Analytic formulation and quantitative solutions of the coupled ULf wave problem

Abstract

In the terrestrial magnetosphere, the inhomogeneous magnetic field and plasma density give rise to a continuous spectrum of field line resonant frequencies. Compressional disturbances with characteristic frequencies lying within the range of the spectrum may couple to transverse oscillations of resonant field lines. The coupling is of particular interest for global compressional modes trapped in the magnetic cavity. These modes decay in time through the coupling, even in the absence of dissipation. The importance of the process is that, through the damping of the global modes, large-scale motion can drive localized field line resonances. In this study, we investigate the mode coupling and examinc the parameter dependence of the damping rate of the global mode. The problem is discussed as an initial value problem in the box model which retains most of the significant physics yet remains mathematically tractable. To treat the coupling, we use the analogy of Landau damping in a homogeneous plasma. From the Laplace transform approach, we obtain the complex frequencies of the compressional wave by finding the singularities of the associated Green's function. Once the complex frequency has been found numerically, we obtain the corresponding waveforms in the box. Many observed wave properties can then be obtained. The calculations agree well with other simulation work and correspond to results obtained for the reflection of radio waves from the ionosphere and for plasma heating by absorption of radiation. ZHU ,•D K•vg•,sor•: COVl,•,gD ULF W,•vgs--ANALYS•S AND SOLUTIONS of electromagnetic waves in overdense plasma, Plasma Ph•ts., 16, 565, 1974.

Development of parallel electric fields at the plasma sheet boundary layer

“…It is well known from field line resonance theory that a three dimensional system is necessary to consider mode conversion at a plasma gradient; for example, in an axisymmetric (m = 0) situation the mode coupling coefficient vanishes [e.g., Zhu and Kivelson, 1988]. Thus, neither of the above approaches models the reduction of the scale size due to phase mixing at the PSBL.…”

Convection and Electrodynamic Signatures in the Vicinity of a Sun-Aligned Arc: Results from the Polar Acceleration Regions and Convection Study (Polar Arcs)

“…The theta aurora, which maps to the boundary between open and closed field lines, is connected to the LLBL on the dayside and the plasma sheet boundary layer (PSBL) on the nightside [Lundin et al, 1990]. This model relies on an alternate view of solar wind -magnetosphere interaction in which the transfer of solar wind energy to the magnetosphere is primarily accomplished not through magnetic merging but through viscous interactions and actual mass transfer in the LLBL [Axford and Hines, 1961;Eastman et al, 1976;Sonnerup, 1980;Zhu and Kivelson, 1988;Stasiewicz, 1989]. Specifically, sun-aligned arcs map to polarization features resulting from finger-like injections of plasma into the LLBL [Lundin and Evans, 1985], which has been shown to widen during quiet times [Williams et al, 1985;Mitchell et al, 1987].…”

Field line resonances in discretized magnetospheric models: an artifact study

“…One possible way to treat these equations is to employ the Laplace transform on the time variable to solve the corresponding initial value problem (Sedlacek, 1971;Zhu and Kivelson, 1988). The Green function of the di erential equation is constructed, and slowly decaying quasi-eigenmodes of the system can be inferred from its singularities.…”