Propagation modes of low- and very-low-latitude whistlers

Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1133–1147www.elsevier.nl/locate/jastp

Propagation modes of low- and very-low-latitude whistlers

Birbal Singha, Masashi Hayakawab; ∗aDepartment of Physics, R.B.S. College, Bichpuri, Agra, India

bUniversity of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182 Japan

Received 6 December 1999; received in revised form 5 June 2000; accepted 26 September 2000

Abstract

The relative merits of ducted and non-ducted propagation of low-latitude whistlers are examined critically in the light ofwork done mostly in the Asian countries, India, China, and Japan since 1965. A growing consensus is found in favour of thenon-ducted pro-longitudinal mode of propagation for nighttime whistlers, and the ducted mode of propagation in the presenceof the equatorial anomaly for daytime whistlers. However, controversy still exists about the propagation mechanism of echotrains of whistlers observed at very low latitudes. An alternative mechanism is suggested involving a nighttime feature of theequatorial anomaly. Some recent unusual results are discussed in more detail: they include the observation of whistler tripletsand the frequency and temporal 8ne structure of whistlers recorded for the 8rst time in a low-latitude ground station. Lastly,further scope for work in the 8eld is indicated. c© 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Low-latitude whistlers; Ionosphere; Magnetosphere

1. Introduction

Ever since Storey (1953) presented a convincing inter-pretation of whistlers based on observations and theory, aconsiderable amount of work has been done in this 8eld allover the globe. An excellent review of the early work onwhistlers and related ionospheric phenomena was presentedby Helliwell (1965). Later, at middle and high latitudes,both satellite and ground-based whistler data were exploitedfully to reveal new facts about the structure and dynamicsof the ionosphere and magnetosphere. These achievementsincluded the discovery of the plasmasphere, plasmapause,and bulge (Carpenter and Park, 1973), identi8cation of themechanisms of ionosphere–protonosphere coupling (Park,1970; Andrews, 1980), and measurement of the magneto-spheric electric 8eld (Carpenter et al., 1972) and electrontemperature (Sazhin et al., 1992, 1993).

Unfortunately, at low latitudes, whistler data have notbeen used for determining ionospheric parameters, the mainreason being that the propagation paths of low-latitude

∗ Corresponding author. Tel.: +81-424-832-161; fax: +81-424-803-801.

E-mail address: [email protected] (M. Hayakawa).

whistlers cannot be determined from their dynamic spectraon frequency-time spectrograms, because the nose frequen-cies of such whistlers are higher than 100 kHz, well abovethe pass band of the receiver and the frequency range ofthe sonagram. The various nose-extension methods devel-oped for determining the nose frequencies of whistler forwhich these frequencies are unobservable do not apply inthe case of low-latitude whistlers (Tarcsai, 1975; Tarcsai,Personal communications, 1977). Further, the propagationmechanism of low-latitude whistlers in the ionosphere andmagnetosphere has been a subject of controversy over theyears. While many workers have favoured ducted propa-gation for these whistlers on the basis of ground data anddirection-8nding measurements (Somayajulu and Tantry,1968; Hayakawa and Ohtsu, 1973; Hayakawa et al., 1985;Ohta et al., 1989), others have not found any convincingevidence for it on the basis of ray-tracing analysis andsatellite measurements (James, 1972; Cerisier, 1973; Singhand Tantry, 1973; Hayakawa and Iwai, 1975; Tanaka andCairo, 1980). The observations of echo trains of whistlers atvery low latitudes (Ondoh et al., 1979; Liang et al., 1985)have fueled the controversy. These problems have beenidenti8ed in previous reviews on low-latitude whistlers also(Somayajulu et al., 1972; Hayakawa and Tanaka, 1978;

1364-6826/01/$ - see front matter c© 2001 Elsevier Science Ltd. All rights reserved.PII: S1364 -6826(00)00218 -2

1134 B. Singh, M. Hayakawa / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1133–1147

Hayakawa and Ohta, 1992; Singh, 1993), but no attempthas been made to resolve the contriversy. In this paper, wediscuss this problem critically and show that a consensusis emerging about the propagation mechanisms of day andnighttime low-latitude whistlers. The exact propagationmechanism of echo trains of whistlers has not been foundas yet, but we suggest here another possibility based onsome nighttime features of the equatorial anomaly. Sincethe propagation mechanism of whistlers is intimately re-lated to their occurrence and dispersion characteristics,we discuss these characteristics brieDy in Sections 2 and3, respectively, for whistlers observed in the three Asiancountries of India, China, and Japan, where major work onlow-latitude whistlers has been done. Then, the propagationmechanisms of night and daytime low-latitude and equato-rial whistlers are discussed in detail in Section 4. Some newrecent results mentioned earlier are discussed in detail inSection 5, and 8nally further scope for work in the 8eld isindicated.

