Journal of Amospher;r and Solar-Trrwsrnal Ph>srcs, Vol. 60, No. 5, pp. 495-50X, 199X c’ 1998 Elsewer Science Ltd

Pergamon PII : Sl364-6826(98)00001-7

All rights reserved. Punted in Great Britain 1364 6826.‘98 Sl900+0.00

Plasmaspheric parameters as determined from whistler spectrograms : a review

R. P. Singh, Ashok K. Singh and D. K. Singh

Atmospheric Physics Lab., Physics Department, Banaras Hindu University, Varanasi-221005, India E-mail : rampal@ banaras.ernet.in

Received 13 August 1996, in recisedforms 13 May 1997 and 18 December 1997, and accepted 19 Drcember 1997

Abstract-We review the information derived from whistler spectrograms (recorded on the ground) about the equatorial magnetic field, equatorial electron density, total electron content of a flux tube, downward transport of flux of electrons, large scale electric fields in the equatorial region, characteristic properties of the ducts present in the plasma, and electron temperature. The above parameters derived from the analysis of whistlers recorded at low latitude ground stations are also included. Thus, it is demonstrated that the probing of the entire plasmasphere can be easily achieved by recording whistler waves at ground based stations scattered in latitude and longitude. ,c> 1998 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION

The electromagnetic waves generated during return strokes of lightning discharges over a wide frequency range under suitable conditions penetrate the iono- sphere and propagate along geomagnetic field lines to the opposite hemisphere where they can be recorded by receiving systems. The waves propagating through the plasma medium are dispersed, high frequencies preceding the low frequencies, and the entire signals are called whistlers. The analysis of whistler dispersion yields information about the medium parameters such as electron density, total electron content of a flux tube (Park et al., 1978 ; Tarcsai et al., 1988 ; Sazhin rt al., 1992 ; Singh, 1993 ; Singh et al., 1993), electron temperature (Scarf, 1962; Guthart, 1965; Sazhin et cd., 1990, 1993), magnetic field and large scale con- vective electric fields (Block and Carpenter, 1974; Park, 1976, 1978 ; Singh, 1995).

The estimation of the parameters of the medium involves various assumptions about the wave propa- gation and about the medium. Some of these assump- tions are :

1. Whistler waves recorded on the ground propagate in a ducted mode or prolongitudinal mode along

Address for correspondence: Dr R. P. Singh, Banaras Hindu University, Atmospheric Research Laboratory, Department of Physics, Varanasi 221005, India. Tel: 0091 542 316801 x2371. Fax: 0091 542 317074.

2.

the geomagnetic field lines. The waves propagating in a non-ducted mode cannot reach the Earth’s surface due to reflection at the lower hybrid res- onance frequency (Kimura, 1985). Whistlers can simultaneously propagate along several ducts (Sazhin et a/., 1992). For field aligned propagation of whistler waves, the wavelength at any given wave frequency increases with decreasing altitude (as the wave travels from the equator towards the Earth’s surface). Due to the divergent nature of the geo- magnetic field, the duct width decreases with decreasing altitude. The wave leaks out from the duct wherever the wavelength becomes of the same order as the duct width (Strangeways, 1986). As a result of the combined effect of wavelength and duct width variations, there is a progressive leakage of downcoming ducted waves. After emerging from the duct the waves may either propagate to the receiving site in a non-ducted mode or penetrate the ionosphere and reach the observation site pro- pagating in the Earth-ionosphere waveguide. This mechanism also explains the observed high dis- persion of some whistlers recorded at low latitudes. The propagating whistler waves interact with ener- getic electrons in the plasmasphere. During such an interaction the wave amplitude may be amplified or attenuated depending upon the nature of the distribution function of the energetic electrons (Kennel and Petschek, 1966; Rycroft, 1991). It is assumed that the wave-particle interaction does not influence the whistler mode wave propagation. this

