Electronics and Communications in Japan, Part 1, Vol. 76, No. 7, 1993 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. 75-B-11, No. 6, May 1992, pp. 309-314

Propagation Characteristics of Very Low Latitude Whistlers by Ray Tracing

Kenji Ohta, Member, Tooru Tomomatsu, and Osamu Takahashi, Nonmembers

Faculty of Engineering, Chubu University, Kasugai, Japan 487

Masashi Hayakawa, Member

Faculty of Electro-Communications, The University of Electro-Communications, Chofu, Japan 182

SUMMARY

Simultaneous measurement made in South China in January 1988 has already indicated that the nighttime whistlers observed at very low latitudes (geomagnetic latitudes, 10" to 14") are attributed to field-aligned propa- gation. On the other hand, a few researchers have suggested, based on the ray-tracing computations, that nighttime whistlers at very low latitudes are due to nonducted pro- pagation.

To solve the discrepancy between the authors' experimental results and the previous ray-tracing studies, extensive two-dimensional ray-tracing calculations have been made for the nonducted propagation of whistlers in the innerplasmasphere in a wide frequency range (1 to 10 kHz). The conditions for nonducted whistlers to penetrate through the ionosphere onto the ground have been discussed to clarify the difference from the experimental results reported here.

Key words: Whistler: ray tracing: very low latitude: nonducted propagation.

1. Introduction

There are two different types of propagation of

whistlers in the magnetosphere: the propagation trapped by field-aligned ducts, and the nonducted propagation based solely on Snell's law [l]. The ray paths of nonducted whistlers are known to deviate from the magnetic field lines. Also, their wave normals in the opposite hemisphere are directedoutward so that they are unable topenetrate through the ionosphere onto the ground [2,3]. Further, the non- ducted whistlers do not follow the same propagation path, so it is very difficult to explain echo-train whistlers by means of nonducted propagation.

Thus it is concluded that the ground-based whistlers observed at high and lower latitudes are attributed to the propagation trapped in field-aligned ducts [4,5]. By con- trast, the enhancement factor for ordinary ducts to trap whistlers at very low latitudes is required to be much more than 100 percent, and this kind of high enhancement factor seems to be very unrealistic [6].

As a result, the propagation mechanism of very low latitude whisuers has recently been studied by several researchers. In 1979, Ondoh et al. concluded that the whistlers at the geomagnetic latitude of 15.3' are attributed to ducted propagation as a result of observing a considerable number of echo-train whistlers at Okinawa. Furthermore, they estimated the lowest latitude cutoff of ground-based

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whistlers tobe 12.9" basedon the simultaneousobservations at multistations, including Ishigaki Island [71.

On the other hand, Liang et al. made the multista- tion network observations in South China and found that whistlers are detected during the nighttime even at the geomagnetic latitude of 5.5". Also, they concluded that there exists a favorable nonducted propagation channel at -10" [81.

The ray-tracing computations by Andrews [9,101 and Thomson [l 11 supported such a nonducted channel at about 10". These authors used the two-dimensional ray-tracing, while Liang et al. used the 3-dimensional ray-tracing, including the realistic ionospheric profile with equatorial anomaly. Although they studied the propagation paths in the magnetosphere over a wide frequency range, no extensive study of the ionospheric transmission condition has been undertaken.

We conducted the observations at the three stations in South China-Zhanjiang (geomag. lat. 10.0" N), Guilin (14.1" N), and Wuchang (19.4" N)-covering the latitude range from 10" to 20" N during the period of the 5th and 1 lth of January 1988. This spaced direction-findmg mea- surement has shown that there exists a stable geomagnetic latitude for ionospheric penetration of whistlers, no frequency dependence on the ionospheric exit regidn, and

strong tendency for those whistlers to propyte towarc! higher latitudes after the ionospheric transmission. It also was suggested that nighttime whistlers taking place at the geomagnetic latitudes of 10" to 14" are due to the field- aligned propagation [12].

To solve the discrepancy between these experimental facts and the previous ray-tracing results, we investigated in detail the propagation characteristics and ionospheric transmission characteristics of nonducted whistlers in the inner plasmasphere over a wide frequency range (1 to 10 kHz) on the basis of two-dimensional ray-tracing compu- tations. This 2-dimensional ray tracing provides information on the propagation path and wave normal direction as functionsof height and latitude. The dipole model is adopted for the earth's magnetic field.