2. Occurrence characteristics of low-latitude whistlers

Studies on low-latitude whistlers have been carried outmainly in India, China, and Japan by means of ground-basedobservations at several stations. We consider only the re-sults obtained at stations with geomagnetic latitudes less than30◦ (L=1:33) because, by a convention adopted here, theseare regarded as low-latitude stations (Hayakawa and Tanaka,1978). Further, only the stations operated on a long-term ba-sis are considered. In Table 1, we give a list of such activestations along with their geomagnetic latitudes and their ge-ographic latitudes and longitudes. The abbreviations of thestation names are given in brackets. The geographic loca-tions of these stations and of the capital cities of their re-spective countries are shown in Fig. 1. Note that the terms‘latitude’ and ‘longitude’ appearing else where in the paperrefer to geomagnetic co-ordinates. The occurrence charac-teristics of whistlers at these stations will now be discussedbrieDy, high-lighting only those points of direct relevanceto the propagation mechanism.

The diurnal and seasonal variations at diIerent stations inthe above-mentioned three countries have been discussed bySomayajulu et al. (1972), Liang et al. (1985) and Hayakawaand Tanaka (1978), respectively. Their results show thatwhistler activity peaks in the months of March in India, butin the month of February in China and Japan. It is generallybelieved that whistler activity at a station depends largelyon lightning activity at its conjugate point in the oppositehemisphere, but Ohta and Hayakawa (1990) did not 8nd anyclear-cut correlation between the two when they comparedwhistler activity at Yamaoko ground station (Geomag. Lat.25◦ N) with thunderstorm activity at its conjugate point.This result suggested that whistler activity at a station iscontrolled more by propagation eIects in the ionosphere andmagnetosphere than by the activity of the source.

The diurnal variations in whistler activity at diIerent sta-tions in the three countries are shown in Fig. 2. The oc-currence rates are plotted against the local times, which are+5:5, +8, and +9 h ahead of Universal Time (UT) in thethree countries, respectively. The results for the Indian sta-tions of Gulmarg, Nainital, and Agra were obtained by tak-ing average values for all the days inMarch, because whistleractivity is found to peak in this month. The data for theJapanese stations of Sakushima and Kagoshima are basedon the winter-time average values. At Okinawa, the whistleroccurrence rate (in whistlers per minute) is shown for thewinter seasons. Since the Chinese workers (Bao et al., 1983;Liang et al., 1985) have not shown their results graphically,we have derived a representative diurnal variation for eachof these two stations from the brief measurements made byHayakawa et al. (1990) in January, 1988.

As seen from the 8gure, the whistler activities at theIndian stations of Gulmarg and Nainital peak during thepost-midnight and early morning hours, whereas at Agrathe activity peaks during the pre-midnight hours. It may benoted here that the activity at Agra is very rare and sporadic,compared to those at Gulmarg and at Nainital (Singh et al.,1980, 1997a), primarily because the latter two stations aresited at relatively high altitudes and latitudes where there ismuch less local and atmospheric noise. An activity similarto that at Agra was also found at Varanasi, which is sitedat an even lower latitude in a plain (Singh, 1993). At thethree Japanese stations, activity was found during two dis-tinct periods: there was a broad maximum at night (night-time whistlers), and a sharp peak around sunset (daytimewhistlers). No such peaks were observed at Okinawa, wherethe whistler activity was enhanced during post-midnighthours. At the Chinese stations also, the activity was rareand sporadic. However, the long-term averages show peakactivity during 0200–0400 LT. No daytime whistlers wereobserved at the Indian and Chinese ground stations, and thisresult has been attributed to heavy absorption in the D-regionof the ionosphere.

Note that, since the observational bases for the data arenot the same at the diIerent stations, our purpose is not tocompare the occurrence rates at these stations: we simplywant to show the local times at which the peak activitiesoccur at these stations. Moreover, we want to see whetherthere is any coincidence in the peaks of the diurnal variationsof activity at pairs of stations located at the same geomag-netic latitude but diIerent longitudes, such as Kagoshimain Japan and Wuchang in China. The peaks in their annualvariations of activity occur in the same month of Febru-ary, and the reason for this might be that the same whistlerswere observed at the two stations, because the down-comingwaves of each whistler extended over a suNciently widerange of geomagnetic longitude. If that were the reason,then their daily variations in activity would be expectedto peak at the same Universal Time, but the results showthat in fact there is no such coincidence. At Kagoshima,the diurnal peak in activity is around 2100 UT (0600 LT),

B. Singh, M. Hayakawa / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1133–1147 1135

Table 1Ground stations in Asia actively involved in observations on low-latitude whistlers

Country Station Geomag. Geographic location(Abbreviation) lat., deg., N

Lat., deg.N Long., deg.E

India Gulmarg (GU) 24.43 34.06 74.40Nainital (NA) 19.01 28.10 78.70Agra (AG) 17.01 27.28 78.20Varanasi (VA) 16.50 25.30 83.00

Japan Sakushima (SA) 24.13 34.71 137.03Kagoshima (KA) 20.66 31.50 130.76Okinawa (OK) 15.01 26.03 127.80

China Wuchang (WU) 19.40 30.50 114.60Zhanjiang (ZN) 10.00 21.30 110.30Yulin (YU) 7.00 18.20 109.50

Fig. 1. Location of the low-latitude ground stations actively engaged in whistler observations. The capital cities New Delhi (DL), Beijing(BJ) and Tokyo (TK) are also marked.

whereas at Wuchang it occurs much earlier around 1900UT (0300 LT). Thus the whistlers observed at each of thesestations must have originated and propagated in meridianplanes close to that of the station concerned, and their wavescame down from the ionosphere over a longitude rangeless wide than the diIerence in longitude between the twostations.