495

496 R. P. Singh, A. K. Singh and D. K. Singh

is violated only for a wave frequency near the elec- tron gyrofrequency. Usually the ground-received whistler wave frequency is less than half the mini- mum electron gyrofrequency along the field line. The non-linear interaction between electrons and the wave causes a deformation of the wave-packet and hence modifies the group velocity (Xu and Yeh, 1990). The effect of this deformation of the wave-packet on the group velocity is neglected, and it is assumed that

dw Q = dk

The plasma is considered to be cold ; i.e. the effect of the thermal velocity of the electrons on the wave propagation is neglected (thermal velocity << phase velocity of the wave). Further, it is assumed that

.r’:, >> .ffHe, where .L, fHp and f are the electron plasma frequency, electron gyrofrequency and wave frequency, respectively. However, in the esti- mation of electron temperature, we have relaxed this condition and have considered wave propa- gation through the thermal plasma. The geomagnetic field lines throughout the region of whistler wave propagation are assumed to be dipolar in nature. They may be deformed during a severe magnetic storm at higher L-values, but the deformation may not appreciably change the propagation time because the total path length is very large. The deformation at lower L-values is negligibly small. The electron density distribution along the field lines is represented by some kind of model (Helliwell, 1965); the most widely used models are diffusive equilibrium models proposed by Park (1972).

The dynamic spectra ofwhistler waves can be classi- fied as spectra containing :

1. initiating sferics and nose frequencies. 2. nose frequencies. 3. initiating sferics but no nose frequencies, and 4. neither nose frequencies nor initiating sferics.

The dynamic spectra of whistlers falling in the first category were initially exploited for the diagnosis of magnetospheric parameters (Allcock, 1959 ; Smith, 1960 ; Carpenter, 1962 ; Helliwell, 1965). For the other categories of whistlers, extrapolation methods have been proposed (e.g. Storey, 1957; Smith and Carp- enter, 1961; Brice, 1965 ; Dowden and Allcock, 1971; Bernard, 1973 ; Corcuff and Corcuff, 1973 ; Ho and Bernard, 1973; Sagredo et al., 1973; Smith et al., 1975; Tarcsai, 1985; Corcuff, 1977; Stuart, 1977).

Both the traditional methods and their extrapolations have been discussed and reviewed by Sazhin et al. (1992). In this paper, without going into the details of the diagnostic techniques, we present some results on the plasmaspheric parameters derived from the exploi- tation of whistler spectra recorded at low, mid and high latitude ground stations. The parameters dis- cussed are electron density, total electron content of a flux tube, electric field, duct properties, etc. The results are reported in the form of figures and tables followed by brief discussions.

2. RESULTS AND DISCUSSION

The form of whistler dynamic spectra is determined by the group delay time of the whistler wave pro- pagating at different frequencies from the source to the receiver. The magnetospheric parameters are derived by determining the nose frequency&, the cor- responding arrival time t, and inverting the integral (Singh et al., 1993)

ReL

t=2

(1)

where t is the time delay for each magnetospheric path, (b, is the geomagnetic latitude of the station above the ionosphere (reference height), +,, is the geo- magnetic latitude of the station, fp is the plas- mafrequency (proportional to the square root of the electron density n), ,&, is the equatorial electron gyr- ofrequency,f’is the wave frequency, L is the Mcllwain parameter, Re is the Earth’s radius and c is the velocity of light.

2.1. Variation of equatorial magnetic$eld

The nose frequency h ( = 0.37 fHr to 0.4 _&) of the whistler wave is used to determine the path of propagation (Helliwell, 1965 ; Sazhin et al., 1992). The present estimation of,f, has an accuracy of about 10%. for diffusive equilibrium,f;, = 0.38 fHI (Sagredo et al., 1973) ; Sazhin et al. (1990) estimated this multiplying parameter to vary between 0.38 and 0.40. The L value along which the whistler wave has propagated is given by

9.56 L=- .fJi$

(2)

where,f;,,, is measured in kHz. Thus, measuring the L

Plasmaspheric parameters derived from whistlers 497

value by using a direction finder (or any other tech- nique), variations in the equatorial magnetic field are studied (Park, 1975).

