Extended lateral heating of the nighttime ionosphere by ground‒based VLF transmitters

Graf, K. L.; Spasojević, M.; Marshall, R. A.; Lehtinen, N. G.; Foust, F.; Inan, U. S.

doi:10.1002/2013ja019337

Cited by 11 publications

(8 citation statements)

References 79 publications

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“…Similarly, the electron temperature change Δ T e , shown in Figure (bottom), is stronger in the direction across B 0 . The absolute magnitude of Δ T e , with a maximum of ∼150 K, is in good agreement with Graf et al [], who calculated a maximum Δ T e =300 K for the 424 kW NPM transmitter.…”

Section: Heating By Vlf Transmitterssupporting

confidence: 90%

“…Instead, for VLF transmitters we use the heating method presented in Rodriguez et al [] and Graf et al [], which updates the electron temperature due to heating, and also includes cooling:

\frac{3}{2} k_{B} N_{e} \frac{normald T_{e}}{normald t} = U - L_{e}

where U = J · E is simply Joule heating, which is trivial to calculate in the FDTD method. The term L e is electron cooling, which includes empirical expressions for rotational, vibrational, and elastic transfer of energy from electrons to N 2 and O 2 as a function of T e , T 0 , N e ,

N_{{normalN}_{2}}

, and

N_{{normalO}_{2}}

; these expressions are listed in detail in Graf et al []. In the time domain method, we discretize equation above using a semiimplicit Euler method, which however does not guarantee stability.…”

Section: Modelmentioning

confidence: 99%

“…They again found agreement to within ±6 dB, and attributed the errors of previous comparisons to simplifying assumptions within the Helliwell formulation, in particular, the assumption of vertical incidence of the wave on the lower ionosphere. Graf et al [] then showed that the region of the ionosphere that is heated by ground‐based VLF transmitters is much more extensive than previously though, extending thousands of kilometers laterally. For lightning, comparison between modeled wave amplitudes and measured amplitudes using the DEMETER satellite data is ongoing.…”

Section: Introductionmentioning

confidence: 99%

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Effect of self‐absorption on attenuation of lightning and transmitter signals in the lower ionosphere

Marshall

2014

JGR Space Physics

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The attenuation of VLF signals from lightning and ground-based VLF transmitters during transionospheric propagation has been the subject of recent interest, as discrepancies have been found between satellite data and model calculations. Previous modeling efforts, however, have not considered the self-absorption effect due to nonlinear heating and ionization in the lower ionosphere. A self-consistent model of ionospheric heating is presented here using a time-domain model of VLF wave propagation through the ionosphere. The model is able to estimate the attenuation of signals due to heating below ∼100 km altitude. In this model, the ionospheric state is updated as the fields propagate, leading to changes in collision frequency and electron density, which in turn affect the wave propagation. We use this model for ground-based VLF transmitters at different frequencies, amplitudes, and latitudes (i.e., magnetic dip angle), and for lightning-generated sferics with different amplitudes, at different latitudes, and using a variety of ionospheric density profiles. We find that the inclusion of self-consistent heating causes a change in the transionospherically propagating wave amplitude that varies considerably with the source amplitude and other parameters. Typical values for the heating contribution to wave attenuation are 1−2 dB for VLF transmitters, but greater than 10 dB for large amplitude lightning discharges. An interesting effect is observed for VLF transmitters and low-amplitude lightning, where the signal is actually enhanced due to heating, rather than attenuated, in the direction propagating across the Earth's magnetic field.

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Section: Heating By Vlf Transmitterssupporting

confidence: 90%

“…Instead, for VLF transmitters we use the heating method presented in Rodriguez et al [] and Graf et al [], which updates the electron temperature due to heating, and also includes cooling:

\frac{3}{2} k_{B} N_{e} \frac{normald T_{e}}{normald t} = U - L_{e}

N_{{normalN}_{2}}

, and

N_{{normalO}_{2}}

; these expressions are listed in detail in Graf et al []. In the time domain method, we discretize equation above using a semiimplicit Euler method, which however does not guarantee stability.…”

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of self‐absorption on attenuation of lightning and transmitter signals in the lower ionosphere

