconditions, Hall and electronic pressure must be taken into account in the Ohm’s law and so one gets Hall Magne-tohydrodynamics (HMHD). In spite of Sallago and Platzeck have shown the existence of Alfvén wings in HMHD, theirstability under such conditions remains to be studied. The aim of this paper is to analyze the stability of an Alfvén wing,in the presence of an incompressible perturbation that has the same symmetry than the structure and polarization, inHMHD. Palumbo has developed an analytical method for the study of the stability of static structures with a symmetryin magnetized plasmas, in the presence of incompressible perturbations with the same symmetry than the structure.Since Alfvén wings are stationary structures, Sallago and Platzeck have shown the stability of such Alfvén wings in MHD conditions by extending Palumbo’s method. In the present paper this method is extended for Alfvén wings in HMHD conditions, and one concludes that in the presence of this kind of perturbations they are stable.