Finite element modeling of nonlinear dispersive field line resonances: Trapped shear Alfvén waves inside field‐aligned density structures

Abstract

[1] Using a new two-dimensional nonlinear finite element model, we investigate the interaction of dispersive shear Alfvén wave (SAW) field line resonances (FLRs) and ion acoustic waves in Earth's magnetosphere. We solve the full set of nonlinear reduced MHD equations self-consistently in arbitrary geometries. Initially, a Cartesian box model is used to demonstrate the reliability of our numerical solution in determining the linear and nonlinear evolution of FLRs. Then the full reduced MHD equations with the effects of electron inertia, ion Larmor radius correction, and electron thermal pressure are solved in dipolar and stretched magnetic topologies. We show that time-dependent dispersion and density steepening lead to localization of a highly structured FLR within an ionospheric (equatorial) density cavity (bump). When nonlinear effects are accounted for, we find that FLRs preferentially form in regions of low wave dispersion. Field line stretching and ponderomotive density redistribution lead to a significant reduction in FLR eigenfrequencies, bringing them into the range of observations. Nonlinear effects also cause a rapid acceleration of the timescale over which small perpendicular spatial scales appear. In our model, it is shown that density perturbations can be comparable to the equilibrium background density.

Nonlinear electron heating by resonant shear Alfvén waves in the ionosphere

“…[16] Here, we combine our theory of Ohmic heating with the FLR numerical model described by Lu et al [2003]. By way of illustration, we drive a magnetic perturbation at the equator, with a frequency matching the Alfvén wave eigenfrequency of 8.6 mHz on the dipolar magnetic shell L = 8.…”

“…The height of the ionosphere is assumed to be 10 km, and the ionospheric boundary is placed at an altitude of 80 km. The finite element model TOPO [Marchand and Simard, 1997] is used to solve the 2D reduced MHD equations [Lu et al, 2003] and 1D equations (6) and (7) for ionospheric electrons. The model for FLRs takes into account the variation of temperature and density along and across the magnetic field lines, along with wave dispersive effects.…”

“…Ionospheric feedback [e.g., Lysak and Song, 2002], involving ionization by precipitating electrons, is one process by which conductivity enhancements may allow shear Alfvén waves to sustain or grow in regions of initially low conductivity. However, it can be shown that in arcs associated with long period field line resonances (FLRs) [e.g., Lu et al, 2003], this process is not very effective [Prakash et al, 2003].…”

A nonlocal wave-wave interaction among Alfvén waves in an intermediate-β plasma

“…[8][9][10] The properties of the KAW have been demonstrated by many experimental investigations in space [11][12][13][14] and laboratory [15][16][17][18] plasmas. In particular, the KAW can play an important role in the acceleration of energetic electrons in Earth's aurora [19][20][21][22][23] and solar flares [24][25][26] as well as the heating of solar coronal plasmas. [27][28][29][30][31] Extensive works have been done to discuss the local interaction process of three Alfvén waves in which the magnitudes of three wavenumbers are comparable.…”

Convective cell generation by kinetic Alfvén wave turbulence in the auroral ionosphere

“…However, it should be mentioned that in the auroral plasma and some ionosphere regions the homogeneity, long perpendicular KAW wavelength, and plasma-b conditions are not fully satisfied. The turbulent cascade and/or phase mixing processes in the density cavities that can be generated by the KAW ponderomotive force 34,49,50 can also cause the KAWs to reach scales of the electron inertial length or even smaller, 25,51 and the electrostatic and magnetostatic CCs are no longer distinct. In these cases more detailed investigations would be needed.…”