The propagation of very low-frequency radio waves in ducts in the magnetosphere

A method is developed to calculate waveguide modes in a plane stratified duct of enhanced or reduced ionization density in an otherwise uniform magneto-ionic medium. It may in principle be applied to ducts with an arbitrary electron density profile, and with dimensions of the order of the wavelength in the medium. Computations are carried out for one simple model with enhanced ionization density and parameters typical of whistler propagation. The fields inside and outside the duct are discussed. It is shown that the energy flux in the inhomogeneous wave outside the physical boundaries of the duct may in certain circumstances be important. The types of waveguide mode which may occur are discussed. In particular there is one mode called the zero-order mode which always propagates even when the duct is very narrow or when the electron density in the duct differs only infinitesimally from that in the uniform medium outside. In the limit where the duct no longer exists this mode becomes a plane wave. When the axis of the duct is curved and there are transverse gradients of ionization density and of magnetic field in the medium outside the duct, all modes may tunnel through a barrier region, in which the wave is evanescent, to a region where the energy is refracted away from the duct. Consideration of this process leads to a criterion for deciding whether a duct is sufficiently strong to maintain guiding.

Download Full-text

The ionosphere as a whispering gallery

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1962.0042 ◽

1962 ◽

Vol 265 (1323) ◽

pp. 554-569 ◽

Cited By ~ 22

Keyword(s):

Electron Density ◽

Spherical Surface ◽

Low Frequency ◽

Electron Density Profile ◽

Whispering Gallery Modes ◽

Radio Waves ◽

Sound Waves ◽

Whispering Gallery ◽

The Earth ◽

Reflexion Coefficient

The propagation of radio waves of very low frequency to great distances is conveniently treated by regarding the space between the earth and the ionosphere as a wave-guide. Several authors have found that the least attenuated modes are profoundly affected by the earth’s curvature. This effect is investigated for several models of the ionosphere. It is found, in particular, that for frequencies greater than about 30 kc/s some modes are possible for which the energy is concentrated in a region near the base of the ionosphere, and the field strength near the ground is small. It is useful to think of such modes as being composed of waves repeatedly reflected at the inside spherical surface of the ionosphere, the rays being chords of this sphere. By analogy with sound waves these modes are called ‘whispering gallery modes’. The theory uses wave admittance and reflexion coefficient variables because these satisfy differential equations which are convenient for integration using a digital computer. The curvature of the earth is allowed for by using the method of the modified refractive index, but the earth’s magnetic field is neglected. Formulae for the m ode condition and the excitation of the various modes by a transmitter are given and discussed. A new way of dealing with an ionosphere having a continuous electron density profile is presented. The results of some numerical calculations are given both for a sharply bounded homogeneous ionosphere and for an exponential profile of electron density.

Download Full-text

Survey of electron density changes in the daytime ionosphere over the Arecibo observatory due to lightning and solar flares

Scientific Reports ◽

10.1038/s41598-021-89662-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Caitano L. da Silva ◽

Sophia D. Salazar ◽

Christiano G. M. Brum ◽

Pedrina Terra

Keyword(s):

Electron Density ◽

Solar Flares ◽

Low Frequency ◽

Lower Ionosphere ◽

Weather Conditions ◽

Optical Observations ◽

Radio Waves ◽

D Region ◽

E Region ◽

Arecibo Observatory

AbstractOptical observations of transient luminous events and remote-sensing of the lower ionosphere with low-frequency radio waves have demonstrated that thunderstorms and lightning can have substantial impacts in the nighttime ionospheric D region. However, it remains a challenge to quantify such effects in the daytime lower ionosphere. The wealth of electron density data acquired over the years by the Arecibo Observatory incoherent scatter radar (ISR) with high vertical spatial resolution (300-m in the present study), combined with its tropical location in a region of high lightning activity, indicate a potentially transformative pathway to address this issue. Through a systematic survey, we show that daytime sudden electron density changes registered by Arecibo’s ISR during thunderstorm times are on average different than the ones happening during fair weather conditions (driven by other external factors). These changes typically correspond to electron density depletions in the D and E region. The survey also shows that these disturbances are different than the ones associated with solar flares, which tend to have longer duration and most often correspond to an increase in the local electron density content.