An interesting point in Fig. 2 is that the nighttime whistleractivities at all the stations except Agra peak between thepost-midnight and early morning hours, though the rate of

occurrence is diIerent at the diIerent stations. Singh andSingh (1979) and Tanaka and Hayakawa (1980) attemptedto explain the diIerences in whistler activity between theIndian and Japanese stations in terms of the variation withgeomagnetic longitude of some features of the equatorialanomaly. Zhou et al. (1988) studied the eIect of longitudeon the occurrence of whistlers in China and Japan by invok-ing the variations with longitude in the ionospheric modelemployed for the ray-tracing computations. They showedthat there is a cross-over latitude around 28◦ geographic,


Fig. 2. Diurnal variation of whistler activity at the low-latitude ground stations in India, China, and Japan. Note that the time axes are notthe same in all cases.


above which whistler occurrence is much higher in Japanthan in China.

From the above results, the following are useful in dis-cussing the propagation mechanism: (i) the whistler activ-ities at the diIerent stations are controlled by propagationeIects in their respective meridian planes; (ii) the varia-tions in whistler activity with geomagnetic longitude in threecountries are inDuenced by the equatorial anomaly; and (iii)daytime whistlers have been observed at the Japanese sta-tions only.

3. Dispersion characteristics

The dispersions of the whistlers observed at the Indianstations range from 10s1=2 to 70s1=2. The lowest dispersionof 10s1=2 was seen at Nainital (Dikshit et al., 1971) and thehighest dispersion of 70s1=2 was observed at Agra, both dur-ing magnetically quiet periods. However, the occurrence ofhighly dispersed whistlers is quite unusual. In Fig. 3, weshow the range of dispersion in a burst of about 45 whistlersobserved during about half an hour after 2300 LT at Agraon 2 April, 1979. Most of these whistlers had dispersionsof 30–35s1=2, while others were of relatively high disper-sion, 50–70s1=2 (Singh et al., 1980; Singh, 1997a). Similarbursts of whistlers had also been noted earlier at Gulmargand at Nainital (Somayajulu et al., 1972). The dispersionsof the whistlers observed at the Chinese stations lie mostlybetween 10s1=2 and 15s1=2, and their variations are corre-lated with f0F2. Whistlers with low dispersions, 12s1=2 orless, were observed at the southern most Chinese stationYongxiang (Geomag. Lat. 5:5◦), showing that whistlers canbe observed even at such low latitudes. At the Japanese sta-tions of Sakushima and Kagoshima, the observed disper-sions were small, but those of the daytime whistlers observedat Sakushima were larger, typically 30–40s1=2.An interesting observation made at the Okinawa ground

station in Japan is that echo trains of whistlers having dis-persions 12; 37; 59s1=2 (Ondoh et al., 1979). Similar echotrains have been observed at the Chinese ground station atZhanjiang (Liang et al., 1985).

Hayakawa and Tanaka (1978) have found an empirical re-lation between the dispersion and the geomagnetic latitude ofpropagation, based on nighttime whistler data obtained at theJapanese ground stations. This relation isD=1:22 (P−0:72)where D is the dispersion in s1=2 and P is the geomagneticlatitude in degrees. From this relation, the maximum disper-sion observed at 30◦ latitude should be about 35s1=2. It fol-lows that all those whistlers with dispersions higher than thisare high-latitude whistlers that have travelled to low-latitudestations in the earth–ionosphere waveguide. However, therelationship between dispersion and latitude given above iscontradicted by the sporadic occurrence of highly dispersedwhistlers at the Indian and Chinese ground stations. Highlydispersed whistlers (D = 25–35s1=2) have also been ob-served at a much lower latitude at the Agra station. We have

Fig. 3. Burst of highly dispersed whistlers observed at the Agrastation. The vertical bars indicate the range of dispersions.

found, by curve-8tting and ray-tracing, that these are actu-ally mid-latitude whistlers (L=2:1–2:4) that have travelledto our stations in the earth–ionosphere waveguide (Chauhanand Singh, 1992). The Chinese workers Bao et al. (1983)have also recorded similar highly dispersed whistlers andhave suggested that an increase in f0F2 is responsible forincreasing the dispersion of these whistlers. However, sincethe ionospheric contribution to dispersion is small, an in-crease in f0F2 is unlikely to increase the dispersion by somuch. From the above results, it appears that the highly dis-persed whistlers (D¿ 25s1=2) are mid-latitude whistlers. Asimilar conclusion has also been drawn, after curve 8ttinganalysis, for similar whistlers recorded at Varanasi station(D. Hamar, personal communication, 1998). In the lightof these 8ndings, the dispersions of the nightime whistlersrecorded during magnetically quiet periods at the stationslisted in Table 1 (L¡ 1:2) should be much less than 25s1=2.

4. Propagation characteristics

Whistlers are known to be propagated in the ionosphereand magnetosphere at middle and high latitudes in two dif-ferent modes: the ducted mode, which is characterised bypropagation in 8eld-aligned columns of enhanced ionisation(Smith, 1961), and the non-ducted mode, in which the prop-agation occurs in normal smoothly varying ionisation. Theexistence of ducts at high L-values has been experimentallyveri8ed by OGO-3 satellite observations (Angerami, 1970).The formation of whistler ducts has also been studied bymany workers theoretically, and it has been suggested thatVLF ducts may be formed by Dux-tube interchange underthe inDuence of localised transverse electric 8elds (Park andHelliwell, 1971; Walker, 1978; Thomson, 1978); however,the origin of these 8elds is still controversial (Rodger et al.,1998).