2.2. Electron dmsity in the plasnmspherr

The integral in eqn (1) can be evaluated by con- sidering some suitable model of the electron density distribution along the geomagnetic field line. From time to time, various models have been proposed such as the gyrofrequency model (electron density pro- portional to geomagnetic field), or diffusive equi- librium models (DE-l, DE-2, DE-3, DE-4) etc. (Sazhin et cd.. 1992). Most widely used are the diffusive equilibrium models, although more recent and modi- fied models incorporating temperature gradients which produce results consistent with satellite measurements (Strangeways, 1986) are available. The model with temperature gradients is complicated to handle and provides refinements to the available results. The effect of temperature gradients is more important at low latitudes as compared to mid/high latitudes.

tler analysis (Tarcsai et al., 1989). At low L-values (L < 2) there is an increasing tendency to under- estimate the electron densities whereas, for L > 2, the errors contribute little to the observed variations in ne,, and N, (total electron content in a flux tube). At low latitudes a substantial part of the whistler path lies in the ionosphere. Park (1972) gave an empirical formula to estimate the time delay due to the iono- spheric path, assuming that the maximum con- tribution comes from the F,-layer of the ionosphere. Usually part of the sub-ionospheric path at low lati- tudes lies in the Earth-ionosphere waveguide and a corresponding correction to the propagation delay should be taken into account. The correction would vary from event to event and can be evaluated only when the source location and ionospheric exit location from the duct are precisely known. At Varanasi such a facility does not exist. Hence, there is the possibility of a systematic error introduced into the data analysis of low latitudes in general and Varanasi station in particular.

In Table 1, the recent results of equatorial electron densities derived from whistler analyses are summar- ised. The variation of equatorial electron density as a function of L value for the whistlers recorded at different stations is shown in Fig. I. The electron den- sity sharply increases as the L value decreases. The average electron density derived from whistlers rec- orded at Tihani (Hungary) and Siple (Antarctica) are superimposed on each other, and show electron den- sity variations between 5 x lo4 electrons cm-’ and lo3 electrons cm-’ as the I!, value changes from 1.4 to 3.5. In the same figure we have presented the electron density derived from whistlers recorded at the low latitude station ofvaranasi (India) which has the same order of magnitude and the same trend. The Varanasi data belongs to moderate magnetic activity (Kp = 3- 4). Tihani data were divided into March to August (Summer) and October to February (Winter) periods. For L > 2.4, there is a lower density in summer than in the winter. Lichtenberger et al. (1991), analysing whistlers recorded on the Intercosmos 24 satellite, reported nrq between 520-400 electrons cmm3 as L changes between 3.40 and 3.65. Tarcsai et a/. (1988) have argued that, as a consequence of the difference between the magnetic and rotational axes of the Earth, the phenomenon depends not only on the magnetic latitude but also on longitude. In the absence of data from the eastern hemisphere, it is not possible to study longitudinal dependencies.

Errors are introduced in the determination of nt,q values due to unavoidable approximations in the whis-

2.3. Totul electron content along uflux tube

Considering the field aligned propagation of whis- tlers, the electron density distribution along the geo- magnetic field line is evaluated and used to estimate the total electron content in a flux tube of unit cross- sectional area at the reference height, which is written as

where B, is the magnetic field at the reference level, B, is the magnetic field at any other point s along the field line, and ds is elementary path length. In the analysis of mid and high latitude whistler data, the reference height is taken as 1000 km. For the analysis of low latitude whistler data, the reference height has been considered as 500 km (Singh et al., 1993). The above integral is evaluated and the variation of total electron content with I, value derived from whistler data is given in Fig. 2. The distribution of total elec- fron content with L-values derived from whistlers rec- orded at Tihani (October-February 1970-74) shows some scatter but is almost constant for L-values between 1.4 and 3.2. The data of Tihani recorded between March to August 1972275 shows a decrease with L values up to L = 2, and thereafter the total electron content increases with L-value. The Siple (1973) data shows an increasing trend for L values between 2.2 and 3.2. The total electron content derived from whistler data of Varanasi is of the same magni- tude, and shows a decreasing trend between L = 2.1

