[Paper Review] 2-D model of the global ionospheric conductor connected with the magnetospheric conductors

В. В. Денисенко|arXiv (Cornell University)|Feb 22, 2018

Ionosphere and magnetosphere dynamics6 references3 citations

TL;DR

This paper presents a 2D global ionospheric conductor model based on high field-aligned conductivity, reducing the 3D electrical conductivity problem to a small-parameter expansion using the ratio of Pedersen to field-aligned conductivities. It shows that auroral zones become equipotential when connected to magnetospheric conductors (cusps and plasma layer), enabling separation of the global conductivity problem into three independent boundary value problems: two polar caps and the main ionospheric region, facilitating modeling of the Global Electric Circuit and ionospheric dynamo fields.

ABSTRACT

A model of the ionospheric global conductor is designed. The ionospheric conductor is considered in the framework of a two-dimensional approximation based on high conductivity in the direction of the magnetic field. Under this assumption the magnetic field lines are equipotential, and the charge transfer between them is determined only by integral Pedersen and Hall conductivities. The model is constructed as the first approximation in the small parameter expansion of the solution of the three-dimensional problems of electrical conductivity. The small parameter is the ratio of Pedersen and field-aligned conductivities. The space distributions of the Pedersen and Hall conductivities are calculated using the empirical models IRI, MSISE, IGRF and applied to construct the maps of the integral conductivities. The parts of the magnetosphere with high conductivity across the magnetic field lines, namely, the cusps and the plasma layer are analyzed. It is shown that the connection of these magnetospheric conductors to the ionosphere in parallel makes the auroral zones equipotential regions. As a consequence, for the ionospheric electric fields, which generators are located in the ionosphere or in the atmosphere, the global problem of electrical conductivity is separated into three independent boundary value problems in three regions: two polar caps and the main part of the ionosphere which includes the mid- and low-latitude parts of the ionosphere. The model can be used for the analysis of the ionospheric part of the Global Electric Circuit, for calculation of the ionospheric dynamo electric field and as a fragment in more complex ionospheric and magnetospheric models.

Motivation & Objective

• To develop a simplified 2D model of the global ionospheric conductor for efficient simulation of large-scale electric fields and currents.
• To address the challenge of modeling electrical conductivity in the ionosphere-magnetosphere system with high field-aligned conductivity.
• To enable separation of the global electrical conductivity problem into independent boundary value problems for improved computational efficiency and physical insight.
• To support the analysis of the ionospheric part of the Global Electric Circuit and ionospheric dynamo electric fields.
• To provide a framework for integration into larger ionospheric and magnetospheric models.

Proposed method

• The model uses a small-parameter expansion of the 3D electrical conductivity equation, with the small parameter being the ratio of Pedersen conductivity to field-aligned conductivity.
• It assumes high field-aligned conductivity, making magnetic field lines equipotential and restricting current transfer between field lines to only Pedersen and Hall conductivities.
• Spatial distributions of Pedersen and Hall conductivities are computed using empirical models IRI, MSISE, and IGRF to generate global maps of integral conductivities.
• The model treats the ionosphere as a 2D conductor connected in parallel to magnetospheric conductors in the cusps and plasma layer, which are shown to make auroral zones equipotential.
• The global problem is decomposed into three independent elliptic boundary-value problems: one for each polar cap and one for the main ionospheric region (mid- and low-latitude ionosphere).
• Numerical solution is based on a finite-difference method applied to the resulting 2D potential equation with mixed-type boundary conditions on auroral and equatorial boundaries.

Experimental results

Research questions

• RQ1 How can the 3D electrical conductivity problem in the ionosphere be effectively reduced to a 2D approximation for large-scale electric field modeling?
• RQ2 What is the impact of connecting high-conductivity magnetospheric regions (cusps and plasma layer) to the ionosphere on the potential structure of the auroral zones?
• RQ3 Under what conditions does the ionospheric electric field problem decouple into independent boundary value problems for the polar caps and main ionospheric region?
• RQ4 To what extent does the 2D model based on small-parameter expansion preserve accuracy compared to full 3D solutions, especially for horizontal scales >100 km?
• RQ5 How can the model be used to improve simulations of the Global Electric Circuit and ionospheric dynamo fields?

Key findings

• The auroral zones become equipotential regions when connected in parallel to high-conductivity magnetospheric regions (cusps and plasma layer), which is a critical simplification for modeling.
• The global electrical conductivity problem splits into three independent boundary value problems: one for each polar cap and one for the main ionospheric region (mid- and low-latitude ionosphere), each with a unique solution.
• The 2D model, based on a small-parameter expansion of the 3D conductivity problem, provides a valid first approximation with minimal error for horizontal scales exceeding 100 km.
• The model enables accurate computation of ionospheric dynamo electric fields and supports analysis of the ionospheric part of the Global Electric Circuit.
• The method allows for efficient integration into larger ionospheric and magnetospheric models, particularly for simulating field-aligned currents and their effects on ionospheric potential distribution.
• The model is robust under the dipole approximation and has been validated through test calculations, with boundary conditions set at the equatorial and auroral boundaries to minimize error in the equatorial electrojet region.