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On the longitudinal effect in whistler propagation characteristics at low latitudes
0032-0633/88 $3.00+0.00 Pergamm Presspk
Pturef.Spruce Sci., Vol. 36, No. 8, pp. 83ti39.1988 printedin Great Britain.
ON THE LONGITUDINAL EFFECT IN WHISTLER PROPAGATION CHARA~ERISTICS AT LOW LATITUDES H. B. ZHOU*
stud J. S. XU
Department of Space Physics, Wuhan University, Wuchang, Hubei, The People’s Republic of China
M. HAYAKAWA
Research Institute of Atmospherics, Nagoya University, Toyokawa, Aicbi 442, Japan
Ah&act-In order to investigate the propagation mechanism of low-latitude whistlers below the geomagnetic latitude of about 20”, we have performed the three-dimensional ray-tracing computations of whistler propagation for the very realistic lower exosphere model including the latitudinal and longitudinal variations as representing the recent satellite measurements of electron and ion compositions. A special emphasis is directed to the longitude effect ; that is, the comparison of propagation characteristics in the Chinese and Japanese meridian planes. It is found that there is a cross-over geographic ktitude of 28” (geomagnetic latitude N 18”) over a few degrees below which the ionospheric transmission condition of downgoing whistlers in the Northern Hemisphere is easily satisfied in the Chinese meridian plane (geographic longitude, 114”E) and above which the Japanese meridian plane (13O”E) is more suitable for the ionospheric transmission. This longitudinal asymmetry is found to result from the combined effect of the difference in the negative latitude gradient of the electron density in those two meridian planes and the longitude gradient. We present an observational example of the comparison of the occurrence rate of night-time whistlers at Wuchang (geographic coordinates 30.SQN, 114.6”E; geomagnetic latitude 19.3%) and Kagoshima (31.5”N, 130.8%; 20.5”N), which seems to be consistent with the above theoretical prediction.
1. INTRODUCI’ION
As reviewed comprehensively by Hayakawa and Tanaka (1978), the propagation characteristics of whistlers in the geomagnetic latitude (A) range above 20” are considerably well understood. However, Hayakawa and Tanaka have indicated that the whistler propagation mechanism at A < 20” is very poorly understood and have suggested the importance of the study of equatorial whistlers in the general whistler propagation studies. The latitudinal variations of whistler characteristics such as the occurrence rate, dispersion etc. have already been investigated (Helliwell, 1965 ; Hayakawa and Ohtsu, 1973 ; Hayakawa and Tanaka, 1978; Liang et al., 1985), and found to be invaluable in the general whistler studies. Additionally, the longitudinal variation of propagation characteristics seems to be useful in the study of whistlers. However, very few reports have been published on this subject ; see Singh and Singh (1979) and Tanaka and Hayakawa (1980). Some obser-
* Now at the Research Centre of Space Science and Technology, Academia Sinica, Beijing, China.
vationai results by these authors have indicated that there exists a longitudinal effect of propagation characteristics of low-latitude (A = 20”-25”) daytime whistlers from the comparison between Japanese and Indian stations. Tanaka and Hayakawa (1980) have attributed this longitudinal difference to the different source activity at the conjugate region of each station, while Singh and Singh (1979) have studied this effect in a different way by assuming a non-ducted propagation in the lower exosphere including the equatorial anomaly. On the other hand, at high latitudes, Denby et al. (1980 ) have discussed a cross meridian refraction of whistler propagation in the magnetosphere including the longitudinal density gradient. In this paper we first study the lon~tudinal effect of whistler propagation properties in the Chinese and Japanese meridian planes on the basis of ray-tracing computations of non-ducted propagation for the realistic night-time density models at these two meridian planes as deduced from recent satellite density measurements. Different factors in the longitude effect of electron density are dealt with separately in order to find the relative importance of each factor in the combined influence of all factors on the whistler 833
H.
834
B. ZHOU
propagation characteristics. Finally, we show an observational result of occurrence rates at nearly the same geomagnetic latitude (A = 19°-200) in these Chinese and Japanese meridians, which is to be compared with the theoretical prediction.