While the mechanisms of duct formation and of whistlerpropagation at middle and high latitudes are fairly well un-derstood, the corresponding mechanisms at low latitudes


are not clear and have been subjects of controversy for along time. We shall now discuss this problem in detail.Since night and daytime whistlers have diIerent occurrenceand dispersion characteristics, their propagationmechanismsmust also be diIerent and hence we discuss the propagationmechanisms of these whistlers separately.

4.1. Propagation mechanism of low-latitude nighttimewhistlers

4.1.1. Ducted propagationThe ducted mode of propagation for low-latitude night-

time whistlers has been favoured by many Indian andJapanese workers on the basis of ground observations, andthey have studied the duct characteristics, i.e., size, lifetime,separation, etc., from the available data (Somayajulu et al.,1972; Hayakawa and Ohtsu, 1973; Ondoh, 1976; Singh,1993). The low-latitude data have also been used to deducethe electric 8eld in the ionosphere (Misra et al., 1980; Khosaet al., 1982). Hayakawa and Tanaka (1978) have classi8edwhistlers into two categories, ducted whistlers which areobserved between 20–30◦ latitude, and PL-mode whistlers(to be discussed later) which are observed below 20◦ lati-tude. On the other hand, the view that ducted propagationcan occur in the low latitude and equatorial ionosphere hasbeen strongly supported by the observation of echo trainsof whistlers at the Okinawa ground station in Japan (On-doh et al., 1979). Further convincing evidence has beenfound from direction-8nding measurement of low-latitudewhistlers in Japan and China (Hayakawa et al., 1985, 1990).

4.1.2. Evidence against ducted propagation of lowlatitude and equatorial whistlers

The 8rst evidence against the ducted mode of prop-agation for low-latitude whistlers came from Singh andTantry (1973), who attempted to study ducted propagationusing ray-tracing computations in a realistic model of a8eld-aligned duct. They showed that trapping of whistlerwaves in a duct of which the base was located at 300 kmaltitude and 25◦ latitude required a 400% increase in theionisation density along the central 8eld line above thebackground density. They concluded that since such a highenhancement of ionisation density was unlikely to occur,ducted propagation for low-latitude whistlers was improb-able. Similar results were obtained by Hayakawa and Iwai(1975) from their ray-tracing computations, and they sug-gested that the necessary enhancement could be providedby the equatorial anomaly.

Further objections were raised by FR-1 satellite observa-tions, in which 8xed-frequency (16.8 kHz) waves were ra-diated from a ground transmitter at L=2:1 and received bythe satellite at 750 km altitude in the zone close to the trans-mitter and also in the conjugate zone. From the wave-normaldirection and the Doppler shifts measured in the conjugatezone it was concluded that (i) non-ducted propagation isthe only mode that occurs in the ionosphere below L= 1:7,

Fig. 4. Calculated enhancement of ionisation density in the ductsalong the 8elds lines at L = 1:7 and 1:5, for a 10% change in L,by the Dux-tube-interchange mechanism.

(ii) ducts extending high in the magnetosphere are termi-nated at the base of the protonosphere (∼ 1000 km), and(iii) waves emerging from the ducts are propagated down-wards mostly in the non-ducted mode (James, 1972;Cerisier, 1973; Tanaka and Cairo, 1980). Termination ofducts at high altitudes, above 1600 km, has also been re-ported by Strangeways et al. (1982), though Ohta et al.(1996) have reported that in exceptional cases ducts mayextend down to ionospheric heights.

The various duct formation mechanisms envisaged up tonow require smoothly varying ionisation above 1000 km.Since the dipole magnetic 8eld lines corresponding to allthe stations given in Table 1 lie entirely in the ionospherebelow 1275 km, where the ionisation is highly irregular be-cause of the presence of the equatorial anomaly, duct for-mation by the best-known mechanisms is not possible. Asan example, we apply here one of the mechanisms and showthat suitable ducts at low L-values are not formed. Assum-ing a 10% change in the L-values, we have calculated theionisation enhancement factors that may occur for ducts inthe range L = 1:2–1:7. We have followed Thomson (1978)in using his expression for the enhancement factor

e =RNint=N −RNback=N; (1)

where N is the background electron density, while RNint andRNback are the changes in the interchanging Dux-tube den-sity and background density, respectively. The detailed ex-pressions for the terms on the right-hand side of Eq. (1) aregiven by Thomson (1978). We adopt a diIusive-equilibriummodel similar to that employed by Singh (1976): at a ref-erence altitude of 400 km, the electron density is of 1:5 ×105 cm−3, the ionic composition is O+ = 95:0%, He+ =4:75%, H+=0:25%, and the electron and ion temperature areboth 1000 K. The percentage variations of the enhancementfactors along the 8eld lines at L= 1:7 and 1:5 are shown inFig. 4; the enhancements of ionisation density in the ductsat the equator are just 17 and 13%, respectively. A similar