2. Ionospheric Model

2ooo/ Parameters at 1 0 0 0 ~ €1 ect ron

Electron Density 3350 (/cm3)

Temperature 980 ( O K )

O+ 10 ( X I

The ionospheric model used in the ray-tracings is based on the diffusive equilibrium model by assuming the ion composition and temperature at the reference height of lo00 km. The lower end of the ionosphere is assumed to be 100 km, and the electron density at the reference height (lo00 km) is taken as 3 x 10' cm-3 by using the average value offoF, observed at Okinawa (geomag. lat. 15"). Also, the ion composition at the reference height is taken as the

100 10' lo2 103 lo4 lo5 lo6 lo7

t 0-

Electron Density ( /cm3) Fig. 1. Profile of background magnetospheric electron density.

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Incident Wave

; / Medium 1

n l

fi Medium 2 Transmitted n2

Wave

Fig. 2. Relationship between incident and transmitted waves.

or not the downgoing whistler penetrates through the ion- osphere [13]. The refractive index for the whistler-mode wave is given by

n v

(2 )

where X and Y are ordinary plasma parameters and are expressed by

Y = fM/f (4)

Here, 4 is the electron plasma frequency, fH is the electron gyrofrequency, and f is the wave frequency; f p and fH are given by the following:

(6) Ro3 same as Andrews such that H': 80percent; He+: 10 percent: 0': 10 percent. The electron temperature is changed widely from 900 to 1050" K to examine the effect of the gradient of ionospheric profile on the ray-tracing results. Figure 1 illustrates an example of the ionospheric profile with T, = 980" K.

f i ~ = J ~ ~ ~ p ( 1 + 3 sin' @ > I "

In Eqs. (5) and (6) the parameters are expressed as follows:

: electrondensityat the position ofcomputation. N cm-':

m : electron mass (= 9.1 1 x kg); 3. Ray-Tracing Computation e : electronic charge (= 1.602 x Q):

E, : dielectric constant of free space (= 8.854 x

fHc, : electron gyrofrequency on the ground at the equator (= 880 ICHZ):

R, : Earth's radius (= 6372 km): R : geocentric distance (km): and 8 : geomagnetic latitude (deg).

F/m); We have assumed that the wave normal of the incident whistler in one hemisphere is vertically upward at the height of 100 km. Whether the wave propagated to the opposite hemisphere is able to penetrate through the iono- sphere is determined by the analysis of wave normal direction there by means of Snell's law. On the assumption that the incident angle in the medium 1 is il and the transmitted angle in the medium 2 is i,, Snell's law gives the following equation with the corresponding refractive indices n, and n2:

s in i~ - nz sin i~ 121

4. Computational Results of Nonducted Propagation

where n, is the refractive index at the height where the ray tracing is terminated. The transmission cone is evaluated by putting i2 = 90" and n2 = 1, and whether or not the final wave normal is within the transmission cone, determines whether

Figure 3 illustrates the relationshipbetween the input and final latitudes at 5 kHz for the ionospheric model with T,=990°K. It is seen from this figure that the good conjugacy is observed for the input latitudes of 10.2" S and

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15.0" S , and the final wave normal directions for these two cases are found to direct vertically downward so that they lie within the transmission cone tobe detected on the ground.

Figure 4 shows the ray path of a whistler started at the input latitude of 10.2" S. As the result of analyses of the ray paths and the corresponding wave normal directions in a wide frequency range from 1 to 10 kHz with a step of 0.1 kHz, the waves with the frequency ranges 1.1 to 1.3 kHz, 7.4 to 8.9 kHz and 9.7 to 9.9 kHz are found to be reflected totally and to be unable to penetrate through the ionosphere onto the ground. By contrast, the whistlers observed in South China in 1988 [ 121 have the frequency components in a wide range from I to 8 kHz, and thus the foregoing computational results seem to contradict our observational facts.

