Electronics and Communications in Japan, Part 1, Vol. 78, No. 5, 1995 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. 77-84, No. 8, August 1994, pp. 437-444

Very Low Latitude Whistlers and the Effect of Earth-Ionosphere Waveguide Propagation

Kenji Ohta, Member, and Akio Shimizu, Nonmember

Faculty of Engineering, Chubu University, Kasugai, Japan 487

Masashi Hayakawa, Member

University of Electro-Communications, Chofu, Japan 182

Shin Shimakura, Member

Faculty of Engineering, Chiba University, Chiba, Japan 260

SUMMARY 1. Introduction

When a sonogram of the nighttime whistlers ob- served in Wuchang, China, at a low latitude (at a geo- magnetic latitude of 19.4"N) was studied in detail, whisker-type spectral components were observed, which may be due to the waveguide propagation effect of the second- and third-order modes, in the spectra of intense whistlers accompanied by echo trains. By applying the field analysis direction-finding method to this part, the propagation characteristics are derived and the results exhibited a tendency identical to that of the characteris- tics of tweek atmospherics. It was found that the whis- tlers transmitted through the ionosphere at a very low latitude in Zhanjiang (geomagnetic latitude of 10.O"N) and exhibited an extremely rare waveguide mode propa- gation after subionospheric propagation of over approxi- mately lo00 km.

There are two propagation modes in the long-dis- tance propagation of the very low frequency (VLF) electromagnetic wave originated in lightning discharges. One of them is the whistler propagation in which the electromagnetic wave from the lightning discharge is transmitted upward through the ionosphere, passes through the magnetospheric propagation path (called the duct) with an electron density enhancement over the surroundings along the geomagnetic field line, and then is transmitted downward through the ionosphere in the opposite hemisphere.

The propagation time f ( S ) of the whistler mode wave is given by [l]

where f (Hz) is the whistler frequency and the value of D (P) is called the dispersion value of the whistler. The unit in the equation is shown in SI system.

Key words: propagation; VLF.

Whistler; tweek; waveguide mode

81 ISSN8756-6621/95/0005-008 1 @ 1995 Scripta Technica, Inc.

( 1 ) - - - - Whistler mode (2)- Waveguide mode (2)

J i

0 100 200 300

Fig. 2. The sonogram of whistler observed at Wuchang: (1) whistler, (2) tweek, and (3) the effect of earth-ionosphere waveguide

propagation. Fig. 1. The Example of ray-path for whistler

and tweek.

ionosphere where the electromagnetic wave is reflected and is given in terms of the speed of light c as

The other propagation mode is the waveguide mode in which the electromagnetic wave propagates over a long distance by multiple reflection between the lower part of the ionosphere and the earth, as shown in (2) of Fig. 1. In this mode, there is no propagation time delay dependent on the frequency. Especially, this mode is observed at night as a tweek sferic with a long sustaining time of about several tens milliseconds near the cutoff frequency of the waveguide.

Figure 2 shows an example of the whistler (1) and its causative tweek sferic (2) in the form of a frequency- time spectrum (sonogram) observed at 03 hours 19 min- utes local time on January 5, 1988, in Wuchang, China (at a geographical latitude of 30.5" and a longitude of 114.6', a geomagnetic latitude of 19.4'). Since the discharge preceding the whistler generated on the other half of the earth propagates over a long distance in the form of a waveguide mode, it is observed as a tweek.

In the tweek sferic, there exist modes correspond- ing to the cutoff frequencies. They are the first mode, second mode, -., from the lower side. This phenomenon is considered to be generated by the interference of the waves when the electromagnetic wave undergoes multiple reflections while it is spread in the entire space [2, 31.

