Jinlei Zheng

Date of Award


Document Type


Degree Name

Master of Science (MS)



Committee Chair

Qiang Hu

Committee Member

Jakobus le Roux

Committee Member

Lingze Duan


Klein-Gordon equation., Magnetohydrodynamic waves., Magnetospheric physics.


Hydromagnetic waves, especially those of frequencies in the range of a few milli-Hz to a few Hz observed in the Earth's magnetosphere, are categorized as Ultra Low Frequency (ULF) waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach in examining the toroidal (transverse) standing Alfvén waves in a background magnetic field by recasting the wave equation into a Klein-Gordon (KG) form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigen-frequency is greater than a cut-off frequency and an evanescent type otherwise. We apply the approach to a compressed dipole magnetic field model of the inner magnetosphere, and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal (transverse) standing Alfvén waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of poloidal standing Alfvén wave in the Earth's magnetosphere. Our analysis based on KG equation yields consistent results which agree with the spacecraft measurements of the wave period and the amplitude ratio between the magnetic field and electric field perturbations. We also present computational results of eigenvalue solutions to the compressional poloidal mode waves in the standard dipole and compressed dipole background magnetic fields. Both the Cartesian and axisymmetric geometries are considered. We conclude that the wave forms obtained via the KG equations are validated and are consistent with other relevant studies. We provide an alternative approach to the study of ULF waves in the Earth's magnetosphere. The implications of our results and outlook to future work are also discussed.



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