2. THREE-DIMENSIONAL DUCTED
PROPAGATION
RAY TRACING
OF NON-
AND THE MODELS
OF
THE LOWER EXOSPHERE
As opposed to previous works, we have used, in this paper, the three-dimensional ray tracing computations (Cairo and Lefeuvre, 1985 ; Muto et al., 1987) as described in Liang et al. (1985). Firstly, the IGRF (1980) model (Peddie, 1982) is employed for the geomagnetic field, instead of the simple dipole field, because the configuration of real fields is considerably modified from the dipole model in our meridian planes (Ondoh et al., 1979). A difficulty of raytracings in a non-dipole field is due to the dependence on magnetic field lines of the electron concentration, e.g. diffusive equilibrium distribution along field lines, and the general treatment for this situation demands too much elaboration. So, in this paper, we have adopted a simplified treatment, assuming that the distribution of electron concentration is spherically stratified and includes the latitudinal and longitudinal variations. The density model to be used in ray-tracings is based on the recent density measurements by the IXS-b satellite (Miyazaki et al., 1982) during the period October 1978-March 1979. As we will be concerned with the night-time observation of whistlers in the Chinese and Japanese meridian planes, we have used the corresponding night-time (L.T. = 22-24 h) data. The electron density, the ion compositions (O+, He+ and H+ ions) and the temperature, which are the key parameters in determining the profile of the diffusive equilibrium model (Angerami and Thomas, 1964) have been measured by this satellite, which has also provided us with the latitudinal and longitudinal effects. The electron density distribution can be described by the following general form N,(r, 0, rp) = No&)
x N0 x NL
(1)
with the effect of the lower ionosphere also included as modelled in Kimura (1966). The background profile is the diffusive equilibrium model, N&r) (r : geocentric distance) (Angerami and Thomas, 1964) and f3and rp are the geographic colatitude and longitude, respectively. The factor N, represents the negative latitude gradient which is symmetrical about the equator and which can be given by
et al.
N0 = l.O+C(r)exp{cr(sin@-sinfIt,)},
(2)
where C(r), a and sin& are the parameters which control the magnitude and distribution range of the latitudinal ionization gradient as modelled by Singh (1976). These parameters are also found to differ at the Chinese and Japanese meridian planes (Miyazaki et al., 1982). A similar kind of model to equation (2) is used by Thomson (1987). Then, the factor NL represents the E-W asymmetrical distribution of densities (or the longitudinal gradient), which can be expressed by NL = l.O+LG
x (7r/l80) x (rp-cp,),
(3)
where LG is the rate of E-W asymmetry (or longitudinal gradient) and p0 is the reference longitude (i.e. qpo=
3. COMPUTATIONAL WHISTLER
RESULTS
OF NON-DIJCI’ED
PROPAGATION
The three-dimensional ray-tracing computations of non-ducted whistler propagation for the model exosphere as described in Table 1 have been performed at a wave frequency of 5 kHz. The ray-tracing is started and stopped at an altitude of 120 km. Figure 1 illustrates the computational results in the form of the final wave normal direction as a function of the final geographic latitude. The final wave normal angle 16) is defined as the absolute angle between the wave normal direction at the final latitude and the vertical downward direction, and so 6 = 0” indicates the final wave normal being directed vertically downward. We find from the figure that there is a significant difference in the propagation features at the Chinese (114”E) and Japanese (130”E) meridian planes and the general characteristic is approximately symmetrical about the cross-over geographical latitude of 28”N (A N 18”).
835
Whistler propagation at low latitudes TABLE 1. THE ELECTRON DENSITY MODEL MOST APPROPRIATE FOR THE SATELLITE DENSITY MEAsuREMENT,INCLUDINGTHELATIlWDINALANDU)NGIWDINALEFFECTS
JL(~-‘) atRbasc
Longitude 114”E (Chinese meridian) 130”E (Japanese)
T,(K)
C
a
1.0 x lo5
1200
0.5
8.0 x 104
1200
0.5
5
sin@, LG 0.94
1.0
15 0.96
1.0
/’
\ : -
\
1 \
0+ = 98.85% He+ = 1.1% H+ = 0.05% at R,, = 6872km
,/114”E \ \
’\
‘\ ’
I 20
\
\
130’E /c rH
// ‘\ -\ \
I 22
\
\
_: \
\
/
\
1’
/
\
\ -__?*\\ I I I 24 26 28 Final
/I
/’ ,/’
N./ 30
Geographic
32
I 34
I 36
I 38 ’
I
Latitude
FIG. ~.~~ERAY-TRACINGCOMPUTA~ONALRESULTFORNON-DUCTEDPROPAGATIONFORTHEMOSTREALISTIC MODELASGIVENINTABLE 1.
The wave normal angle at the final geographic latitude is plotted at the Chinese and Japanese meridian planes. Below the cross-over latitude the final wave normal angle 1st is much smaller at 114”E meridian than at 130”E meridian such that whistlers in the 114” meridian at these geographic latitudes are able to penetrate through the ionosphere onto the ground, as theoretically suggested by Helliwell (1965) and later experimentally confirmed by Hayakawa and Iwai (1975). A few degrees around the geographic latitude of 26” in the Chinese meridian is the range where the ionospheric transmission condition is well fulfilled. On the other hand, the final wave normal directions of whistlers at geographic latitudes less than the crossover latitude seem to be located outside the transmission cone in the Japanese meridian plane, being unable to transmit the ionosphere onto the ground. Above the cross-over latitude, the situation is completely reversed such that the ionospheric penetration condition is much more easily fulfilled in the Japanese meridian plane, and the range of a few degrees around the geographic latitude of 30” is the channel of ground reception. Further, the computed dispersion value around the cross-over latitude is not inconsistent with the observed value. In these calculations we have to add that the deviation of ray paths from the initial
magnetic meridian plane is very small, of the order of less than 2.0”. In the computations of Fig. 1, all the factors including the longitude difference of negative latitude gradients and the longitude variation of electron density are taken into account altogether. In order to understand the relative importance of each factor in the density model (Table I), we first investigate the EastWest asymmetrical effect of the negative latitude gradient of electron density, that is, the different latitudinal variations at the two meridian planes of China and Japan. Table 2 indicates the model for which we adopt the different latitudinal variations of the negative latitude gradient at those two meridians with other factors being neglected [i.e. NL = 1.0 (or LG = O.O)]. The computation result is illustrated in Fig. 2 in the same format as in Fig. 1. Next, the effect of the longitudinal gradient of density is separately treated in Fig. 3, with no latitudinal effect (C = 0.0 or NB = 1.0) as given in Table 3. In Figs 2 and 3 the real magnetic field is automatically included. So, finally the effect of the geomagnetic field is only considered in Fig. 4, in which the same electron density without any latitudinal and
836
m~-31
at Rbass = 6872 km
Longitude
T(K)
C
a
114’E
1.0 x IO5
1200 0.5
130”E
1.0 x lo5
1200 0.5
sin@,
5
O+ = 98.85% He+ = 1.1% H+ = 0.05%
0.94
15 0.94
R&=&2
km
114”E !
