Alfvén Wave Parallel Electric Field in the Dipole Model of the Magnetosphere: Gyrokinetic Treatment

Abstract

A mechanism for generation of the parallel electric field by Alfvén wave in the dipole model of the magnetosphere in full gyrokinetics is proposed. The parallel electric field of the Alfvén mode is caused by the coupling of the Alfvén and electrostatic modes due to the plasma inhomogeneity and field line curvature in presence of the trapped hot electrons. The parallel electric field is described by an inhomogeneous integral equation arising from the averaging of the bounce motion of hot electrons. It was found that the parallel electric field is localized near the ionosphere at the heights below 0.5 Earth's radius. For typical Alfvén wave amplitudes observed in space, the parallel electric field potential reaches the values of several kV, which can provide enough acceleration for the precipitating auroral electrons.

Integral Equations for Problems on Wave Propagation in Near-Earth Plasma

“…where n is the number density, ε = v 2 /2 is the particle energy per unit mass, v is particle velocity, and ε 0 j is the temperature. Hereinafter, the index j indicates the belonging to the protons (p) or the electrons (e), respectively " [12].…”

“…The ULF waves are characterized by the frequencies ω much lower than the gyrofrequency ω c . Such modes are conventionally considered in the gyrokinetics framework, where the wave's electromagnetic field is described by three variables: "φ is the electrostatic potential, b is the parallel magnetic field, and ψ is the potential related to the parallel vector potential, as A = −(ic/ω)∂ψ/∂l " [12]. In this case, the transverse and parallel electric fields of the wave are the following, respectively:…”

“…This is a plausible situation since the admixture of cold electrons in the plasma should short-out the parallel electric fields [14]. "In this case, we can consider the perpendicular Ampere's law Equation ( 9) and vorticity Equation ( 10) independent of the quasi-neutrality condition (11)" [12]. To simplify, we neglect the contribution of hot electrons since β p β e .…”

“…where ω c is the gyrofrequency, g ⊥ = g 1 g 2 " [12]. The operatorsL T define the toroidal operator as follows:L…”

“…Such formalism is called gyrokinetics and was developed in papers [8][9][10]. This paper aims to review some results in the studies of the ULF waves in the Earth's magnetosphere obtained with the integral equations [11,12].…”