The cutoff frequency f,, of the n-th mode is de- termined by the height h of the lower edge of the

Also, the delay propagation time t at the frequency fo near the cutoff frequency by the waveguide mode propa- gation is given by the following in terms of the propaga- tion distance d of the electromagnetic wave [4]:

Even if the whistler travels downward and the waveguide mode is used for a long-distance transmission, the whistler with a long sustaining time such as tweeks is rarely observed near the cutoff frequency of the wave- guide. This is because the transmission angle is narrow at the time the whistler penetrates downward through the ionosphere and the 0th mode is rarely excited [5, 61. Rare exceptions include the example of observation of the whistler with a first-order mode cutoff by Araki and Kamiyama [5] and an example of the waveguide propa- gation effect of the first- and second-order modes by Shimakura et al. [ 6 ] . No analysis on the direction of arrival and the polarization characteristics at each fre- quency important for understanding the propagation characteristics has been carried out to date.

In the digital observation [7] we carried out in Wuchang, China, on January 5, 1988, it was found that there exists a long whisker-shaped sustaining time

82

40" a, -0 c, c,

a

2: 30"N .A

V

c Q m

..4

20"N a, W

10"N

I I I II I z(Zenith1 Wave Normal

1 0 0 " E l l O ' E 1 2 0 " E 130'E

Geographic Long1 tude i: Incident Angle e :Azimuthal Angle

Fig. 3. The observation points of whistlers in China.

(henceforth noted as a whisker part) indicating the char- acteristics of the waveguide mode propagation as well as the tweek sferic near the cutoff frequency.

In this paper, by analyzing the observation data of the three electromagnetic field components [7], it is found that the whisker part observed in the sonogram is an extremely rare observation example generated by the waveguide mode. propagation of the whistler. Its propaga- tion characteristics are analyzed.

2. Observation of VLF Electromagnetic Waves at a Very Low Latitude in China

The multipoint simultaneous observation of whis- tlers at a low latitude was carried out for the first time by Ondoh et al. [8]. To understand the propagation mechanism of the whistler, we planned a multipoint simultaneous observation at different latitudes but almost identical longitude [9]. For seven days, from January 5 through 11, 1988, a multipoint simultaneous observation of nighttime whistlers was carried out from 00 hour 00 minutes till 04 hour 00 minutes local time everyday at three points, including a very low latitude region in China shown, in Fig. 3, namely, Zhanjiang (geomagnetic latitude of 10.OoN), Guilin (14.1°N), and Wuchang (19.4"N) [7, 101. For the meaning of this observation, the reader should consult [9].

During the observation period, the largest number of nighttime whistlers was observed on January 5 [7]. It

Fig. 4. Coordinate system for direction finding.

was reported that these whistlers arrived with a right- handed polarization from the zenith of Zhanjiang, that there is no frequency dependence in the downward trans- mission point of the ionosphere, that there were many echo train whistlers observed, and that the propagation was along the magnetic line of force as the propagation below the ionosphere is strongly directed toward higher latitude [lo]. The whistler transmitted down in the iono- sphere above Zhanjiang has propagated in a waveguide mode to Wuchang, which is about 1000 km away. From the analysis by a digital sonogram [ 111, it was found that there is a whisker-shaped part in the whistler. No whis- ker was observed in the sonograms of the identical whistler observed in Zhanjiang and Guilin. Also, the frequency of occurrence of the whistler was the highest around 02 hour 40 minutes on January 5 [7]. Hence, we have used the whistler observation data from 02 hour 20 minutes to 03 hour 20 minutes on January 5 for the analysis of the whisker.

3. Analysis Method

The three electromagnetic field components of the whistler observed in January 1988 were digitized by a 16-bit A-D converter at a conversion speed of 8 ps and an FFT analysis was carried out with a data length of 2048. From the foregoing operation, the amplitude ratio and the phase difference of the two horizontal magnetic field components in reference to the one vertical electric field were measured at a resolution of 62.5 Hz [12]. The propagation characteristics of the whisker were derived by the field analysis direction-finding method.