calculation at L= 1:4 shows no enhancement. These calcu-lated enhancements are much less than 300–400% requiredin the ducts at the low L-values (Singh and Tantry, 1973).Further, the computed enhancements are much less than atL = 3, where an equatorial enhancement of 30% has beenobtained (Thomson, 1978). This result suggests that the for-mation of ducts at the low L-values corresponding to thestations of Table 1 (L¡ 1:2) is not possible. On the otherhand, there are ample evidences for the duct formation inthe mid-latitude ionosphere. For example, Kranski (1977)and Stuart (1977) suggested that most of the whistlers ob-served on the ground have propagated in ducts in the rangeL = 2:6–3:6. Later, Tanaka et al. (1987) and Nishino etal. (1990) conducted 8xed-frequency whistler-mode exper-iments at L=1:9 and obtained results consistent with ductedpropagation in mid-latitude ionosphere. These results are inline with the enhancements obtained theoretically at L= 3.

Hayakawa and Ohta (1992) also recognised that the prop-agation mechanism of low-latitude nighttime whistlers isnot fully understood. It was for this reason that Ohta et al.(1996) postulated a diIerent mechanism for duct formationin the low-latitude ionosphere.

Further results based on ray-tracing studies of whistler-mode 8xed-frequency transmitter signals and of naturalwhistlers (to be described in the next sub-section) havesuggested that ducted propagation for low latitude andequatorial nighttime whistlers anywhere below 30◦ is notnecessary.

4.1.3. Pro-longitudinal (PL) propagation: a possiblesolution

Since ducted propagation for low-latitude whistlers ishighly controversial, the question arises as to how thesewhistlers might be propagated to ground in the absence ofducts. Here, a new type of propagation mechanism, knownas the pro-longitudinal (PL) mode, was examined for itspossible reference to low-latitude whistlers. The PL modewas discovered by Scarabucci (1969) using satellite data to-gether with a ray-tracing analysis of high-latitude whistlerpropagation in a model magnetosphere that included a neg-ative latitudinal gradient of electron density at L= 4 due tothe plasmapause. The PL mode is de8ned as involving prop-agation in which the wave-normal angle along the entireray path is always less than a characteristic wave-normalangle m for which the component of the refractive-indexvector along the magnetic-8eld line is minimum, i.e.

@@

(� cos ) = 0: (2)

The wave-normal angle is de8ned as the angle between thewave-normal and earth’s magnetic 8eld. It is measured fromthe magnetic 8eld direction, positive clockwise and negativeanticlockwise. The PL mode propagation produces ray tra-jectories and=or travel times similar to those for purely lon-gitudinal propagation. Whistlers exhibiting the characteris-tics of PL-mode propagation have been observed on the ISIS

Fig. 5. (a) PL-mode ray path computed for low-latitude whistlersobserved at Gulmarg station (solid line), compared with the 20◦

Field line (broken line). (b) Variation of the wave-normal anglealong the path.

satellite and also on the ground (Thomson, 1977; Thomsonand Dowden, 1977).

PL-mode propagation was examined for the case oflow-latitude whistlers 8rst by Singh (1976). He developeda model that included a maximum of electron density at theequator, and computed ray paths for whistler waves thatsatis8ed all the conditions for the PL-mode. One of theseray paths is shown in Fig. 5; it is for waves of frequency5 kHz starting at 20◦ N latitude, at an altitude of 120 km,with the wave-normal vertical. A dipole model was usedfor the earth’s magnetic 8eld. Here, it may be mentionedthat, as per usual convention, the ray path is traced fromstarting point in the northern hemisphere to the exit pointin the southern hemisphere (negative values of latitudesto the right of the origin) while the whistlers were in factreceived in the northern hemisphere having their origin inthe southern hemisphere. This may not create confusionbecause the model used for the electron density is symmet-rical with respect to the magnetic equator and the same isalso true for the magnetic 8eld, hence the path is reversible.The variation of the wave-normal angle along the propaga-tion path is also shown. As it may be seen, the ray path is


Fig. 6. Computed PL-mode ray paths, starting at 300 km altitude and various magnetic latitudes (solid lines), with the initial wave-normalangles R as marked. Also shown are the 8eld lines that pass through these starting points (broken lines), with their initial latitudes marked.The ray path that starts at 25◦ is almost 8eld-aligned and resembles ducted propagation.

symmetrical with respect to the equator, and the associatedwave-normal angles are small also, being largest at theinitial and 8nal points and zero at the top.

The 8nal wave normal at the conjugate point is directedalmost vertically downward, so it may lie in the transmis-sion cone and the waves may propagate to ground. Invokingthis mode, Singh (1976) explained the frequent occurrenceof whistlers at Gulmarg station on 9 March, 1970, duringthe magnetic storm of 6–10 March, 1970. He showed fromAlouette satellite data that latitudinal gradients of the typeassumed in the model did indeed exist around the equatoron the day of observation.

Later, using data from 8xed-frequency transmitter exper-iments, Andrews (1978, 1979) computed ray paths similarto the above, but starting from the lower latitude of 10◦

and without including any horizontal gradients of electrondensity. He found that the dispersion along such paths isremarkably constant with frequency, even though the pathitself is mostly not 8eld-aligned and is somewhat dependenton frequency. He suggested that this path may well be theone taken by the whistlers of very low dispersion recordedat Okinawa (Ondoh et al., 1979).

