Inductive ionospheric solver for magnetospheric MHD simulations

Abstract

Abstract. We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ∼10 V km −1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).

Theory of Cowling channel formation by reflection of shear Alfven waves from the auroral ionosphere

“…Time‐dependent Hall currents can lead to significant induction fields (curl E ≠ 0) and couple to FAC. This has been investigated for the horizontally homogeneous ionosphere [ Yoshikawa and Itonaga , , ; Buchert and Budnik , ; Yoshikawa , , , ; Vanhamäki et al ., ; Vanhamäki , ]. In the presence of conductivity gradients, a time‐dependent Cowling effect with polarization and secondary fields can obviously occur.…”

Introduction to Spherical Elementary Current Systems

“…The components of the transfer matrices M 1,2 can be calculated using Eqs. (2.7) and (2.8), as explained in detail by Vanhamäki (2011). Figure 2.3 illustrates how an irrotational potential field can be modeled with just CF elementary systems.…”

“…This is very similar to using spherical harmonic functions in solving differential equations. For example, Vanhamäki et al (2006) and Vanhamäki (2011) have used the elementary systems for solving ionospheric induction problems starting from Ohm's law and Maxwell's equations. Meanwhile, Vanhamäki and Amm (2007) introduced a new, local variant of the KRM (Kamide-Richmond-Matsushita) method (Kamide et al 1981) for calculating the ionospheric electric field from ground magnetic data and estimated ionospheric conductances.…”

Ionospheric Joule heating and Poynting flux in quasi‐static approximation

“…In this study we concentrated on electrostatic phenomena by assuming that ∇ × E = 0. This is usually a good approximation, but inductive effects may be important in some very dynamical auroral phenomena [ Vanhamäki et al , 2007; Vanhamäki , 2011]. We plan to address the general topic of electrodynamic Joule heating and Poynting flux in a future study.…”

“…This is usually a good approximation, as most changes in ionospheric current systems are quasi-static. However, we note that inductive effects may be important in some very dynamical auroral phenomena [Vanhamäki et al, 2007;Vanhamäki, 2011] and also in Alfvén wave reflection at the ionosphere [e.g., Yoshikawa and Itonaga, 1996;Buchert, 1998;Lysak and Song, 2001]. Inductive effects on the energy balance of Alfvén wave reflection have been discussed by Yoshikawa [2002aYoshikawa [ , 2002b.…”