0
20
22
24
26
Final
28
30
C&graphic
32
34
36
38
4o”
Latitude
FIG. 2. THE CXXPUTATIONAL RESULT FOR THE MODEL IN TABLE ~,INCLUDING DIPPeReNcEIN~NEGATIVELAnTUDEGRADIENTINTHE~ANDJ~~~~S.
ONLY THE UJNGITWINAL
Al4’E I I I ;
20
22
24
26 FM1
FIG. 3. THE ~~~A~ONAL
28
32
34
36
38*
Geographic Latitude
RESULT FOR THE MODEL ~NG~~ALG~~OF~D~~.
longitudinal effects [C = O.O(NB= 1.0) and LG = O.O(N, = 1.0) in Table 31 is assumed at the two meridians. Even for the same electron density profile in Fig. 4, the propagation characteristics become con-
30
130’E
IN TABLE
3,
TAKING
mm
ACCXXJNT ONLY
siderably asymmetrical at the of the non-dipole effect of the cross-over geographic latitude 23”, which seems to be shifted
THE
two meridians because geomagnetic field. The in Fig. 4 is located at by about 5” compared
837
Whistler propagation at low latitudes TABLE 3. Trrs PARAME TERS OF THE MODEL To STUDY THE EASTWESTASYMMETRICALDISTRIBLITION,WITHOuTANYLATITLJDlNALEF'FECT (No = 1.0)
Longitude
N,,,(cn-3)
T(K)
LG
C 0+ = 98.85% He+ = 1.1% H+ = 0.05% at R ,._= 6872 km
114”E 1200
1.0 x IO5
2.0
0.0
130”E
4
Ii\
1 \ \ T
114”E
20” -
-
\ t 3 2
5
\\
/
’
/
\ ‘\ 1, ‘V”\ ,/’
-
I& 0
I
t
20
22
24
Final FIG. 4. THE COMPUTATIONAL
’ / V’
I
,: ,’
26
I
I
I
I
I
1
28
30
32
34
36
38’
Geographic
Latitude
RESULT FOR THE MODEL INCLUDING ONLY THE EFFECT OF THE NON-DIPOLE GEOMAGNETIC FIELD.
with Figs 1, 2 and 3 and the difference in 161 at the two meridians is considerably large. Then we make a comparison of the results in Figs 1,2 and 3. It is easily seen that the two separate effects involved in Figs 2 and 3 play completely opposite roles in the resultant Fig. 1. For example, the cross-over geographic latitude in Fig. 2 is located nearly at the same latitude as in Fig. 1, while that in Fig. 3 is about 2” below the cross-over latitude in Fig. 1. A comparison of Fig. 1 with Figs 2 and 3 indicates that the factor associated with Fig. 2 (i.e. the difference of negative latitude gradient in the Chinese and Japanese meridian planes) has the effect of enhancing the difference in 161in those two meridians, while the longitude gradient as dealt with separately in Fig. 3 considerably reduces the difference in 161in the two meridians. Then, we have the moderate difference in 161as in Fig. 1 as the joint combination of Figs 2 and 3. Hence we can conclude that the final Fig. 1 is the consequence of the two important factors (the difference of the negative latitude gradients in the Chinese and Japanese meridians and the longitude gradient) and that the former effect
seems slightly more influential than the latter effect. The geomagnetic field seems to play a rather minor role. In the above calculations, we implicitly assume that a strong difference in the source activity of thunderstorms in the Southern Hemisphere in the Chinese and Japanese meridian planes does not exist, and we assume that the propagation characteristics are much more influential than the source effect, as suggested by Hayakawa and Tanaka (1978). 4. OBSERVATIONAL
RESULT
OF THE LONGITUDE
EFFECT IN WHJSTLER OCCURRENCE WUCHANG
RATE AT
AND KAGOSHIMA
To make a comparison with the theoretical raytracing implications in Section 3, we have investigated the variation of occurrence rate at the same latitude but separate in longitude, Chinese and Japanese meridian planes. Wuchang (geographic coordinates 30S”N, 114.6”E; geomagnetic latitude 19.3”N) was chosen as a Chinese station, and the corresponding
H.