Table 1 shows the frequency variation of the dis- persion and ionospheric penetration latitude. These values are deduced from the values in the height range of 101 k 1 km. The whistler dispersion D is given by Eq. (7) as a function of delay time I (s) and wave frequencyf(Hz)

Table 1 also indicates that the dispersion has a tendency to increase with the increase of wave frequency. Also, it is found that the ionospheric transmission latitude shifts toward higher latitude with increasing frequency such that the deviation in latitude over the frequency range of 1 to 8 ldIz is about 15 km. In contradiction with this theoretical prediction, the ionospheric exit points did not show any frequency dependence.

4O"N

-0 Q, 30" 3 u u .C(

2: 20"N - (D c u. .M

10"

0 ,

I I

lo's 20's 30"s I n i t i a l Latitude

Fig. 3. Relationship between input and final latitude at 5 kHz.

We summarize the ray-tracing computational results as follows.

(1) The ground reception of nonducted whistlers seems to be restricted to mine frequency bands.

(2) The dispersion value increases with increasing frequency.

(3)The ionospheric exit point seems to shift to higher latitudes.

Table 1. Relationships between frequency, dispersion, and ionic transmission latitude

6.9 100.72 14.46 10.22

9.2 101.50 14.63 10.23 ~____ ______

*Asterisk indicates that transmission through ionosphere did not occur.

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Altitude (km) 1500

/ -- -ITooi MFne t i c F i e 1 d Line

\ /

/ t

/

- _ - - _ 0"

lo" Geomagnetic Latitude 10's

LV - - : Wave Normal D1 rectlon

\

\

\ \

Fig. 4. The ray path of a whistler which can be transmitted through the ionosphere in the northern hemisphere (5 Wz).

11.(

2 10.1 Y

aJ '0 3 w w .d

2 10.1 U

w aJ c 0

.4

g 9.1 aJ W

9.(

* I

I " I I I 1 00 950 1000 1051

Electron Temperature ( O K )

Fig. 5. Relationship between electron temperature and geomagnetic latitude of transmitted wave.

These theoretical results are also valid for another input latitude of 15" for which we expect a good conjugate propagation and we had the same tendency for varying the electron temperature.

We also have investigated the variation of the final geomagnetic latitude with the electron temperature, and Fig. 5 is the result. The deviation in the final geomagnetic latitude is the corresponding variation by varying the fre- quency. The initial latitude is set to be conjugate for that electron temperature. From this figure, the ionospheric exit

point moves toward higher latitudes with the increase of electron temperature, and when the conjugate propagation is possible at the geomagnetic latitude of loo, the electron temperature is found to be about 960" K.

5. Conclusions

Two-dimensional ray-tracing computations of non- ducted whistlers have been made to investigate whether or not the ground-based whistlers at very low latitudes are propagated along magnetic field lines. To compare the present theoretical results with our previous experimental results in South China, we must consider the more realistic model for the earth's magnetic field such as the IGRF model instead of the dipole model used here.

Ondoh et al. [7] have estimated that the apex of the magnetic field line of IGRF passing through the geomag- netic latitude of 15" in 1 10" E of the Chinese meridian plane is about 250 km above that of the dipole model. However. since the real magnetic field can be well approximated by the corresponding dipole model by taking into account its apex height, the present computations are valid.

When the ionospheric density profile is changed as in Fig. 5, the ionospheric exit latitude and propagation channel may change so that the direct comparison of these with our previous experimental results is not so important.

In this paper, we wanted to point out the presence of two propagation channels, and the detailed considerations of the ionospheric transmission possibility are important for comparison with the observations.

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By comparison with our previous spaced measure- ment made in South China by means of the field-analysis direction finding, the following discrepancies are elucidated from the present study:

1. While the observed whistlers have their frequency components from 1 to 8 kHz, nonducted whistlers cannot penetrate through the ionosphere at the frequency below 2.5 kHz.

2. While the ionospheric exit points of observed whistlers exhibit no frequency dependence, the nonducted whistlers are found to have a tendency to shift to higher latitudes with the increase of frequency.

On the basis of the discrepancies from the observed facts, the whistlers at very low latitudes (geomag. lat.. 10" to 14") in South China are not considered to be due to nonducted propagation, and the propagation by field- aligned irregularities proposed by Hayakawa et al. is highly probable [ 141.