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The measurement principle of the direction of arrival of the whistler and the polarization parameters by the field analysis method are described briefly. In the observation coordinate system in Fig. 4, the direction of arrival (azimuth angle of 0 and the incident angle of i ) of the VLF electromagnetic wave incident on the obser- vation point after downward transmission in the iono- sphere are given by [ 131

where M, - z, My - z, 4x - z, and +y - are the ampli- tude ratios and phase differences of the horizontal mag- netic field components induced in orthogonal loop anten- nas expanded in the east-west and south-north directions with respect to the vertical electric field component induced in the vertical antenna.

As shown in Fig. 4, the incident wave can be decomposed into the TM wave component (with a mag- netic field component normal to the incident plane) and the TE wave component (with a magnetic field compo- nent parallel to the incident plane). The polarization of the incident wave can be defined by the following equa- tion as the ratio of the magnetic field component H, in the incident plane and the one H , normal to the incident plane [ 141:

P=Hli / l€~ = u - j v (6)

The polarization parameters (u , v) are given by the fol- lowing [ 131:

u= -(M,-= cos dX-, sin i+ sin O)/cos i cos 8 (7)

v = MX+ sin q L z sin i/cos i cos O (8)

The measurement errors AO, A i , Au, and Av of these quantities, viz. the azimuth angle 0, the incident angle i, and the polarization parameters u and v, depend on the measured values of the output voltage and the phase difference from each antenna [12]. However, in the analysis data described below, they are A0 < 5 " , h i C 2", Au C 0.1, and Av C 0.1.

The direction of arrival of the whistler derived by this field analysis (0, i) indicates the downward trans- mission point of the ionosphere. In the case of the long- distance propagation in which the observation point and

12 - 10 N I r 8 Y

2:44 (LT) Jan. 5, 1988 (Wuchang)

0 ' I I n 0 100 200 300

Time (ms)

Fig. 5. The analyzed whistler and subiono- spheric dispersion effect.

the transmission point are far apart, the direction also indicates the multiple reflection points in the ionosphere.

Hence, whether the direction indicated by (0, i ) is the downward transmission point of the ionosphere or the final reflection point in the ionosphere can be estimated from the distribution of the incident angle, polarization parameters, and the phase difference between the two horizontal magnetic field components induced in the orthogonal antenna [15]. Also, it has already been report- ed that the field analysis developed for the measurement of the direction of arrival of the whistler transmitting downward in the ionosphere is also useful for the analy- sis of the propagation characteristics of the week sferics reflected by the ionosphere [16].

4. Analysis Results

Figure 5 shows a typical sonogram for a very low latitude whistler observed in Wuchang at 02 hour 44 minutes on January 5. The dispersion value given by Eq. (1) is 10.5 [ 101. From the analysis of the sonogram, the cutoff frequency& of the tweek sferic at the first mode is about 1.725 kHz [16]. The cutoff frequencies of the first-order mode through the fourth-order mode of the tweek sferic are easily recognized. On the other hand, only the second-order mode and the third-order mode (arrows in the figure) are detected slightly in regard to the whisker of the whistler. If this whisker is caused by the waveguide propagation, the first mode that should be detected most strongly was not discriminated since it is buried in the harmonic noise generated by the commer- cial power transmission lines.

The analysis of the wave dynamic characteristics at the cutoff frequency of the tweek sferic has been carried

84

W (270'

W ( 2 7 0 " )

frequency band of the whistler itself is broad over 6.125 to 2.0625 kHz, only one point of data indicating the strongest intensity was used at each frequency.

Figure 6 shows the distributions of the azimuth angle of amval 0 for which 0 is divided into 36 and the Occurrence rates are given in the radial direction. Figure 6(a) indicates the arriving azimuth angles in the whisker part of the whistler, whereas Fig. 6(b) indicates those for the whistler itself. In both Figs. 6(a) and (b), the azimuth angles in 200" to 210" are seen and hence the whisker and the whistler itself observed in Wuchang arrive almost in the same direction. Also, this angle is in the direction of Zhanjiang from Wuchang. The result therefore agrees with the analysis results in that their downward transmis- sion point exists above Zhanjiang for the whistler on January 5 [ 101.