498 R. P. Singh, A. K. Singh and D. K. Singh

Table 1. Some results of equatorial electron density, neq

Station Results References

Varanasi L = 1.07

Nainital L = 1.12

Gulmarg L = 1.2

SofiaL=l.6

Tihany L = 1.8

Panska Ves

Poitiers Riga, L = 2.8

Kerguelen Eights

Hebrides L = 3.38

Kerguelen L = 3.7

Belgrano L = 4.5

Halley L = 4.3

Stanford L = 2

Siple, L = 4

Chilbolton L = 2.4

South Uist L = 3.4

The electron density linearly decreases from 5 x 10’ crnm3 at L = 2.1 to 1 x lo3 cme3 at L = 2.7 during magnetic storm periods (8-9 March 1991).

Singh, 1995

5.2 x lo4 cm-’ at L = 1.07 (during magnetic storm) on 19 March Singh et al., 1993 1977.

6.8 x IO4 cm-’ at L = 1.12 (during magnetic storm) on 25 March Singh et al., 1993; Lalmani et al., 1971. 1992 3 x 103-3 x 10’ cmm3 at L = 1.63.3 for whistlers recorded on Khosa et al., 1990; Lalmani et al. 18-19 April 1971 during quiet periods. 1996

7.3 x IO4 cm-’ at L = 1.2 (during magnetic storm) on 6 February Singh et al., 1993 1986

(3.74.9) x 10’ cm-j during night time and (6.5-8.0) x IO3 cm-3 during day time at L - 1.8.

Electron density decreases from 2.0 x IO4 cmm3 -5 x 10’ crnm3 at L = 1.4 to 3.2. Day to day filling of the plasmasphere after magnetic disturbances continues for several days without exhibiting saturation.

neq decreases from 3 x lo2 to 3 x 10’ cm-’ at L = 2.0 to 2.75

Method proposed by Ho (1974) and modified by Corcuff (1977) gives the maximum accuracy in the determination of equatorial electron density.

3.3 x 10’ cm-’ has been observed at L = 3.3 (Scotland)

ncq at L = 3.54.0 decreases from 5.5 x lo2 to 3.0 x lO*cm-’ at the beginning of storm, neq determined from whistler observation is compared with in situ measurements onboard GEOS- 1

Evening plasmaspheric bulge at LT - 19 h 30 m and L = 4.8 has been observed. Equatorial electron density at L = 4.56 is 220 cme3 and total electron content is 3.52 x 1On electrons cm-’ tubee’.

log neq decreases almost linearly from lo1 to 10’ cm-j with increasing L from 2.5 to 6.0.

Diurnal variations of neq at L > 3.5 are small as compared with storm variations. Significant amount of plasma from the plasmasphere is dumped into the ionosphere during magnetospheric disturbances

Plasmapause is observed at L = 3.4, neq decreases from 10’ to 0.9 cme3 on 8 March 1970, 17.03 UT, Kp = 8.

Plasmapause is observed at L = 5.0, tzeq decreases from 4 x lo* to 10’ cm-’ on 2 July 1970, 19.45 UT, Kp = 1. It is shown that ncq at L - 5 are reduced by a factor - 2.2 and - 1.3, when the effects of intense and weak ring currents are taken into account.

Ralchovski, 1976

Tarcsai et al., 1988

Tarcsai, 1985

Jiricek & Tarcsai, 1980

Corcuff et al., 1977

Rycroft, 1973

Corcuff and Corcuff, 1982

Lester and Smith, 1980

Hamar et al., 1992

Park et al., 1978

Park, 1973

Mathur and Rycroft, 1972

Mathur and Rycroft, 1972.

Plasmaspheric parameters derived from whistlers 499

m- ‘E 1oooc s

I I 1 I / I

1.2 1.4 1.8 1.8 2 2.2 2.4 2.8 2.8 3 3.2 3.4 3.8

L-VALUE Fig. 1. Variation of electron density (cm-‘) with L-value.