If we assume the ordinary ducted propagation, the enhancement factor necessary for trapping whistlers at very low latitudes is more than 100 percent. However. such an enhancement factor is never observed. Furthermore, the comparison of nighttime whistlers with the electron density profile observed by satellites indicates only the enhance- ment factor of the order of 10 percent [15] for nighttime whistlers. Hence. the propagation mechanism ot very low latitude whistlers requires further investigation, in- cluding different kinds of possible mechanisms such as whispering-gallery mode [ 161.

As future problems, further ray-tracing studies are required based on the IGRF magnetic field model.

Acknowledgement. The authors are grateful to Dr. K. Baba of Chubu University and Dr. K. Hatton of Nagoya University for their suggestions on the ray-tracing compu- tations. Thanks are also due to Dr. S. Shimakura of Chuba University for his useful comments and to Prof. H. Eguchi and Prof. 0. Mikami of Chubu University for their support. The equipment used in the analyses of this paper is based on the financial support of private institutions. and the authors thank Prof. K. Sasaki of Chubu University.

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R.A. Helliwell. Whistlers and Related Ionospheric Phenomena, pp. 43-51, Stanford Univ. Press. CA ( 1965). K. Maedaand 1. Kiinura. Calculation of the propagation

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M. Hasegawa, M. Hayakawa, and J. Ohtsu. On the conditions of duct trapping of low-latitude whistlers. Ann. Geophs., 4, pp. 317-324 (1978). T. Ondoh, M. Kotani. T. Murakami, S. Watanabe, and Y. Nakamura. Propagation characteristics of low- latitude whistlers. J. Geophys. Res., 84, pp. 2097-2 104 (1979). B.X. Liang, T. Bao. and J.S. Xu. Propagation charac- teristics of nighttirne whistlers in the region of equa- torial anomaly. J. Atmosph. Terr. Phys., 47,999- 1007 (1985). M.K. Andrews. Nonducted whistler-mode signals at low latitudes. J. Atmosph. Terr. Phys.. 40, pp. 429-436 (1978).

Phys., 15, pp. 62-65 (1959).

35, pp. 1685-1619 (1973).

10. M.K. Andrews. On whistlers with very small disper- sion. J. Atmosph. Terr. Phys., 41. pp. 231-235 (1979).

11. N.R. Thornson. Ray-tracing the paths of very low latitude whistler-mode signals. J. Atmosph. Terr. Phys.,

12. K. Ohta, M. Hayakawa, S. Shimakura, and H. Eguchi. Determination of the direction of origin of very low latitude noctural whistlers in China by simultaneous multipoint measurements. IEICEJ J73-B-II, 4, pp.

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AUTHORS (from left to right)

Kenji Ohta graduated in 1966 from the Dept. of Comms., Faculty of Eng., Shinshu Univ. and k a m e Research Associate of Chubu Univ. the same year, He also has a Dr. of Eng. degree. He has been engaged for a long time in the development of the observing equipment for spherics and whistlers and also in signal processing. At present, he is Associate Professor at Chubu Univ. and is a member of the Society of Atmospheric Electricity of Japan. He received an award from the society.

Tooru Tomomatsu graduated in 1989 from Chubu Univ., where he obtained a master’s degree in 1991. He is currently with Kawasaki Heavy Industries. As a graduate student he worked on the propagation of very lowlatitude whistlers.

Osamu Takahashi graduated in 1990 from Chubu Univ. and entered the master’s program. He has been engaged in research on propagation of VLF waves in the magnetosphere. After obtaining a master’s degree. he joined SONY company.

Mashashi Hayakawa graduated in 1966 from Nagoya Univ., where he obtained a master’s degrees in 1968. In 1970 he obtaineda Dr. of Eng. degreeand becameResearch Assdiateof the Research Institute of Atmospherics, Nagoya Univ., Associate Professor in 1979, and Professor at the Univ. of Electro-Communications in 1990. He was Visiting Lecturer at Sheffield Univ.. UK, during 1975- 1976 and Visiting Professor of CRPE, Orleans, France in 1980- 1981. He has been working on the observational and theoretical study on the generation and propagation of plasma waves in the magnetosphere and ionosphere. Recently. he has been engaged in the study of wave-particle and wave-wave interactions based on the direction finding on board satellites. He is a member of the Japan Society of Geomagnetism and Geoelectricity and of the Society of Atmospheric Electricity of Japan. In 1983 he was awarded the Tanakadae Prize, and in 1989 the Society Award of the Atmospheric Electric Society.

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