838
B. ZHOUei al.
(a)
g z
:tIJ 0
4
8
12
16
*'
LT . .
(b)
0
4
8
12
16
2o
L.T.
FIG.S.?~E~NGI~EEFFECT~NTHEDIURNALVARL~T~ONOFOCCUKRENCERATEOFWH~STLERS.
(a) Wuchang and (b) Kagoshima. The observation period is February 1983.
Japanese station is Kagoshima (3 1YN, 130.8”E ; 20.5”N), these two stations being located just around A = 20”. Figure 5 shows the diurnal variations of average occurrence rate at those stations during the observation period of February 1983. As seen from Fig. 5, the whistler activity is only seen in the nighttime hours (L.T. = O-S h) at both stations, without any peak in the evening hours at A 3 25” by Hayakawa and Tanaka (1978). The peak occurrence takes place at L.T. N 5 h at Wuchang and the corresponding peak is found at L.T. N 4 h at Kagoshima. The occurrence is defined as the number of whistlers per minute and it is seen that the occurrence rate at Kagoshima is higher than that at Wuchang, which seems to be in good agreement with the theoretical prediction in Fig. 1 in the previous section. However, the comparison of the occurrence rate requires some caution because of the different antenna and receiver systems at different stations, which is discussed briefly here. The antenna at Wuchang is a rectangular oneturn loop ariel with a baseline of 50 m and a height of 6 m (5’ = 300 m’) and the signals are amplified by about 100 dB, while the one-turn loop antenna at
Kagoshima is located in a valley, forming an inverted triangle with a baseline of 90 m and a depth of 35 m (S = 1575 m2) and then the signals are amplified by 70 dB. Taking into account overall the antenna and receiver systems, we can safely say that the occurrence rate is higher at Kagoshima than at Wuchang. Unfortunately simultaneous data at a lower latitude such as A w 15” from the Chinese and Japanese meridian planes are not available, and so we cannot study whether the comparison of whistler activity at such lower latitudes further supports our theoretical prediction or not. Further investigation on this subject will be required. 5. CONCLUSION
The longitude variations of electron density in the Chinese and Japanese meridian planes have been satisfactorily modelied, and we have performed the threedimensional ray-tracing computations of ray paths for the very realistic density model in order to study the longitude effect of whistler propagation characteristics at lower latitudes. We have found a cross-
m at low latitudes
over geographic latitude of 28”N above which the ionospheric transmission of whistlers is very easily fulfilled in the Japanese but not in the Chinese meridian, and below which we have the reverse situation. Also, it is found that both the difference in negative latitude gradient at those two meridian planes and the longitudinal gradient are equally important in determining the overall propagation characteristics. Hence, as understood from the previous works, the latitudinal variation of whistler properties is very important for the study of whistler propagation mechanism, but we would also like to emphasize the importance of the longitudinal variation of whistler characteristics, especially at low latitudes as studied in this paper. would like to express our sincere thanks to Profs B. X. Liang and Z. T. Bao and other members of the Space Physics Group of Wuhan University, Dr S. Shimakura of Chiba University and Dr K. Ohta of Chubu University for useful discussions. One of the authors (M.H.) is grateful to Dr A. Kimpara, Emeritus Professor of Nagoya University, for his continued encouragement and to Takeda Science Foundation for its financial support to this work. Acknowledgements-We
REFERENCES Angerami, J. J. and Thomas, J. 0. (1964) Studies on planetary atmospheres, 1. The distribution of ions and electrons in the earth’s exosphere. J. geophys. Res. 69,4537. Cairo, L. and Lefeuvre, F. (1985) Localization of sources of ELF/‘VLF hiss observed in the magnetosphere; threedimensional ray tracing. J. geophys. Rex 91,4352. Denby, M., Bullough, K., Alexander, P. D. and Rycroft, M. J. (1980) Observational and theoretical studies of a cross meridian refraction of VLF waves in the ionosphere and magnetosphere. J. atmos. terr. Phys. 42, 51. Hayakawa, M. and Iwai, A. (1975) Magnetospheric ducting
839
of low latitude whistlers as deduced from the rocket measurement of their wave normal directions. J. atmos. terr. Phys. 37, 1211. Hayakawa, M. and Ohtsu, J. (1973) Ducted propagation of low latitude whistlers deduced from the simultaneous observations at multi-stations. J. atmos. terr. phys. 35, 1685. Hayakawa, M. and Tanaka, Y. (1978) On the propagation of low-latitude whistlers. Rev. Geophys. Space Phys. 16, 111. Helliwell, R. A. (1965) Whistlers and Related Ionospheric Phenomena. Stanford University Press, Stanford. Kimura, I. (1966) Effects of ions on whistler mode ray tracing. Radio Sci. 1, 269. Liang, B. X., Bao, Z. T. and Xu, J. S. (1985) Propagation characteristics of nighttime whistlers in the region of equatorial anomaly. J. atmos. terr. Phys. 47, 999. Miyazaki, S., Iwamoto, I., Sagawa, E. and Mori, H. (1982) Global features of the topside ionospheric parameters obtained from the ISS-b observations: COSTAR Symp. on Results from ZMS Spacecraft, Ottawa, Canada. Muto, H. and Hatakawai M. (1987) Ray-tracing study of the propagation of whistler-mode VLF emissions with frequency abov:one half the gyrofrequency. Planet. Space Sci. 35, 1397. Ondoh, T., Kotaki, M., Murakami, T., Watanabe, S. and Nakamura. Y. (1979) Pronaaation characteristics of lowlatitude whistlers. J. $eopiysyRes. 84, 2097. Peddie. N. W. (1982) International aeomaanetic reference field’; the third generation. J. Geoma’gn. Gioelect. 34, 309. Singh, B. (1976) On the ground observation of whistlers at low latitudes. J. geophys. Res. 81, 2429. Singh, H. and Singh, B. (1979) Longitudinal variation in the characteristics of low latitude whistlers. Znd. J. Radio Space Phys. 8, 37.