- E (90 ' )

Fig. 6 . The azimuthal angles at cutoff frequency of dispersion effect

(a) and whistler (b).

out previously and the polarization parameters (u, v ) given by Eqs. (7) and (8) are (0, -1) near the cutoff frequency of the waveguide, indicating that the polariza- tion is in the left-handed circular [16]. Here, no details will be given for the propagation characteristics of the tweek, but they are given in [16].

In the whisker portion of the whistler, the fre- quency band of the first mode cannot be confirmed due to harmonic noise. Therefore, the frequency band of the second mode was analyzed. Also, to compare the results with those for the whisker portion, the whistler itself was analyzed.

Since the duration of the whisker is very short, i.e., 15 ms, and the frequency band analyzable was limited to 3.750 to 3.500 kHz, three to four data are used which are obtained by shifting the analysis time by 512 ps at each frequency. Also, since the analyzable

Figure 7 shows the characteristics of the polariza- tion parameters (u, v ) . Similar to Fig. 6, Fig. 7(a) shows the parameters in the whisker part while Fig. 7(b) indi- cates the parameters for the whistler itself. Also, Fig. 7(c) shows the average values of the polarization param- eters at each frequency in Fig. 7(a).

From Figs. 7(a) and (c), it is found that, as the cutoff frequency is approached, (u, v) becomes (u, v) = (0, -1). This is similar to the characteristic of (u, v ) of the tweek [16]. It is found that the whisker part of the whistler also arrives with a left-handed circular polariza- tion or an elliptic polarization extremely close to the circular polarization. Compared to (u, v) of the tweek sferic [16], (u, v ) in Fig. 7(a) fluctuates somewhat. This is considered to be caused by the fact that the intensity of the arriving wave is weak at about -30 dB and the time duration is only about one-thirtieth in comparison with the tweek sferic so that the number of data is small at the cutoff frequency.

On the other hand, (u, v ) of the whistler itself shown in Fig. 7(b) is distributed widely and no frequency dependence as in the case of whisker part was observed. Also, as it became clear in Fig. 7(c) that (u, v ) of the whistler itself is different from the one where the polar- ization characteristics of the whisker at the cutoff fre- quency approach u = 0, v = - 1 .

It is possible to estimate that the whistler transmit- ted downward through the ionosphere above Zhanjiang with a right-handed circular polarization [ 101 changes to an elliptical polarization during the propagation over a long distance [18].

85

30 I 1

U

3500.011~ 3562.5Hz -

V (a)

(Hz)

3700

* V E 0, 3

3600 LL

3500

2o I L -4 -2 0 2 4

a P U L

-2 0 2 V

(b)

-8 -6 -4 -2 0

( C )

Po 1 a r i za t i on Parameter

Fig. 7. The Occurrence distribution of polarization parameter of (a) dispersion effect, (b) whistler, and (c) frequency dependence of (a).

Figure 8 shows the reflection points of the whisker Figure 8(a) indicates the ionospheric reflection and the whistler itself arriving at the observation point at point in the whisker part of the whistler, while Fig. 8(b) Wuchang. Here, the center of the circle indicates Wu- indicates that of the whistler itself. The reflection point chang, which is the observation point. The reflection of the whisker shown in Fig. 8(a) approaches the obser- points are projected to the ionospheric altitude of 100 vation point (with a smaller incident angle) as the fre- km. quency is decreased. At the cutoff frequency of the

86

W

N

W

S

N

E

S

Fig. 8. The distribution of ionospheric reflection points of dispersion effect (a) and whistler (b).

second mode v;C = 3.5 kHz), the incident angle is i = 0". This indicates the same tendency as the characteris- tics that as the tweek approaches the cutoff frequency, the incident angle decreases and approaches the incident angle of i := 0" at the cutoff frequency [lo]. The final reflection point of the whistler itself in the ionosphere is located at a radius of 20 to 80 km from the observation point. There was no correlation observed between the frequency variation and the magnitude of the reflection radius. Therefore, only the representative frequencies are noted in the figure.

