Abstract
Abstract. Hydromagnetic waves, especially those of frequencies in the range of a few millihertz to a few hertz 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 to examining the toroidal standing Aflvén 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 eigenfrequency is greater than a critical frequency and a decaying 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-mode standing Alfvén waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of a poloidal standing Alfvén wave in the Earth's magnetosphere. Our analysis based on the 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.
Highlights
Hydromagnetic waves are common phenomena in space plasmas
An alternative approach to describing the toroidal Alfvén standing waves in an axisymmetric background magnetic field has been given by McKenzie and Hu (2010), where the wave equations were cast along an individual field line and transformed into a Klein–Gordon (KG) form
In the case of a transverse poloidal mode, we show that the wave equation can be cast as a KG form along a field line
Summary
Hydromagnetic waves are common phenomena in space plasmas. The associated magnetic and electric field perturbations are observed both on the ground and from space in the Earth’s magnetosphere. An alternative approach to describing the toroidal (transverse) Alfvén standing waves in an axisymmetric background magnetic field has been given by McKenzie and Hu (2010), where the wave equations were cast along an individual field line and transformed into a Klein–Gordon (KG) form This approach was further formalized and applied to the Earth’s dipole magnetic field. In Dai et al (2013), an event of a fundamental-mode standing poloidal wave was identified from the Van Allen Probes measurements They obtained the wave period of the azimuthal electric field and the associated radial magnetic field oscillations, the relative ratio of wave amplitudes, and the relative phase shift at the spacecraft location in the inner magnetosphere.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
