Finite element modelling of TdeV edge and divertor with E*B drifts

[1] We present theory and ground-based observations of field-line resonances (FLRs) excited in Earth's magnetosphere. Three FLR observations are reported, which correspond to large-scale standing shear Alfvén wave (SAW) oscillations on nightside field lines extending from premidnight to close to dawn. The eigenfrequencies for these events are modeled using a nonorthogonal covariant-contravariant analysis of the ideal magnetohydrodynamic (MHD) equations. This allows us to use a general field-line topology, an example of which is computed using the Tsyganenko 1996 magnetic field model. We show that field-line stretching, along with assumptions regarding the distribution of density along field lines, is sufficient to explain the observed FLR frequencies. Then, we consider dispersive effects operating at the level of the electron inertial scale near the ionosphere or the ion-acoustic gyroradius in the vicinity of the equatorial plane. Specifically, we estimate the spatial saturation widths and phase mixing timescales based on a simple model of dispersive SAWs. By considering a new model for ionospheric Pedersen conductivity modification by field-aligned currents in SAWs and numerical (finite element model) solutions to the reduced MHD equations, we model specific FLR observations in an approximate axisymmetric field topology. We discuss the interplay of linear and nonlinear phase mixing, along with gradients in dispersion and time-dependent losses due to Pedersen conductivity enhancements.

Section: Solutions To the Reduced Mhd Equations With Dispersion And Imentioning

confidence: 99%

Magnetospheric field‐line resonances: Ground‐based observations and modeling

Rankin

Кабин

et al. 2005

“…In our calculations, depending on the spatial scale of dispersive effects being considered, much more refined meshes with nonuniform resolution are used. Spurious perpendicular diffusive transport is avoided by aligning the mesh with the magnetic flux surfaces [ Marchand and Simard , 1997].…”

Section: Numerical Approachmentioning

confidence: 99%

“…Our nonperturbative treatment allows us to investigate the complete dynamics of growth and saturation of wave fields and density perturbations under realistic magnetospheric conditions. Nonlinear and dispersive effects have been incorporated into the finite element code first developed by Marchand and Simard [1997] and the effects of electron inertia and thermal dispersion in a dipolar and stretched magnetic field are presented.…”

Section: Introductionmentioning

confidence: 99%

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

Rankin

Marchand

et al. 2003

[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.

“…A two dimensional finite element code TOPO, developed by Marchand and Simard [1997], is used to solve the system of coupled partial differential ‐ by imposing appropriate boundary conditions. TOPO solves equations of the form

\sum_{l = 1}^{N} (Z_{italickl} \frac{\partial}{\partial t} U_{l} + \nabla \cdot (A_{italickl} U_{l}) + \nabla \cdot (\overset{true\to}{B_{kl}} \cdot U_{l}) + C_{italickl} U_{l} + D_{italickl} \cdot U_{l}) + S_{k} = 0

where U l 's are unknown and A kl , B kl , C kl , D kl are known coefficients.…”

Section: Modelmentioning

confidence: 99%

“…[14] A two dimensional finite element code TOPO, developed by Marchand and Simard [1997], is used to solve the system of coupled partial differential equations (11)-(16) by imposing appropriate boundary conditions. TOPO solves equations of the form…”

Section: Numerical Approachmentioning

confidence: 99%

Modeling of ionospheric magnetic field perturbations induced by earthquakes

Imtiaz¹,

Marchand²

2012

[1] The objective of this study is to present a simple coupled seismo-ionospheric model to account for magnetic field perturbations in response to geophysical phenomena such as Earthquakes or tsunamis. For this purpose, we include a simple gravity wave model in the two dimensional mid latitude ionosphere model SAMI2. Following an earthquake, the disturbances in the neutral atmosphere density and velocity associated with gravity waves propagate vertically upward up to ionospheric altitudes 150-350 km, where significant coupling between the neutral atmosphere and the ionosphere occurs. As a result, a rapid variation in the ionospheric plasma density and temperature is observed associated with the photoionization of the perturbed neutral density. This variation in the electron density leads in turn to a variation in the total electron content (TEC). Strong variations in the TEC are observed close to the epicenter which correspond to large plasma density perturbations in this region associated with the ion acoustic mode. The calculation of magnetic perturbations is based on a set of reduced MHD equations. These are solved numerically using the finite element code TOPO coupled with the mid latitude ionospheric model SAMI2. The coupling between the two codes accounts for the variations in neutral gas density and the collisional drag force between ions and neutrals. Two wave modes are considered: the shear Alfvén mode and the compressional mode. The results of the magnetic field perturbations and of ions' velocity perturbations associated with the shear Alfvén and the compressional modes are presented. Variations in the TEC values are also computed for the compressional mode by taking into account the density perturbations transverse to the magnetic field. The results representing TEC perturbations associated with the compressional mode show strong variations at high latitudes both as a function of time and latitude.