Marshall

2014

JGR Space Physics

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“…VLF/LF radio wave transmission is heavily influenced by the state of the bottom of the lower ionosphere, which is known as the ionospheric D (daytime) or E (nighttime) region. Both the phase and amplitude of the radio wave are extremely sensitive to the electron density profile (EDP) in the ionospheric D/E region, and hence to the solar and cosmic radiation (Graf et al, 2013;Inan et al, 2010;Lehtinen & Inan, 2008;Peter & Inan, 2007;Thomson, 1993Thomson, , 2005Thomson, , 2010; Thomson et al, 2004Thomson et al, , 2007Thomson et al, , 2017; Thomson & Clilverd, 2000, 2001; Thomson & McRae, 2009). Recent advances in lightning detection have raised interest in probing the ionospheric D/E region with lightning sferics (radio atmospherics).…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Ray Theory Model With the Finite Difference Time Domain Model for Lightning Sferic Transmission in Earth‐Ionosphere Waveguide

et al. 2019

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The lightning sferic has been shown to be a valuable radio signal for detecting perturbations of the lower ionosphere caused by the lightning activity itself and by other terrestrial and space events (Shao et al., 2012, https://doi.org/10.1038/ngeo1668). Adding to many existing methods, we have recently proposed an improved ray theory (RT) model for investigating the lightning sferic transmission in the Earth‐ionosphere waveguide (Qin et al., 2017, https://doi.org/10.1002/2016JD025599). In the present study, a further modification to the RT model was made to increase its accuracy in modeling the lightning sferic in a broader frequency band and a larger distance range. The modification included two aspects: a new incident angle finding technique and a novel method for deriving the high‐order hop series. To quantitatively evaluate the effectiveness of the modification, a comparative study of this modified RT model with its previous version and the full‐wave finite difference time domain model was carried out. The results showed that this modified RT model did better than its previous version and was in close agreement with the full‐wave finite difference time domain method in modeling the lightning sferic in frequencies bands lower to 3, 5, and 7 kHz for distances up to 500, 800, and 1,000 km, respectively.

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“…The HF‐heating effect in the ionosphere and the reflection and penetration waves of a HF transmitter were investigated with a mode theory‐based finite element model [ Lehtinen and Inan , , ]. More recently, a large‐scale computational model involving both the wave propagation and physical heating effects was developed to study the perturbation of ionosphere from a VLF transmitter [ Graf et al ., ]. A ray theory (wave hop)‐based full‐wave electromagnetic model that calculates the ionosphere reflection taking the concern of Fresnel diffraction was developed by Jacobson and Shao [; ].…”

Section: Introductionmentioning

confidence: 99%

An improved ray theory and transfer matrix method‐based model for lightning electromagnetic pulses propagating in Earth‐ionosphere waveguide and its applications

et al. 2017

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An improved ray theory and transfer matrix method‐based model for a lightning electromagnetic pulse (LEMP) propagating in Earth‐ionosphere waveguide (EIWG) is proposed and tested. The model involves the presentation of a lightning source, parameterization of the lower ionosphere, derivation of a transfer function representing all effects of EIWG on LEMP sky wave, and determination of attenuation mode of the LEMP ground wave. The lightning source is simplified as an electric point dipole standing on Earth surface with finite conductance. The transfer function for the sky wave is derived based on ray theory and transfer matrix method. The attenuation mode for the ground wave is solved from Fock's diffraction equations. The model is then applied to several lightning sferics observed in central China during day and night times within 1000 km. The results show that the model can precisely predict the time domain sky wave for all these observed lightning sferics. Both simulations and observations show that the lightning sferics in nighttime has a more complicated waveform than in daytime. Particularly, when a LEMP propagates from east to west (Φ = 270°) and in nighttime, its sky wave tends to be a double‐peak waveform (dispersed sky wave) rather than a single peak one. Such a dispersed sky wave in nighttime may be attributed to the magneto‐ionic splitting phenomenon in the lower ionosphere. The model provides us an efficient way for retrieving the electron density profile of the lower ionosphere and hence to monitor its spatial and temporal variations via lightning sferics.

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Extended lateral heating of the nighttime ionosphere by ground‒based VLF transmitters

Cited by 11 publications

References 79 publications

Effect of self‐absorption on attenuation of lightning and transmitter signals in the lower ionosphere

Effect of self‐absorption on attenuation of lightning and transmitter signals in the lower ionosphere

A Comparative Study of the Ray Theory Model With the Finite Difference Time Domain Model for Lightning Sferic Transmission in Earth‐Ionosphere Waveguide

An improved ray theory and transfer matrix method‐based model for lightning electromagnetic pulses propagating in Earth‐ionosphere waveguide and its applications

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