Tanaka, Y. and Hayakawa, M. (1980) Longitudinal effect in the enhancement of daytime whistler activity at low latitudes. Ann. GPophys. 36, 577. Thomson, N. R. (1987) Ray-tracing the paths of very low latitude whistler-mode signals. J. atmos. terr. Phys. 49, 321.
Pturef.Spruce Sci., Vol. 36, No. 8, pp. 83ti39.1988 printedin Great Britain.
ON THE LONGITUDINAL EFFECT IN WHISTLER PROPAGATION CHARA~ERISTICS AT LOW LATITUDES H. B. ZHOU*
stud J. S. XU
Department of Space Physics, Wuhan University, Wuchang, Hubei, The People’s Republic of China
M. HAYAKAWA
Research Institute of Atmospherics, Nagoya University, Toyokawa, Aicbi 442, Japan
Ah&act-In order to investigate the propagation mechanism of low-latitude whistlers below the geomagnetic latitude of about 20”, we have performed the three-dimensional ray-tracing computations of whistler propagation for the very realistic lower exosphere model including the latitudinal and longitudinal variations as representing the recent satellite measurements of electron and ion compositions. A special emphasis is directed to the longitude effect ; that is, the comparison of propagation characteristics in the Chinese and Japanese meridian planes. It is found that there is a cross-over geographic ktitude of 28” (geomagnetic latitude N 18”) over a few degrees below which the ionospheric transmission condition of downgoing whistlers in the Northern Hemisphere is easily satisfied in the Chinese meridian plane (geographic longitude, 114”E) and above which the Japanese meridian plane (13O”E) is more suitable for the ionospheric transmission. This longitudinal asymmetry is found to result from the combined effect of the difference in the negative latitude gradient of the electron density in those two meridian planes and the longitude gradient. We present an observational example of the comparison of the occurrence rate of night-time whistlers at Wuchang (geographic coordinates 30.SQN, 114.6”E; geomagnetic latitude 19.3%) and Kagoshima (31.5”N, 130.8%; 20.5”N), which seems to be consistent with the above theoretical prediction.
1. INTRODUCI’ION
As reviewed comprehensively by Hayakawa and Tanaka (1978), the propagation characteristics of whistlers in the geomagnetic latitude (A) range above 20” are considerably well understood. However, Hayakawa and Tanaka have indicated that the whistler propagation mechanism at A < 20” is very poorly understood and have suggested the importance of the study of equatorial whistlers in the general whistler propagation studies. The latitudinal variations of whistler characteristics such as the occurrence rate, dispersion etc. have already been investigated (Helliwell, 1965 ; Hayakawa and Ohtsu, 1973 ; Hayakawa and Tanaka, 1978; Liang et al., 1985), and found to be invaluable in the general whistler studies. Additionally, the longitudinal variation of propagation characteristics seems to be useful in the study of whistlers. However, very few reports have been published on this subject ; see Singh and Singh (1979) and Tanaka and Hayakawa (1980). Some obser-
* Now at the Research Centre of Space Science and Technology, Academia Sinica, Beijing, China.
vationai results by these authors have indicated that there exists a longitudinal effect of propagation characteristics of low-latitude (A = 20”-25”) daytime whistlers from the comparison between Japanese and Indian stations. Tanaka and Hayakawa (1980) have attributed this longitudinal difference to the different source activity at the conjugate region of each station, while Singh and Singh (1979) have studied this effect in a different way by assuming a non-ducted propagation in the lower exosphere including the equatorial anomaly. On the other hand, at high latitudes, Denby et al. (1980 ) have discussed a cross meridian refraction of whistler propagation in the magnetosphere including the longitudinal density gradient. In this paper we first study the lon~tudinal effect of whistler propagation properties in the Chinese and Japanese meridian planes on the basis of ray-tracing computations of non-ducted propagation for the realistic night-time density models at these two meridian planes as deduced from recent satellite density measurements. Different factors in the longitude effect of electron density are dealt with separately in order to find the relative importance of each factor in the combined influence of all factors on the whistler 833
H.
