Electromagnetic Field Solutions in an Isotropic Medium With Weakly-Random Fluctuations in Time and Some Applications in the Electrodynamics of the Ionosphere

Nijimbere, Victor; Campbell, Lucy

doi:10.2528/pierb18102003

Cited by 3 publications

(12 citation statements)

References 17 publications

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“…As a result of this, there is no magnetohydrodynamic problem to solve. To get around these inconsistencies, we consider that the ionosphere is a weakly-dispersive time-dependent linear isotropic medium as in Nijimbere and Campbell [22], and thus, we obtain the expressions for E, H, B and α,el to substitute in the momentum Equation (1) and in the energy Equation (3).…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…(10) that will give a solution representing a direct current electric field. Following [22], we solve Eq. (10) subject to the initial conditions…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…(21) with respect to z and Eq. (22) with respect x and subtracting one equation from another to eliminate the pressure terms. This gives…”

Section: Streamfunction-vorticity Formulationmentioning

confidence: 99%

“…The magnetic flux density is indeed linear in time. Thus, using Faraday's law of induction, we should obtain a constant electromotive force (voltage), showing that the ionosphere acts as a direct current dynamo [22].…”

Section: Stochastic Modelling: the Ionosphere As A Weakly-random Timementioning

confidence: 99%

“…However, electrodynamic processes have to be taken into consideration. Furthermore, to take into account the presence of random scatters in the medium, the ionosphere can be considered to be an isotropic medium with weakly-random fluctuations in time as in [22], and thus we can model the ionospheric disturbances in terms of stochastic partial differential equations (SPDEs). Our purpose is to simulate the nonlinear interactions between the electromagnetic field and the medium.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Modelling of Electro-Magnetohydrodynamic Disturbances (E-Mhd) in a Two-Dimensional Configuration in the Vertical Plane in the Ionosphere: Small Scale and Medium Scale Ionospheric Disturbances

Nijimbere¹,

Campbell²

2020

PIER B

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We have simulated ionospheric disturbances generated by the buoyancy and electrodynamic effects in a two-dimensional configuration in the vertical plane in the ionospheric F region using a simple two-dimensional mathematical model for internal gravity waves propagating in the lower atmosphere, and we have investigated the characteristics (e.g., buyoancy frequency, wavenumber, wavelength, speed) of the ionospheric disturbances. We find that electrohydrodynamic effects are mainly responsible for small scale non-travelling ionospheric disturbances, while magnetohydrodynamic effects are responsible for travelling ionospheric disturbances, including small scale travelling ionospheric disturbances (SSTIDs), medium scale travelling ionospheric disturbances (MSTIDs) and large scale travelling ionospheric disturbances (LSTIDs). Our results are in agreement with the results obtained from observations.

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Section: Mathematical Modellingmentioning

confidence: 99%

“…(10) that will give a solution representing a direct current electric field. Following [22], we solve Eq. (10) subject to the initial conditions…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…(21) with respect to z and Eq. (22) with respect x and subtracting one equation from another to eliminate the pressure terms. This gives…”

Section: Streamfunction-vorticity Formulationmentioning

confidence: 99%

Section: Stochastic Modelling: the Ionosphere As A Weakly-random Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Modelling of Electro-Magnetohydrodynamic Disturbances (E-Mhd) in a Two-Dimensional Configuration in the Vertical Plane in the Ionosphere: Small Scale and Medium Scale Ionospheric Disturbances

Nijimbere¹,

Campbell²

2020

PIER B

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A mathematical model for the numerical simulations of traveling ionospheric disturbances/atmospheric gravity waves generated by the Joule heating

Nijimbere

2020

Physics of Fluids

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Traveling ionospheric disturbances (TIDs) and atmospheric gravity waves (AGWs) generated by the Joule heating produced from intensified auroral electrojet and/or intense particle precipitation in the auroral and subauroral regions during geomagnetic storms and which propagate downward toward the lower (neutral) atmosphere are numerically simulated using a simple two-dimensional mathematical model for internal gravity waves propagating in the lower atmosphere. An explicit expression for the Joule heating is obtained, and the characteristics of the simulated TIDs/AGWs (e.g., buoyancy frequency, wavenumbers, cutoff wavelength, speed, structures) are also examined and compared with the results obtained from observations. As may be seen in the observations, small-scale TIDs/AGWs with wavelengths shorter than 100 km, medium-scale TIDs/AGWs with wavelengths of several hundred kilometers, and large-scale TIDs/AGWs with wavelengths longer than 1000 km generated by the Joule heating were modeled and numerically simulated. For example, observations have revealed that the Joule heating can generate TID/AGW pairs. The developed numerical model was used to simulate medium-scale TID/AGW wave packet pairs, and the results (wavelength, speed, structure) are in agreement with SuperDARN observations reported by Sofko and Huang, 2000. TIDs/AGWs with shorter horizontal wavelengths are more trapped than those with longer wavelengths (medium- and large-scale TIDs/AGWs). Their cutoff horizontal wavelength was approximated using the linear stability theory of AGWs. The approximated cutoff horizontal wavelength suggests that not all simulated small-scale disturbances with horizontal wavelengths shorter than 100 km are traveling as may be seen in the observations.

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On the Classical Electrodynamics in Dispersive Time-Dependent Linear Isotropic Media

Nijimbere¹

2019

PIER C

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The goal of this study is to conduct an analytical study of the properties (permittivity and permeability or refractive index) of a dispersive time-dependent linear isotropic medium interacting with electromagnetic fields. It is found that the permittivity and permeability of the time-dependent dispersive medium may either have an exponential profile in time or a sinusoidal profile in time. The permittivity and permeability can vanish or can be negative as in metamaterials. Therefore, the refractive index can vanish, so the electromagnetic wave can propagate at an infinite speed (c 3 • 10 8 m/s). It is also shown that the permittivity and the permeability can simultaneously be negative as in left-handed metamaterials (LHM). The general electric field and magnetic field solutions are derived, and the electric and magnetic flux densities are evaluated. The wave dispersion relation is also analysed. The obtained solutions can be used to validate experimental results by applying the initial and boundary conditions which are appropriate to the experimental setup.

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Electromagnetic Field Solutions in an Isotropic Medium With Weakly-Random Fluctuations in Time and Some Applications in the Electrodynamics of the Ionosphere

Cited by 3 publications

References 17 publications

Numerical Modelling of Electro-Magnetohydrodynamic Disturbances (E-Mhd) in a Two-Dimensional Configuration in the Vertical Plane in the Ionosphere: Small Scale and Medium Scale Ionospheric Disturbances

Numerical Modelling of Electro-Magnetohydrodynamic Disturbances (E-Mhd) in a Two-Dimensional Configuration in the Vertical Plane in the Ionosphere: Small Scale and Medium Scale Ionospheric Disturbances

A mathematical model for the numerical simulations of traveling ionospheric disturbances/atmospheric gravity waves generated by the Joule heating

On the Classical Electrodynamics in Dispersive Time-Dependent Linear Isotropic Media

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