The causative sferic of the whistler observed on January 5 was generated at a distance 800 km to 1500 km from the conjugate point (entrance to the duct) of Zhanjiang 1191. There is a possibility that the whisker part of the whistler was generated by the waveguide mode propagation before the causative sferic reached the entrance to the duct. However, if the whistler is consid- ered to be generated by the meek generated before the

duct entrance, the whisker part should have been strongly observed in the whistler observed at Zhanjiang in corn- parison with other observation points. No whisker was observed either at Zhanjiang or at Guilin. And the polar- ization characteristics at the whistler and the whisker are different. These analysis results strongly suggest that the whisker appeared during the propagation from Zhanj iang to Wuchang.

From these propagation characteristics, the whisker part of the whistler observed at Wuchang is considered to be generated by the whistler transmitted downward in the ionosphere at Zhanjiang and the propagation in the waveguide mode to Wuchang over 1000 km.

5. Conclusions

A multipoint simultaneous measurement of the VLF electromagnetic wave including the very low latitude region in China was carried out in January 1988 [lo]. In the nighttime whistler observed on January 5 at Wuchang (geological latitude of 30.5"N, longitude of 114.6' and geomagnetic latitude of 19.4"N), a long whisker compo- nent with a long duration was observed on a sonogram near the cutoff frequency, considered to be caused by the waveguide mode propagation similar to the tweek. The propagation characteristics of this whisker were derived by the field analysis method. The following results were obtained.

(1) The whisker has a left-handed elliptical polar- ization which approaches the left-handed circular polar- ization near the cutoff frequency.

(2) As the cutoff frequency is approached, the incident angle i approaches 0".

This characteristic has the same tendency as that of the propagation characteristics of the tweek [ 161.

It has been known that the whistler observed on January 5 has a downward transmission point in the ionosphere in the zenith of Zhanjiang and arrives with a right-handed circular polarization [ 101.

(3) The arriving directions of the whistler itself and the whisker are almost identical. This direction is toward Zhanjiang from Wuchang.

(4) The whisker observed by the sonogram was observed only in Wuchang and was not in Zhanjiang and Guilin, which is about 500 km from Zhanjiang.

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From the observations and analysis results of the foregoing, the whisker part of the whistler near the cutoff frequency observed in the sonogram was clearly generated during the propagation from Zhanjiang to Wuchang over 1000 km in the form of a waveguide mode. Hence, its propagation characteristics are identical to the wave dynamic characteristics of the tweek [16].

The lightning discharge has a wide radiation angle and generates many modes from the Oth, lst, 2nd, .-, modes easily. By the long-distance propagation, the tweek is generated. However, it has been considered that there is no overlapping of the trapping cone along other magnetic lines of force and the transmission cone trans- mitting downward in the ionosphere in the whistler which propagates through the duct at very low latitude [3]. However, recently, the duct propagation perpendicularly falling down in the ionosphere has been analyzed by Nakamura [201. In general, it is not clear why the very low latitude whistler transmitting downward in the iono- sphere with a narrow exit angle can have a cutoff fre- quency of the waveguide mode.

According to Shimakura et al. [6], the requirements for the whistler to have the first- and second-order cutoff characteristics are:

(1) the intensity of the whistler itself is strong,

exit angle to generate the Oth-order mode depending on the slope of the ionosphere, the propagation distance is only 1000 km. Further, due to the condition that no slope of the ionosphere by geomagnetic disturbance and the equatorial anomaly exist, the whisker part of the whistler indicating the waveguide mode propagation was not very long.

In the observation results of the whstler observed at a very low latitude, it is transmitted downward almost vertically in the ionosphere [ 10, 111. It is necessary to study why these whistlers become a waveguide propaga- tion exhibiting the first-, second-, and thrd-cutoff char- acteristics.

