New method for solving inductive electric fields in the non-uniformly conducting ionosphere

Vanhamäki, Heikki; Amm, O.; Viljanen, A.

doi:10.5194/angeo-24-2573-2006

Cited by 11 publications

(22 citation statements)

References 11 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3.1 is a modification of the inductive solver presented by Vanhamäki et al (2006) and employed by . The main difference is the type of input data used in the solver: Vanhamäki et al (2006) assumed that the potential part of the ionospheric electric field is available, whereas here we use the FAC provided by a magnetospheric MHD simulation. Also the local elementary system -based KRM method developed by is closely related to the solver presented in this article.…”

Section: Discussionmentioning

confidence: 99%

Inductive ionospheric solver for magnetospheric MHD simulations

Vanhamäki

2011

Ann. Geophys.

Self Cite

View full text Add to dashboard Cite

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).

show abstract

Section: Discussionmentioning

confidence: 99%

Inductive ionospheric solver for magnetospheric MHD simulations

Vanhamäki

2011

Ann. Geophys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, we here choose a different way to solve equation : We expand

{\overset{true\to}{italicE}}_{2}

into spherical elementary current (vector) systems (SECS), in a similar way as exercised by, e.g., Amm and Viljanen [] or Vanhamäki et al . []. For that, we define n positions

{\overset{true\to}{italicr}}_{i}

, i = 1,…, n on which the parameters assumed as known are given (by observations and/or by models) and m positions

\overset{true\to}{italicr}'_{j}

, j = 1,…, m where we place poles of curl‐free SECS that will be used to expand the vector field

{\overset{true\to}{italicE}}_{2}

.…”

Section: Theorymentioning

confidence: 99%

“…[9] Therefore, we here choose a different way to solve equation (2): We expand ! E 2 into spherical elementary current (vector) systems (SECS), in a similar way as exercised by, e.g., Amm and Viljanen [1998] or Vanhamäki et al [2006]. For that, we define n positions !…”

Section: Theorymentioning

confidence: 99%

General solution for calculating polarization electric fields in the auroral ionosphere and application examples

et al. 2013

Self Cite

View full text Add to dashboard Cite

[1] We devise an approach to calculate the polarization electric field in the ionosphere, when the ionospheric conductances, the primary (modeled) or the total (measured) electric field, and the Cowling efficiency are given. In contrast to previous studies, our approach is a general solution which is not limited to specific geometrical setups, and all parameters may have any kind of spatial dependence. The solution technique is based on spherical elementary current (vector) systems (SECS). This way, we avoid the need to specify explicit boundary conditions for the searched polarization electric field of its potential which would be required if the problem was solved in a differential equation approach. Instead, we solve an algebraic matrix equation, and the implicit boundary condition that the divergence of the polarization electric field vanishes outside our analysis area is sufficient. In order to illustrate our theory, we then apply it to two simple models of auroral electrodynamic situations, the first being a mesoscale strong conductance enhancement in the early morning sector within a relatively weak southward primary electric field, and a morning sector auroral arc with only a weak conductance enhancement, but a large southward primary electric field at the poleward flank of the arc. While the significance of the polarization electric field for maximum Cowling efficiency is large for the first case, it is rather minor for the second one. Both models show that the polarization electric field effect may not only change the magnitude of the current systems but also their overall geometry. Furthermore, the polarization electric field may extend into regions where the primary electric field is small, thus even dominating the total electric field in these regions. For the first model case, the total Joule heating integrated over the analysis area decreases by a factor of about 4 for maximum Cowling efficiency as compared to the case of vanishing Cowling efficiency. Furthermore, for this case the resulting total electric field structurally shows a strong resemblance to that frequently observed during auroral omega band events.Citation: Amm, O., R. Fujii, H. Vanhama¨ki, A. Yoshikawa, and A. Ieda (2013), General solution for calculating polarization electric fields in the auroral ionosphere and application examples,

show abstract

“…Vanhamäki et al (2006 described a way to solve the ionospheric induction problem using so called Cartesian Elementary Systems (CECS). This calculation scheme is essentially a finite element method for the curl and divergence of the ionospheric electric field, where CECS are used to represent the curl and divergence of the electric field and currents in one grid cell.…”

Section: Modelling Induction With Elementary Current Systemsmentioning

confidence: 99%

“…The calculation method developed by Vanhamäki et al (2006 uses the thin-sheet approximation, so that the ionosphere is handled as a 2-D sheet. One possible way to study induction effects in 3-D ionosphere would be to include a second thin sheet in the model.…”

Section: Modelling Induction With Elementary Current Systemsmentioning

confidence: 99%

Towards understanding the electrodynamics of the 3-dimensional high-latitude ionosphere: present and future

Amm

Aruliah²,

Buchert

et al. 2008

Ann. Geophys.

Self Cite

View full text Add to dashboard Cite

Abstract. Traditionally, due to observational constraints, ionospheric modelling and data analysis techniques have been devised either in one dimension (e.g. along a single radar beam), or in two dimensions (e.g. over a network of magnetometers). With new upcoming missions like the Swarm ionospheric multi-satellite project, or the EISCAT 3-D project, the time has come to take into account variations in all three dimensions simultaneously, as they occur in the real ionosphere. The link between ionospheric electrodynamics and the neutral atmosphere circulation which has gained increasing interest in the recent years also intrinsically requires a truly 3-dimensional (3-D) description. In this paper, we identify five major science questions that need to be addressed by 3-D ionospheric modelling and data analysis. We briefly review what proceedings in the young field of 3-D ionospheric electrodynamics have been made in the past to address these selected question, and we outline how these issues can be addressed in the future with additional observations and/or improved data analysis and simulation techniques. Throughout the paper, we limit the discussion to high-latitude and mesoscale ionospheric electrodynamics, and to directly data-driven (not statistical) data analysis.

show abstract

New method for solving inductive electric fields in the non-uniformly conducting ionosphere

Cited by 11 publications

References 11 publications

Inductive ionospheric solver for magnetospheric MHD simulations

Inductive ionospheric solver for magnetospheric MHD simulations

General solution for calculating polarization electric fields in the auroral ionosphere and application examples

Towards understanding the electrodynamics of the 3-dimensional high-latitude ionosphere: present and future

Contact Info

Product

Resources

About