834
B. ZHOU
propagation characteristics. Finally, we show an observational result of occurrence rates at nearly the same geomagnetic latitude (A = 19°-200) in these Chinese and Japanese meridians, which is to be compared with the theoretical prediction.
2. THREE-DIMENSIONAL DUCTED
PROPAGATION
RAY TRACING
OF NON-
AND THE MODELS
OF
THE LOWER EXOSPHERE
As opposed to previous works, we have used, in this paper, the three-dimensional ray tracing computations (Cairo and Lefeuvre, 1985 ; Muto et al., 1987) as described in Liang et al. (1985). Firstly, the IGRF (1980) model (Peddie, 1982) is employed for the geomagnetic field, instead of the simple dipole field, because the configuration of real fields is considerably modified from the dipole model in our meridian planes (Ondoh et al., 1979). A difficulty of raytracings in a non-dipole field is due to the dependence on magnetic field lines of the electron concentration, e.g. diffusive equilibrium distribution along field lines, and the general treatment for this situation demands too much elaboration. So, in this paper, we have adopted a simplified treatment, assuming that the distribution of electron concentration is spherically stratified and includes the latitudinal and longitudinal variations. The density model to be used in ray-tracings is based on the recent density measurements by the IXS-b satellite (Miyazaki et al., 1982) during the period October 1978-March 1979. As we will be concerned with the night-time observation of whistlers in the Chinese and Japanese meridian planes, we have used the corresponding night-time (L.T. = 22-24 h) data. The electron density, the ion compositions (O+, He+ and H+ ions) and the temperature, which are the key parameters in determining the profile of the diffusive equilibrium model (Angerami and Thomas, 1964) have been measured by this satellite, which has also provided us with the latitudinal and longitudinal effects. The electron density distribution can be described by the following general form N,(r, 0, rp) = No&)
x N0 x NL
(1)
with the effect of the lower ionosphere also included as modelled in Kimura (1966). The background profile is the diffusive equilibrium model, N&r) (r : geocentric distance) (Angerami and Thomas, 1964) and f3and rp are the geographic colatitude and longitude, respectively. The factor N, represents the negative latitude gradient which is symmetrical about the equator and which can be given by
et al.
N0 = l.O+C(r)exp{cr(sin@-sinfIt,)},
(2)
where C(r), a and sin& are the parameters which control the magnitude and distribution range of the latitudinal ionization gradient as modelled by Singh (1976). These parameters are also found to differ at the Chinese and Japanese meridian planes (Miyazaki et al., 1982). A similar kind of model to equation (2) is used by Thomson (1987). Then, the factor NL represents the E-W asymmetrical distribution of densities (or the longitudinal gradient), which can be expressed by NL = l.O+LG
x (7r/l80) x (rp-cp,),
(3)
where LG is the rate of E-W asymmetry (or longitudinal gradient) and p0 is the reference longitude (i.e. qpo=
3. COMPUTATIONAL WHISTLER
RESULTS
OF NON-DIJCI’ED
PROPAGATION
The three-dimensional ray-tracing computations of non-ducted whistler propagation for the model exosphere as described in Table 1 have been performed at a wave frequency of 5 kHz. The ray-tracing is started and stopped at an altitude of 120 km. Figure 1 illustrates the computational results in the form of the final wave normal direction as a function of the final geographic latitude. The final wave normal angle 16) is defined as the absolute angle between the wave normal direction at the final latitude and the vertical downward direction, and so 6 = 0” indicates the final wave normal being directed vertically downward. We find from the figure that there is a significant difference in the propagation features at the Chinese (114”E) and Japanese (130”E) meridian planes and the general characteristic is approximately symmetrical about the cross-over geographical latitude of 28”N (A N 18”).
835
Whistler propagation at low latitudes TABLE 1. THE ELECTRON DENSITY MODEL MOST APPROPRIATE FOR THE SATELLITE DENSITY MEAsuREMENT,INCLUDINGTHELATIlWDINALANDU)NGIWDINALEFFECTS
JL(~-‘) atRbasc
Longitude 114”E (Chinese meridian) 130”E (Japanese)
T,(K)
C
a
1.0 x lo5
1200
0.5
8.0 x 104
1200
0.5
5
sin@, LG 0.94
1.0
15 0.96
1.0
/’
\ : -
\
1 \
0+ = 98.85% He+ = 1.1% H+ = 0.05% at R,, = 6872km
,/114”E \ \
’\
‘\ ’
I 20
\
\
130’E /c rH
// ‘\ -\ \
I 22
\
\
_: \
\
/
\
1’
/
\
\ -__?*\\ I I I 24 26 28 Final
/I
/’ ,/’
N./ 30
Geographic
32
I 34
I 36
I 38 ’
I
Latitude
FIG. ~.~~ERAY-TRACINGCOMPUTA~ONALRESULTFORNON-DUCTEDPROPAGATIONFORTHEMOSTREALISTIC MODELASGIVENINTABLE 1.