Liang et al. (1985) have reported on the occurrence ratesof very low-latitude whistlers observed simultaneously at

8ve stations in China with almost the same dispersion, andwith maximum occurrence at Zhanjiang (geomagnetic lat.10◦). From this, they inferred the existence of a preferredpath near this latitude. They also produced some ray tracingresults that are consistent with those of Andrews (1978,1979).

Using ray-tracing computations, Thomson (1987) repro-duced all the principal properties of 8xed-frequency signalspropagated through the ionosphere between NPM in Hawaiand Dunedin, New Zealand, by considering non-ductedpaths between the altitudes of 700 and 1400 km (corre-sponding to invariant latitudes between 10 and 26◦).The above results clearly indicate that, for low- and

very-low-latitude whistlers, ducted propagation is not nec-essary because all the major characteristics of such whistlersare very well reproduced by non-ducted propagation in thepresence of horizontal=or vertical gradients in the ionisationdensity. Here, we draw attention to a new feature of thelow-latitude whistler paths, namely a special form of the PLmode that resembles the ducted mode. In Fig. 6, we show anumber of PL-mode ray paths computed for the frequencyof 5 kHz, starting from diIerent initial latitudes in the range15–30◦ with slightly diIerent initial wave normal angles at300 km. The ionospheric model is the same as that adopted


by Singh (1976) and mentioned in Section 4.1.2. Of specialinterest is the ray path along the 25◦ 8eld line; it is almost8eld-aligned, and the wave-normal angle varies in the samemanner as in a VLF duct but more slowly. Also the 8nalwave-normal is directed vertically downwards, as requiredfor propagation to the ground. Therefore we suggest thatthe whistler waves entering the ionosphere at many pointsat low latitudes may follow paths similar to the above andpropagate to the ground with characteristics similar to thosefor ducted propagation.

4.1.4. Whistler echo trainsEven for the echo trains of whistlers observed at Okinawa

in Japan (Ondoh et al., 1979) and at Zhanjiang in China(Liang et al., 1985), ducted propagation has been ruled out.Thomson (1987) suggested that the echoing was due topartial reDections from the sharp boundary at the base ofthe ionosphere. Hayakawa et al. (1990) and Hayakawa andOhta (1992) postulated 8eld-aligned propagation producedby either (i) PL-mode waves reDected from the ground, or(ii) 8eld-aligned irregularities caused by 8eld-aligned cur-rents and transverse electric 8elds generated by lightning,or (iii) spread-F irregularities during magnetic storms. Us-ing three-dimensional ray tracing, Ohta et al. (1997) havediscussed, whether the echo trains are caused by ground orby ionospheric reDections; they have suggested ionosphericreDections to be more plausible in view of the signi8cantlosses during ground reDections.

Although, the above possibilities are quite likely and mayaccount for the echo trains, there is another possibility thathas not been looked into and requires thorough attention. Itis well known that the equatorial anomaly during daytime ischaracterised by two ionisation peaks centred on a particular8eld line, and separated by a trough at the equator. Duringnighttime, these two peaks coalesce into a single peak at theequator, and the anomaly is limited to a very small latitudi-nal range of ±5◦ (Rastogi, 1959). We suggest that the outerboundary of this anomaly forms a kind of duct within whichequatorial whistlers are trapped and propagated between thetwo hemispheres, in a manner similar to the high-latitudewhistlers that are guided along the plasmapause acting asa waveguide (Inan and Bell, 1977); thus the whistlers arepropagated to and fro between the two hemispheres. Atthe base of the ionosphere, a fraction of the whistler en-ergy escapes to the ground at each hop of propagation tobe received as echo trains, at the Okinawa and Zhanjiangstations.

4.1.5. E:ect of ionospheric irregularitiesIn Section 3, we mentioned that the highly dispersed

whistlers propagated in the middle- and high-latitude iono-sphere are occasionally recorded at low-latitude groundstations, where they are mistaken for low-latitude whistlers.Normally the downcoming whistler waves emerging fromthe lower ionosphere have their wave-normals oriented

towards the pole. However, if there exists an irregular-ity at the exit point, the wave-normal may be scatteredso as to point toward the equator, and in such a case thewaves may be observed at lower latitudes. The eIect ofionospheric irregularities on the day-to-day variation ofwhistler activity on the ground has been recognised for along time. Ever since Kimura (1966) suggested the pos-sibility that whistler-mode waves might be scattered fromsporadic-E layers, the high-latitude whistlers observed atthe low-latitude stations have been interpreted in termsof this mechanism (Singh, 1997a). Spread-F irregulari-ties have also been found to inDuence whistler activity onthe ground (James, 1972; Hayakawa et al., 1990). Singhet al. (1979) and Singh and Singh (1980) explained theunusual upper and lower cut-oI frequencies and bandedstructures observed in low-latitude whistlers as the resultsof specular reDections from sporadic-E layers. Singh andJain (1986) examined the eIect of spread-F irregularitieson whistler propagation at low-latitudes. They showed thatan irregularity of 10 km thickness and 5% amplitude makesthe wave-normal direction of downcoming waves almostvertical at the base of the F-region, in such a way thatthe waves may penetrate the lower ionosphere and reachthe ground. They also found that such irregularities were

Fig. 7. (a) Whispering-gallery-mode ray path computed for 16:2◦

initial latitude with an ionospheric model including the equatorialanomaly. (b) Variation of L-value along the path. (c) Variation ofthe wave-normal angle.