Download Full-text

Classification of X-ray solar flares regarding their effects on the lower ionosphere electron density profile

Annales Geophysicae ◽

10.5194/angeo-26-1731-2008 ◽

2008 ◽

Vol 26 (7) ◽

pp. 1731-1740 ◽

Cited By ~ 46

Author(s):

D. P. Grubor ◽

D. M. Šulić ◽

V. Žigman

Keyword(s):

Electron Density ◽

Solar Flares ◽

Low Frequency ◽

Lower Ionosphere ◽

Electron Density Profile ◽

Height Range ◽

X Ray ◽

Reflection Height ◽

Single Trace

Abstract. The classification of X-ray solar flares is performed regarding their effects on the Very Low Frequency (VLF) wave propagation along the Earth-ionosphere waveguide. The changes in propagation are detected from an observed VLF signal phase and amplitude perturbations, taking place during X-ray solar flares. All flare effects chosen for the analysis are recorded by the Absolute Phase and Amplitude Logger (AbsPal), during the summer months of 2004–2007, on the single trace, Skelton (54.72 N, 2.88 W) to Belgrade (44.85 N, 20.38 E) with a distance along the Great Circle Path (GCP) D≈2000 km in length. The observed VLF amplitude and phase perturbations are simulated by the computer program Long-Wavelength Propagation Capability (LWPC), using Wait's model of the lower ionosphere, as determined by two parameters: the sharpness (β in 1/km) and reflection height (H' in km). By varying the values of β and H' so as to match the observed amplitude and phase perturbations, the variation of the D-region electron density height profile Ne(z) was reconstructed, throughout flare duration. The procedure is illustrated as applied to a series of flares, from class C to M5 (5×10−5 W/m2 at 0.1–0.8 nm), each giving rise to a different time development of signal perturbation. The corresponding change in electron density from the unperturbed value at the unperturbed reflection height, i.e. Ne(74 km)=2.16×108 m−3 to the value induced by an M5 class flare, up to Ne(74 km)=4×1010 m−3 is obtained. The β parameter is found to range from 0.30–0.49 1/km and the reflection height H' to vary from 74–63 km. The changes in Ne(z) during the flares, within height range z=60 to 90 km are determined, as well.

Download Full-text

Measurement of electron density profile in the lower ionosphere during nighttime by rocket observations of MF and VLF radio waves

Electronics and Communications in Japan (Part I Communications) ◽

10.1002/(sici)1520-6424(200002)83:2<20::aid-ecja3>3.0.co;2-m ◽

2000 ◽

Vol 83 (2) ◽

pp. 20-28 ◽

Cited By ~ 1

Author(s):

Masayoshi Mambo ◽

Tetsuo Fukami ◽

Toshimi Okada ◽

Isamu Nagano ◽

Iwane Kimura

Keyword(s):

Electron Density ◽

Density Profile ◽

Lower Ionosphere ◽

Electron Density Profile ◽

Radio Waves

Download Full-text

Remote sensing planetary waves in the midlatitude mesosphere using low frequency transmitter signals

Annales Geophysicae ◽

10.5194/angeo-29-1287-2011 ◽

2011 ◽

Vol 29 (7) ◽

pp. 1287-1293 ◽

Cited By ~ 19

Author(s):

E. D. Schmitter

Keyword(s):