The wave normal angle at the final geographic latitude is plotted at the Chinese and Japanese meridian planes. Below the cross-over latitude the final wave normal angle 1st is much smaller at 114”E meridian than at 130”E meridian such that whistlers in the 114” meridian at these geographic latitudes are able to penetrate through the ionosphere onto the ground, as theoretically suggested by Helliwell (1965) and later experimentally confirmed by Hayakawa and Iwai (1975). A few degrees around the geographic latitude of 26” in the Chinese meridian is the range where the ionospheric transmission condition is well fulfilled. On the other hand, the final wave normal directions of whistlers at geographic latitudes less than the crossover latitude seem to be located outside the transmission cone in the Japanese meridian plane, being unable to transmit the ionosphere onto the ground. Above the cross-over latitude, the situation is completely reversed such that the ionospheric penetration condition is much more easily fulfilled in the Japanese meridian plane, and the range of a few degrees around the geographic latitude of 30” is the channel of ground reception. Further, the computed dispersion value around the cross-over latitude is not inconsistent with the observed value. In these calculations we have to add that the deviation of ray paths from the initial
magnetic meridian plane is very small, of the order of less than 2.0”. In the computations of Fig. 1, all the factors including the longitude difference of negative latitude gradients and the longitude variation of electron density are taken into account altogether. In order to understand the relative importance of each factor in the density model (Table I), we first investigate the EastWest asymmetrical effect of the negative latitude gradient of electron density, that is, the different latitudinal variations at the two meridian planes of China and Japan. Table 2 indicates the model for which we adopt the different latitudinal variations of the negative latitude gradient at those two meridians with other factors being neglected [i.e. NL = 1.0 (or LG = O.O)]. The computation result is illustrated in Fig. 2 in the same format as in Fig. 1. Next, the effect of the longitudinal gradient of density is separately treated in Fig. 3, with no latitudinal effect (C = 0.0 or NB = 1.0) as given in Table 3. In Figs 2 and 3 the real magnetic field is automatically included. So, finally the effect of the geomagnetic field is only considered in Fig. 4, in which the same electron density without any latitudinal and
836
m~-31
at Rbass = 6872 km
Longitude
T(K)
C
a
114’E
1.0 x IO5
1200 0.5
130”E
1.0 x lo5
1200 0.5
sin@,
5
O+ = 98.85% He+ = 1.1% H+ = 0.05%
0.94
15 0.94
R&=&2
km
114”E !
0
20
22
24
26
Final
28
30
C&graphic
32
34
36
38
4o”
Latitude
FIG. 2. THE CXXPUTATIONAL RESULT FOR THE MODEL IN TABLE ~,INCLUDING DIPPeReNcEIN~NEGATIVELAnTUDEGRADIENTINTHE~ANDJ~~~~S.
ONLY THE UJNGITWINAL
Al4’E I I I ;
20
22
24
26 FM1
FIG. 3. THE ~~~A~ONAL
28
32
34
36
38*
Geographic Latitude
RESULT FOR THE MODEL ~NG~~ALG~~OF~D~~.
longitudinal effects [C = O.O(NB= 1.0) and LG = O.O(N, = 1.0) in Table 31 is assumed at the two meridians. Even for the same electron density profile in Fig. 4, the propagation characteristics become con-
30
130’E
IN TABLE
3,
TAKING
mm
ACCXXJNT ONLY
siderably asymmetrical at the of the non-dipole effect of the cross-over geographic latitude 23”, which seems to be shifted
THE
two meridians because geomagnetic field. The in Fig. 4 is located at by about 5” compared
837
Whistler propagation at low latitudes TABLE 3. Trrs PARAME TERS OF THE MODEL To STUDY THE EASTWESTASYMMETRICALDISTRIBLITION,WITHOuTANYLATITLJDlNALEF'FECT (No = 1.0)
Longitude
N,,,(cn-3)
T(K)
LG
C 0+ = 98.85% He+ = 1.1% H+ = 0.05% at R ,._= 6872 km
114”E 1200
1.0 x IO5
2.0
0.0
130”E
4
Ii\
1 \ \ T
114”E
20” -
-
\ t 3 2
5
\\
/
’
/
\ ‘\ 1, ‘V”\ ,/’
-
I& 0
I
t
20
22
24
Final FIG. 4. THE COMPUTATIONAL
’ / V’
I
,: ,’
26
I
I
I
I
I
1
28
30
32
34
36
38’
Geographic
Latitude
RESULT FOR THE MODEL INCLUDING ONLY THE EFFECT OF THE NON-DIPOLE GEOMAGNETIC FIELD.