Fig. 8. Whistler triplets recorded at Agra station.

present in the ionosphere during magnetic storms, at timeswhen intense whistler activity was observed on the ground.Since spread-F is generally a nightime phenomenon thatoccurs mostly within ±20◦ latitude around the equator andis positively correlated with magnetic storms, it may play auseful role in enabling low-latitude whistlers to propagateto the ground.

4.2. Propagation mechanism of daytime whistlers

The occurrence characteristics of whistlers at theJapanese stations of Sakushima and Kagoshima have re-vealed the existence of evening peaks in whistler activity.Considering the high dispersion involved, together withthe experimental results from rocket measurements ofwave-normal direction and the theoretical results from raytracing, ducted propagation in the equatorial anomaly wassuggested as the explanation (Iwai et al., 1974; Hayakawaand Iwai, 1975). Hasegawa and Hayakawa (1980) haveshowed by ray-tracing computations that two modes, thewhispering-gallery mode and the PL mode, existed inthe anomaly, and that either or both of them may beresponsible for daytime whistler propagation to ground.A whispering-gallery-mode ray path computed for thefrequency of 3 kHz, starting with wave-normal angle 0◦

from the geomagnetic latitude 16:2◦, is shown in Fig. 7along with the variation of L-value and of the associatedwave-normal angle. The characteristics of this ray pathalong with those computed at other frequencies of 1 and

10 kHz reproduced almost all the features of the recordedwhistlers. Later, Ohta et al. (1984) and Hayakawa et al.(1990) showed from direction 8nding measurements thatwhistlers were circularly polarised; hence they propagatedin a ducted mode on the outer Dank of the equatorialanomaly.

The view that ducted propagation occurs in the equa-torial anomaly is supported by our recent observation ofwhistlers at Agra station using a crossed-loop antenna. Thedetails of the experimental set-up were given by Singh etal. (1997a). By this means, we recorded whistler triplets forthe 8rst time at a low-latitude station. In Fig. 8, we showthree whistler triplets in the frequency range 2–3.75 kHzthat occurred at almost constant time intervals. The disper-sion of each whistler is 14s1=2. Other features of the tripletsare described by Singh et al. (1997b). We believe that thethree whistlers of the triplet propagated along slightly diIer-ent paths in the equatorial anomaly at Japanese longitudes(which were on the morning side of the earth at the timewhen the triplets were recorded at Agra) and reached ourstation through the earth–ionosphere waveguide. Daytimepropagation near the equator caused the equatorial erosionof the high-frequency components of the whistlers, and theconstant time intervals between the triplets were due to theconstant time intervals between the causative lightning dis-charges. This interpretation 8nds support from the fact thatsuch triplets were recorded on two occasions by the North–South loop antenna only, which received signals best fromthe easterly and westerly directions; on this occasion the


waves may have come from the East, after escaping fromthe ionosphere at Japanese longitudes.

At 8rst glance the explanation for the triplets may appearto be unrealistic on the ground that (i) they cannot look sostrong even after travelling all the way from Japanese lon-gitudes to Agra (more than 5000 km away) specially overland (ii) the dispersion of each component of the triplet can-not be the same if they travel along diIerent paths and (iii)the repetition of the causative lightning strokes of the threetriplets at equal interval of time seems to be unlikely. In orderto answer these we may mention here that we have exam-ined other explanations for these triplets also: for example,they may possibly be high-latitude multiphase VLF emis-sions which propagated to our station via earth–ionospherewaveguide mode, or, they may be low-latitude whistler echotrains. These explanations are not found satisfactory for thereasons that the time separation between the triplets∼0:380sis much small compared to 2–6s found in the case of suchemissions observed at the high latitudes, and whistler echotrains require hop-to-hop increase in the dispersion whichis not so here. Hence, the proposed explanation is the onlyone that looks satisfactory. The signals are strong becausethey are propagated mostly in the nightside of the earth inthe absense of D-region absorption. The propagation of thethree components of the triplets along slightly diIerent pathwith almost the same dispersion is also justi8ed particularlylooking at the diIerent upper cut oI frequencies in the com-ponents of the triplets which are possible due to equatorialerosion along diIerent paths only. The alternate explanationthat three components of the triplets were caused by diIer-ent Dashes of the same stroke and propagated along samepath does not explain the diIerent upper cut oI frequenciesof the components. The diIerent paths considered here maynot be separated so much as to eIect the dispersion signif-icantly. Further, since the ionisation in the anomaly is de-creasing with height, it is possible that small increase in thepath length may be compensated by the eIect of reducingionisation so that the travel times remain almost the samefor each component. Finally, the constant time interval be-tween the three triplets may be due to multiple strokes of thelightning, or three diIerent lightning discharges occurring atconstant time interval of 0:380s. This explanation is justi8edon the ground that the periodicity in multistroke lightning of3–100 ms is well known (Uman, 1969). In the present case,though the periodicity is much higher, it may be justi8ed inview of the rare and unusual occurrence of the triplets.

