Alfvén waves and wings in nonuniform plasmas

Abstract

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.

Alfvén wings in nonuniform plasmas: analysis using curvilinear coordinates

“…which are similar to those that are valid when the background fields vary in a rectilinear direction (Sallago and Platzeck 2000). Equation 6takes into account only the γ component of the equation of motion (Palumbo and Platzeck 1998).…”

“…In almost every case, a uniform background velocity, magnetic field, density, and plasma pressure are supposed. In a recent work, Sallago and Platzeck (2000) have analyzed Alfvén waves and wings in nonuniform magnetized plasmas using the magnetohydrodynamic (MHD) aproximation; the background fields were supposed to vary in a direction perpendicular to the background velocity and magnetic field, which lie in a plane. They showed the existence, under certain conditions, of nonlinear Alfvén waves and Alfvén wings; the Alfvén group velocity is given by an expression similar to that for Alfvén waves in the uniform-plasma case.…”

The dispersive Alfvén wave in the time-stationary limit with a focus on collisional and warm-plasma effects

“…The term "Alfvén wing" is used to describe a stationary wave resulting from moving conductors, for example in the case of Io orbiting within Jupiter's magnetosphere 22 or as a result of a conducting tether orbiting with a spacecraft. 23 In these cases, the structure of the stationary wave is imposed by the source, although Chust et al 22 argue that additional filamentation can result. In contrast, the nonlinear two-fluid model described here and by Knudsen 19 predicts a self-consistent StA wave whose structure arises from intrinsic properties of the current sheet in which the wave forms.…”

Alfvén waves and wings in Hall magnetohydrodynamics

“…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.…”

“…Alfvén waves with a Hall term have been studied by other authors [ Mattei , 1969; Ovenden et al , 1983; Woodward and McKenzie , 1994a, 1994b; Pokhotelov et al , 1996], but they linearize the magnetohydrodynamic equations or impose particular dependencies for the perturbations. In a similar way as it is done by Sallago and Platzeck [2000], instead of linearizing the magnetohydrodynamic equations and searching monochromatic waves, we impose the conditions that the perturbation 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 perturbation be incompressible, there exist a relation between the velocity and induction magnetic field perturbations, and a magnitude called total generalized pressure remain constant in the disturbed region. It is proved in section 2 that large‐amplitude Alfvén waves can propagate, when the electronic pressure and Hall terms are taken into account, if a condition on the spatial dependence of the current density is fulfilled.…”