Electron Density ◽

Planetary Wave ◽

Low Frequency ◽

Lower Ionosphere ◽

Signal Amplitude ◽

Propagation Path ◽

Polar Regions ◽

Radio Waves ◽

Good Proxy ◽

Winter Time

Abstract. Very low and low radio frequency (VLF/LF) propagation responds sensitively to the electron density distribution in the lower ionosphere (upper mesosphere). Whereas propagation paths crossing subpolar and polar regions are frequently affected by forcing from above by particle precipitations, mid- and lowlatitude paths let forcing from below be more prominent. Our observations (2009–2011) show, that the low frequency propagation conditions along the midlatitude path from Sicily to Germany (52° N 8° E) using the NSY 45.9 kHz transmitter (37° N 14° E) prove to be a good proxy of mesosphere planetary wave activity along the propagation path. High absorption events with VLF/LF propagation correlate to the well known winter time D-layer anomaly observed with high frequency (HF) radio waves. VLF/LF propagation calculations are presented which show that the radio signal amplitude variations can be modeled by planetary wave modulated collison frequency and electron density profiles. The other way around wave pressure amplitudes can be inferred from the VLF/LF data.

Download Full-text

A High Latitude Model for the E Layer Dominated Ionosphere

Remote Sensing ◽

10.3390/rs13183769 ◽

2021 ◽

Vol 13 (18) ◽

pp. 3769

Author(s):

Sumon Kamal ◽

Norbert Jakowski ◽

Mohammed Mainul Hoque ◽

Jens Wickert

Keyword(s):

Electron Density ◽

Geomagnetic Latitude ◽

Peak Height ◽

Electron Density Profile ◽

Radio Waves ◽

Occurrence Probability ◽

Satellite Mission ◽

Primary Relationships ◽

Future Prediction ◽

Electron Density Profiles

Under certain conditions, the ionization of the E layer can dominate over that of the F2 layer. This phenomenon is called the E layer dominated ionosphere (ELDI) and occurs mainly in the auroral regions. In the present work, we model the variation of the ELDI for the Northern and Southern Hemispheres. Our proposed Neustrelitz ELDI Event Model (NEEM) is an empirical, climatological model that describes ELDI characteristics by means of four submodels for selected model observables, considering the dependencies on appropriate model drivers. The observables include the occurrence probability of ELDI events and typical E layer parameters that are important to describe the propagation medium for High Frequency (HF) radio waves. The model drivers are the geomagnetic latitude, local time, day of year, solar activity and the convection electric field. During our investigation, we found clear trends for the model observables depending on the drivers, which can be well represented by parametric functions. In this regard, the submodel NEEM-N characterizes the peak electron density NmE of the E layer, while the submodels NEEM-H and NEEM-W describe the corresponding peak height hmE and the vertical width wvE of the E layer electron density profile, respectively. Furthermore, the submodel NEEM-P specifies the ELDI occurrence probability %ELDI. The dataset underlying our studies contains more than two million vertical electron density profiles covering a period of almost 13 years. These profiles were derived from ionospheric GPS radio occultation observations on board the six COSMIC/FORMOSAT-3 satellites (Constellation Observing System for Meteorology, Ionosphere and Climate/Formosa Satellite Mission 3). We divided the dataset into a modeling dataset for determining the model coefficients and a test dataset for subsequent model validation. The normalized root mean square deviation (NRMS) between the original and the predicted model observables yields similar values across both datasets and both hemispheres. For NEEM-N, we obtain an NRMS varying between 36.1% and 47.1% and for NEEM-H, between 6.1% and 6.3%. In the case of NEEM-W, the NRMS varies between 38.5% and 41.1%, while it varies between 56.5% and 60.3% for NEEM-P. In summary, the proposed NEEM utilizes primary relationships with geophysical and solar wind observables, which are useful for describing ELDI occurrences and the associated changes of the E layer properties. In this manner, the NEEM paves the way for future prediction of the ELDI and of its characteristics in technical applications, especially from the fields of telecommunications and navigation.