5. Some unusual whistlers observed at Agra and theirdirections of propagation

Recently, at our Agra station, we have developed a direc-tion 8nding technique for low-latitude whistlers that is sim-ilar to the 8eld-analysis and crossed-loop-antenna methodsof Okada et al. (1977). The details of the experimental setup are given by Singh et al. (1997a). Using the new set-up,

we have recorded some very unusual whistlers for the 8rsttime at a low-latitude ground station. These include whistlertriplets, frequency and temporal 8ne-structure whistlers, andmulti-Dash whistlers associated with ELF hiss (Singh et al.,1997b). The whistler triplets are those already shown inFig. 8 and discussed in sub-section 4:2. In Figs. 9a and b, weshow the frequency and temporal 8ne-structure whistlers,respectively. The 8ne structures in these whistlers are in-terpreted in terms of interference between multiple signalsradiated from multi-stroke lightning. Since the dispersionsof these whistlers are very high, 72s1=2 and 42s1=2, respec-tively, we presume them to be high- and middle-latitudewhistlers, for the reasons discussed earlier. The geomagneticlatitudes of reception of these whistlers were determinedapproximately from the relation given by Hayakawa andTanaka (1978) and found to be 59.73 and 35:35◦, respec-tively. It is worthwhile to mention here that the applied rela-tion is purely empirical and satisfactory for low-dispersionwhistlers only. For high-dispersion whistlers (D ∼ 72s1=2)this relation may not be very accurate because whistlers ofsuch dispersions are very common even at a lower latitudestation of Stanford whose geomagnetic latitude is 44◦ N,much less than 59:73◦ N obtained from the empirical rela-tion. The frequency-8ne-structure whistlers were receivedby the N–S loop antenna only, hence they propagated to ourstation from the East or West. The azimuthal direction ofarrival for temporal-8ne-structure whistlers was determinedby studying the amplitude variation of the signals obtainedfrom the two loop antennas at the frequency of 3.5 kHz, bothon an analog chart recorder and also on a personnel com-puter using a data acquisition system and analysis software.From the amplitude ratio, the azimuthal direction of arrivalwas found to be 36◦ to the East of North. The typical struc-tures of these whistlers may not have been caused by instru-ments because many whistlers and emissions were recordedprior to and after the observation of these whistlers whichdid not show such structures.

6. Conclusion

From the detailed results presented in Section 4 regardingthe propagation mechanism of low latitude and equatorialwhistlers, it is clear that most of the low-latitude workers inIndia, China, and New Zealand have favoured non-ductedpropagation for low- and very-low-latitude whistlers. Eventhe Japanese workers, who were the 8rst to realise that thepropagation mechanism of these whistlers was not fully un-derstood, have lately favoured the non-ducted mode. Thusthere is now a consensus about the propagation mechanismof these whistlers among the various workers. The ductedmode in the presence of the equatorial anomaly for daytimewhistlers is now better understood. However, the occurrenceof echo trains of whistlers at very low latitudes needs morestudy, and the suggested mechanism involving the nighttimeequatorial anomaly may possibly account for the propaga-tion of such whistlers.


Fig. 9. Further types of multiple whistler recorded at Agra station: (a) frequency-8ne-structure whistlers; (b) temporal-8ne-structure whistlers.

7. Suggestions for further work

1. Although the propagation mechanisms of day andnighttime whistlers are well understood, the same cannotbe said of echo-train whistlers, and further work is needed

in order to arrive at a de8nite conclusion about their propa-gation mechanism.2. Polarisation measurements for daytime whistlers in

the equatorial anomaly region in Japan and for nighttimewhistlers in China showed circular polarisation, from which


it was concluded that these whistlers propagated in the iono-sphere in ducted mode and arrived at the receiver from theionosphere just overhead. This raises the question of whatis the polarisation of PL-mode whistlers, which needs to beinvestigated thoroughly.3. Daytime whistlers were observed in the Japanese sta-

tions only: no such whistlers were observed in the Indianand Chinese stations. The reason for this diIerence is notclear because none of the Indian or Chinese workers haspublished the details of their observations. It may be notedthat Singh (1997b) conducted daytime whistler observationsat certain periods in the year 1991 and recorded a number ofVLF emissions. In the light of this result, the question arisesof why he did not observe any daytime whistler. Hence, ex-tensive daytime observations are needed so as to arrive at ade8nite conclusion.4. Up to now, only meagre attempts have been made to

use the low-latitude whistler data to determine ionosphericparameters. Since a consensus has now been reached abouttheir propagation mechanism and propagation paths, thelow-latitude data should also be exploited for this purpose.5. Co-ordinated observations are required at the Indian,

Chinese and Japanese stations to study the longitudinalpropagation, i.e. propagation, from one meridian plane tothe other.

Acknowledgements

One of the authors (B.S.) is grateful to the Department ofScience & Technology, Government of India, for 8nancialsupport in the form of a major research project under the allIndia co-ordinated programme of Ionosphere–ThermosphereStudies (AICPITS), Phase II. The authors also thank Mr.Raghuraj Singh, Mr. P.K. Mishra and Mr. Raj Pal Singhat Agra for their help in the preparation and typing of themanuscript and in the preparation of the 8gure.

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Documents

Propagation modes of low- and very-low-latitude whistlers