with Figs 1, 2 and 3 and the difference in 161 at the two meridians is considerably large. Then we make a comparison of the results in Figs 1,2 and 3. It is easily seen that the two separate effects involved in Figs 2 and 3 play completely opposite roles in the resultant Fig. 1. For example, the cross-over geographic latitude in Fig. 2 is located nearly at the same latitude as in Fig. 1, while that in Fig. 3 is about 2” below the cross-over latitude in Fig. 1. A comparison of Fig. 1 with Figs 2 and 3 indicates that the factor associated with Fig. 2 (i.e. the difference of negative latitude gradient in the Chinese and Japanese meridian planes) has the effect of enhancing the difference in 161in those two meridians, while the longitude gradient as dealt with separately in Fig. 3 considerably reduces the difference in 161in the two meridians. Then, we have the moderate difference in 161as in Fig. 1 as the joint combination of Figs 2 and 3. Hence we can conclude that the final Fig. 1 is the consequence of the two important factors (the difference of the negative latitude gradients in the Chinese and Japanese meridians and the longitude gradient) and that the former effect
seems slightly more influential than the latter effect. The geomagnetic field seems to play a rather minor role. In the above calculations, we implicitly assume that a strong difference in the source activity of thunderstorms in the Southern Hemisphere in the Chinese and Japanese meridian planes does not exist, and we assume that the propagation characteristics are much more influential than the source effect, as suggested by Hayakawa and Tanaka (1978). 4. OBSERVATIONAL
RESULT
OF THE LONGITUDE
EFFECT IN WHJSTLER OCCURRENCE WUCHANG
RATE AT
AND KAGOSHIMA
To make a comparison with the theoretical raytracing implications in Section 3, we have investigated the variation of occurrence rate at the same latitude but separate in longitude, Chinese and Japanese meridian planes. Wuchang (geographic coordinates 30S”N, 114.6”E; geomagnetic latitude 19.3”N) was chosen as a Chinese station, and the corresponding
H.
838
B. ZHOUei al.
(a)
g z
:tIJ 0
4
8
12
16
*'
LT . .
(b)
0
4
8
12
16
2o
L.T.
FIG.S.?~E~NGI~EEFFECT~NTHEDIURNALVARL~T~ONOFOCCUKRENCERATEOFWH~STLERS.
(a) Wuchang and (b) Kagoshima. The observation period is February 1983.
Japanese station is Kagoshima (3 1YN, 130.8”E ; 20.5”N), these two stations being located just around A = 20”. Figure 5 shows the diurnal variations of average occurrence rate at those stations during the observation period of February 1983. As seen from Fig. 5, the whistler activity is only seen in the nighttime hours (L.T. = O-S h) at both stations, without any peak in the evening hours at A 3 25” by Hayakawa and Tanaka (1978). The peak occurrence takes place at L.T. N 5 h at Wuchang and the corresponding peak is found at L.T. N 4 h at Kagoshima. The occurrence is defined as the number of whistlers per minute and it is seen that the occurrence rate at Kagoshima is higher than that at Wuchang, which seems to be in good agreement with the theoretical prediction in Fig. 1 in the previous section. However, the comparison of the occurrence rate requires some caution because of the different antenna and receiver systems at different stations, which is discussed briefly here. The antenna at Wuchang is a rectangular oneturn loop ariel with a baseline of 50 m and a height of 6 m (5’ = 300 m’) and the signals are amplified by about 100 dB, while the one-turn loop antenna at
Kagoshima is located in a valley, forming an inverted triangle with a baseline of 90 m and a depth of 35 m (S = 1575 m2) and then the signals are amplified by 70 dB. Taking into account overall the antenna and receiver systems, we can safely say that the occurrence rate is higher at Kagoshima than at Wuchang. Unfortunately simultaneous data at a lower latitude such as A w 15” from the Chinese and Japanese meridian planes are not available, and so we cannot study whether the comparison of whistler activity at such lower latitudes further supports our theoretical prediction or not. Further investigation on this subject will be required. 5. CONCLUSION
The longitude variations of electron density in the Chinese and Japanese meridian planes have been satisfactorily modelied, and we have performed the threedimensional ray-tracing computations of ray paths for the very realistic density model in order to study the longitude effect of whistler propagation characteristics at lower latitudes. We have found a cross-
m at low latitudes
over geographic latitude of 28”N above which the ionospheric transmission of whistlers is very easily fulfilled in the Japanese but not in the Chinese meridian, and below which we have the reverse situation. Also, it is found that both the difference in negative latitude gradient at those two meridian planes and the longitudinal gradient are equally important in determining the overall propagation characteristics. Hence, as understood from the previous works, the latitudinal variation of whistler properties is very important for the study of whistler propagation mechanism, but we would also like to emphasize the importance of the longitudinal variation of whistler characteristics, especially at low latitudes as studied in this paper. would like to express our sincere thanks to Profs B. X. Liang and Z. T. Bao and other members of the Space Physics Group of Wuhan University, Dr S. Shimakura of Chiba University and Dr K. Ohta of Chubu University for useful discussions. One of the authors (M.H.) is grateful to Dr A. Kimpara, Emeritus Professor of Nagoya University, for his continued encouragement and to Takeda Science Foundation for its financial support to this work. Acknowledgements-We
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839
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