The effect of asymmetry on toroidal hydromagnetic waves in a dipole field

104

The asymptotic temporal behavior of hydromagnetic waves in a model of the inner magnetosphere is shown to be characterized by guided modes. The basic hydromagnetic wave equation is derived and applied to a cylindrical model of the inner magnetosphere. This model offers a good representation of the spatially dependent field line frequencies present in a dipole field. The initial value problem for the symmetric toroidal mode is solved, and its singularities are treated by Fourier superposition. Singularities also are present in the asymmetric poloidal mode wave equation and are shown to be logarithmic. Fourier superposition leads to the solutions for the electric and magnetic fields, which are asymptotic in time. The results indicate decay of the poloidal modes and domination by the toroidal modes, i.e., field line control of the propagation. At the latitude at which the maximum amplitude of a particular frequency occurs, the wave becomes linearly polarized. The asymptotic micropulsation periods depend on the characteristic field line periods and are usually longer at higher latitudes. Undamped guided waves lead to some terms, such as change density and parallel current density, that increase linearly with time. The inclusion of loss mechanisms in the wave equation, e.g., conductivity, limits the guided modes and prevents such nonphysical effects from occurring.

Section: Equations and Modelsmentioning

confidence: 99%

A theory of latitude dependent geomagnetic micropulsations: The asymptotic fields

Radoski¹

1974

104

“…Dungey [1954] was the first to point out that the origin of geomagnetic pulsations observed at high latitudes is the eigenmode oscillations of the geomagnetic field lines. Much effort has gone into the explanation of geomagnetic pulsations in terms of magnetospheric shear Alfvtn waves [e.g., Radoski and Carovillano, 1966; Radoski, 1967Radoski, , 1972; in general, they have assumed infinite conductivity boundary conditions at the end of magnetic field lines on the ionosphere, but geomagnetic pulsations actually pass through the ionosphere and atmosphere before it reaches the ground, so it reflects not only pure MHD waves at the magnetosphere but also the electrical •Department of Earth and Planetary Sciences, Kyushu University, Fukuoka, Japan.…”

Section: Introductionmentioning

confidence: 99%

Eigenmode analysis of field line oscillations interacting with the ionosphere‐atmosphere‐solid earth electromagnetic coupled system

Yoshikawa

Itonaga

Fujita³

et al. 1999

Abstract. In order to understand the effect of ionosphere on the localized toroidal magnetic shell oscillation (field line oscillation), we have constructed a rectangular box model for the magnetosphere-ionosphere-solid earth system including the anisotropically conducting ionosphere and performed the eigenmode analysis of the magnetohydrodynamic (MHD) waves in the model. We have found that the eigenmodes of field line oscillation are effectively controlled by the height-integrated Pedersen and Hall conductivities, meaning that the fieldaligned current (FAC) in the magnetosphere is closed to both the Pedersen current and the Hall current. The divergent Hall current, that is, the Hall current, which closes the FAC, is a newfound current that is driven by the Hall effect of the ionospheric inductive (rotational) electric field. The divergent Hall current brings into sharp relief by considering the ionosphere to be inductive, and it inevitably requires the electromagnetic coupling between the magnetosphere, ionosphere, atmosphere, and solid earth. The nature of the ionospheric current associated with the standing shear Alfvtn mode is also analyzed in detail by using the concept of wave reflection and mode conversion at the inductive ionosphere. In particular, we emphasize that the magnetic flux sustained by the rotational Hall current, that is, accompanied by the radiation of fast magnetosonic wave to the magnetosphere and atmospheric poloidal magnetic wave to the atmosphere, should be taken into account for magnetosphereionosphere coupling of FAC.

“…Oscillation period Radoski [1972] calculated eigenperiods associated with pure toroidal oscillations that include a longitudinal asymmetry proportional to e •m•, where qb is geomagnetic longitude. The calculations use an undistorted dipole magnetic field and were done for a number of different m values, or modes, and for several harmonics (n values) of a few modes.…”

Section: Wave Modes and Harmonicsmentioning

confidence: 99%

“…It is necessary to introduce some theoretical model for the hydromagnetic oscillation in order to distinguish between harmonics, to determine how important it is that the satellite is not directly on the geomagnetic equator, and to evaluate the significance of the observed wave amplitude and period. We have used the axially symmetric m -0 solutions to the wave equation in a dipole magnetic field [Radoski, 1972] in order to stqdy the differences between the n = 1 and n = 2 harmonics. These are the simplest available solutions in dipole coordinates and can provide a rough estimate of the variations to be expected along a field line.…”

Section: Wave Modes and Harmonicsmentioning

confidence: 99%

“…Radoski calculated eigenperiods for various toroidal oscillation modes and harmonics by assuming that the plasma density is given by p = po(a/r) 6, where p0 is a constant, a is the radius of the earth, and r is the radial distance. Figures 1 and 3 of Radoski [1972] were used to obtain predicted periods for various modes at L = 8.2 when p0 = 7.2 X 10 -•9 g/cm 3. We then used the constancy of po/T 2, where T is the wave period, to see how much p0 must be changed from the characteristic value used by Radoski in order to agree with the observed period of T = 250 s. The required ion density at the equator is finally given by poll •.…”

Section: Wave Modes and Harmonicsmentioning

confidence: 99%

See 1 more Smart Citation

Hydromagnetic waves excited during an ssc

Kaufmann¹,

Walker²

1974

The effects of hydromagnetic perturbations that were excited by an ssc were seen at L=8.2, −12° geomagnetic latitude, 0610 geomagnetic local time in Explorer 12 energetic particle and magnetic field data, and on ground magnetograms. The entire day side magnetosphere was compressed by 2–3 RE in 2–3 min. This compression and the accompanying increase in magnetopause currents produced a 25‐γ enhancement of the magnetic field at the satellite and a worldwide 45‐γ enhancement at the ground. Energetic electron fluxes rose sharply at the satellite, indicating that particles moved earthward and were accelerated as the magnetic field was compressed. An additional 15‐γ 2‐min enhancement of the magnetic field was seen at the satellite. This pulse did not significantly enhance energetic electron fluxes and did not produce worldwide ground effects, though associated perturbations are present in some ground records. The pulse appears to represent a localized compressional magnetoacoustic wave that was excited by the rapid magnetopause motion. Finally, a damped toroidal oscillation with an initial amplitude of 26 γ, a period of 250 s, and an exponential damping time of 400 s was seen at the satellite. This oscillation could not be seen at any available ground station, the indication being that it was confined in latitude or longitude. The damping could be produced either by the coupling of energy between wave modes or by finite ionospheric conductivity. The wave period agrees with predictions if the density of plasma on the field line varies with radial distance as r−6, with ρ=4 to 12 ions/cm³ at the equator. An initial energy input of 4 × 1020 dL to 2 × 1021 dL ergs can produce the observed wave amplitude, if plasma at all longitudes between the L and the L + dL shells is involved in the oscillation.