Download Full-text

Estimation of the electron density profile in the D region from rocket measurement of VLF signals from a ground based transmitter

Electrical Engineering in Japan ◽

10.1002/ecja.4400641110 ◽

1981 ◽

Vol 64 (11) ◽

pp. 68-74

Author(s):

Isamu Nagano ◽

Masayoshi Mambo ◽

Tetsuo Fukami ◽

Koji Namba ◽

Iwane Kimura

Keyword(s):

Electron Density ◽

Density Profile ◽

Electron Density Profile ◽

Rocket Measurement ◽

D Region

Download Full-text

Radio and Electrical Measurements on Glacial Streams

Journal of Glaciology ◽

10.3189/s0022143000008753 ◽

1987 ◽

Vol 33 (114) ◽

pp. 239-242

Author(s):

M. E. R. Walford

Keyword(s):

Electrical Conductivity ◽

Water Channel ◽

Water System ◽

Low Frequency ◽

Water Channels ◽

Radiative Loss ◽

Radio Waves ◽

Electrical Measurements ◽

Water Conductivity ◽

Glacier Surface

AbstractWe discuss the suggestion that small underwater transmitters might be used to illuminate the interior of major englacial water channels with radio waves. Once launched, the radio waves would naturally tend to be guided along the channels until attenuated by absorption and by radiative loss. Receivers placed within the channels or at the glacier surface could be used to detect the signals. They would provide valuable information about the connectivity of the water system. The electrical conductivity of the water is of crucial importance. A surface stream on Storglaciären, in Sweden, was found, using a low-frequency technique, to have a conductivity of approximately 4 × 10−4 S m−1. Although this is several hundred times higher than the conductivity of the surrounding glacier ice, the contrast is not sufficient to permit us simply to use electrical conductivity measurements to establish the connectivity of englacial water channels. However, the water conductivity is sufficiently small that, under favourable circumstances, radio signals should be detectable after travelling as much as a few hundred metres along an englacial water channel. In a preliminary field experiment, we demonstrated semi quantitatively that radio waves do indeed propagate as expected, at least in surface streams. We conclude that under-water radio transmitters could be of real practical value in the study of the englacial water system, provided that sufficiently robust devices can be constructed. In a subglacial channel, however, we expect the radio range would be much smaller, the environment much harsher, and the technique of less practical value.

Download Full-text

Radial density profile and stability of capillary discharge plasma waveguides of lengths up to 40 cm

High Power Laser Science and Engineering ◽

10.1017/hpl.2021.6 ◽

2021 ◽

Vol 9 ◽

Author(s):

M. Turner ◽

A. J. Gonsalves ◽

S. S. Bulanov ◽

C. Benedetti ◽

N. A. Bobrova ◽

...

Keyword(s):

Laser Pulse ◽

Electron Density ◽

Density Profile ◽

Pulse Propagation ◽

Spot Size ◽

Capillary Discharge ◽

Electron Density Profile ◽

Plasma Waveguide ◽

Wakefield Acceleration ◽

Plasma Wakefield

Abstract We measured the parameter reproducibility and radial electron density profile of capillary discharge waveguides with diameters of 650 $\mathrm{\mu} \mathrm{m}$ to 2 mm and lengths of 9 to 40 cm. To the best of the authors’ knowledge, 40 cm is the longest discharge capillary plasma waveguide to date. This length is important for $\ge$ 10 GeV electron energy gain in a single laser-driven plasma wakefield acceleration stage. Evaluation of waveguide parameter variations showed that their focusing strength was stable and reproducible to $<0.2$ % and their average on-axis plasma electron density to $<1$ %. These variations explain only a small fraction of laser-driven plasma wakefield acceleration electron bunch variations observed in experiments to date. Measurements of laser pulse centroid oscillations revealed that the radial channel profile rises faster than parabolic and is in excellent agreement with magnetohydrodynamic simulation results. We show that the effects of non-parabolic contributions on Gaussian pulse propagation were negligible when the pulse was approximately matched to the channel. However, they affected pulse propagation for a non-matched configuration in which the waveguide was used as a plasma telescope to change the focused laser pulse spot size.

Download Full-text