The overall research on the whistler, tweek, and waveguide propagation effects of this whistler is consid- ered to provide an interesting clue for the understanding of the VLF electromagnetic wave propagation from the magnetosphere to the ionosphere and in the region be- tween the ionosphere and the ground.

Acknowledgement. The work reported here has been supported by a research grant for collaboration with Nagoya University, Solar Terrestrial Environment Labo- ratory. The authors thank Dr. Y. Tanaka and Dr. M. Nishino. They also acknowledge the guidance by Prof. H. Eguchi and Prof. 0. Mikami of Chubu University.

(2) the exit angle of the downward transmission in the ionosphere is large,

REFERENCES (3) the propagation energy is concentrated in the

limited azimuth angles, and

(4) the propagation distance of the waveguide mode is large.

More than 10 percent of the whistlers transmitted downward from zenith of Zhanjiang is accompanied by echo train whistler [7], which suggest the existence of an extremely stable duct. This means a good propagation condition by the duct, and it indicates a propagation to- ward higher latitudes. Therefore, the whistler with a strong intensity concentrates its propagation energy in the direction of Wuchang toward higher latitude. Due to the downward transmission in the ionosphere, whistlers with the cutoff characteristics of the extremely rare second- and third-waveguide mode propagations were observed.

In comparison with the observation example by Shmakura et al. [6] in which the distance of the wave- guide mode propagation exceeds 3000 km and the wide

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AUTHORS

Kenji Ohta received his B.E. degree from the Department of Communication Engineering, Shinshu University, in 1966 and his Dr. of Eng. degree later. In 1966, he became a Research Associate at Chubu Institute of Technology. Since then, he has been engaged in development of sferic observation equipment, particularly automatic observation equipment for the whistler, and signal analysis. Presently, he is a Professor at Chubu University. He is a member of the Japan Atmospheric Electricity Society. He received an Award from the Japan Atmospheric Electricity Society in 1991.

89

AUTHORS (from left to right)

Akio Shimizu received his B.E. degree from the Department of Electronic Engineering, Chubu University, in 1991 and is presently in the graduate program. He is engaged in research on waveguide mode propagation effect of very low latitude whistlers.

Masashi Hayakawa received his B.E. and M.S. degrees in 1966 and 1968, respectively, from Department of Electrical Engineering, Nagoya University, his Dr. of Eng. degree later. In 1970, he became a Research Associate at Nagoya University, Research Institute of Atmospherics. In 1979, he became an Associate Professor. In 1991, he became a Professor at the University of Electro-Communications. In 1975-76, he was on leave at the University of Sheffield in the United Kingdom and in 1980-81, he was a Visiting Professor at Laboratoire de Physique de 1’Environnements in France. He has been engaged in observational and theoretical studies on the propagation and generation mechanisms of space plasma waves. Recently, he has been carrying out research on interactions between wave and particle and between wave and wave as well as the earthquake prediction by means of the electromagnetic waves. He is a member of the Earth Electromagnetics-Earth Planetary Society and the Japan Atmospheric Electricity Society. He received a Tanakadate Award from Japan Earth Electromagnetic Society in 1983 and an Award from Japan Atmospheric Electricity Society in 1989.

Shin Shimakura received his B.E. and M.S. degrees in 1968 and 1970, respectively, from the Department of Electrical Engineering, Kanazawa University, and his Dr. of Eng. degree in 1973 from Nagoya University, In that year, he became a Research Fellow under the Academic Promotion Fund. In 1974, he became a Research Associate at the Faculty of Engineering, Chiba University. At present, he is a Professor in the Department of Electrical and Electronic Engineering. He has been engaged in research on generation and propagation of plasma waves in magnetospheric and ionospheric plasma, especially the signal analysis of the VLF/ULF waves, measurement of the direction of arrival and estimation of the wave energy distribution. He is a member of Earth Electromagnetic-Earth Planetary Society and Japan Atmospheric Electricity Society. In 1989, he received an Award from the Japan Atmospheric Electricity Society.

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