X Varanad(Mar.91) + Tlhany(Oct-Feb70-74

= Tlhany(Mar-Aug72-75)

0 Siple(1973)

+ t t

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 L-VALUE

Fig. 2. Variation of electron content (electrons cmm2 tube-‘) in a flux tube with L-Value

500 R. P. Singh, A. K. Singh and D. K. Singh

and 2.7. In spite of the rapidly decreasing volume of the geomagnetic flux tubes, the increase in N, at lower L-values is unrealistic and can be explained by the electron density enhancement of the ducting struc- tures above the ambient electron density. The analysis of whistlers always yields the electron density of the ducting structures. At L > 2, density enhancements - 10% are sufficient to duct whistlers, whereas at low latitudes (L < 2.0) enhancement factors of - 100% are required for the ducted propagation of whistlers (Singh and Tantry, 1973; Tanaka and Hayakawa, 1985). Hence, there is an overestimation of the elec- tron density and total electron content in a flux tube from the analysis of whistler data recorded at low latitudes.

Analysing whistler data recorded at low latitude Indian stations, Indian scientists (Lalmani et ul., 1992, Singh et al., 1993, Singh and Singh, 1997) have reported that the total electron content in a flux tube - 10” electrons cm-’ tubee’ during a magnetic storm period (Kp > 4). The estimated ionization flux trans- ported downward is of the order of 10” electron cm-’ sect ‘, Singh et al. (1993) have also argued on the basis of reported data that the downward transported flux increases with an increase in magnetic activity, which clearly supports the idea that large magnetic activity causes a movement of the plasmapause closer to the surface of the Earth. Park et ul. (1978) have shown that during magnetic disturbances the size of the plas- masphere is reduced and the density levels are also reduced inside the smaller plasmasphere. Recently, Lalmani et (11. (1996) analysing quiet time whistlers reccrded at Nainital (geomagnetic latitude = 19^ N), reported electron tube contents - 10” electrons cm-l tubee’ and a downward transported flux - IO8 elec- trons cm.-’ sect’, which is in close agreement with values reported by others (Andrews, 1980 ; Poulter et al., 1981a, b; Saxton and Smith, 1989).

Andrews (I 980) analysing whistler mode signals received at New Zealand transmitted from the NZK transmitter in Seattle (USA), reported a downward radial plasma drift near L = 2.3 in the late evening hours to be (l-3) x IO’ electrons cm-’ sec.‘. Poulter et ul. (1981a, b) using data from the ATS-6 satellite bea- con experiment showed a downward transported flux (0.883.0) x IO* electrons cm-* sect’ during night hours and an upward flux (0.83.0) x IO8 electrons cm-’ set’ in the daytime for quiet periods. Saxton and Smith (1989) used whistler mode signals from VLF transmitters NAA and NSS in the North East USA and deduced a transported flux - (l-3) x 10’ electrons cm-’ set’ near L = 2.5 during quiet periods. Plasma fluxes have also been reported from incoherent scatter radar data (Evans, 1975; Evans

and Holt, 1978; Vickrey et ul., 1979) but it is not meaningful to compare these results with the results derived from whistler data (Saxton and Smith, 1989).

Park (1973) analysed whistlers recorded at a net- work of stations extended from L = 2 to 6 before, during and after substorms and showed that the total electron content in a flux tube before the substorm increased with L value up to L = 4 and then became almost constant. The tube content clearly showed a large depression beyond L - 2.7 after the substorm. Further, he concluded that before the substorm the plasmasphere was relatively full and smoothly vary- ing, and that there was no evidence of large scale irregularities in the plasma distribution. Immediately after the substorm onset, the plasmaspheric tubes in the forenoon sector were convected inward across L shells and drained rapidly through the ionosphere. The estimated downward flux was 10’ electrons cm-* set’. This is corroborated by ionosonde records showing an enhancement of,f;,F? during the substorm (Park, 1973). Tarcsai (1985) showed a diurnal vari- ation of the total electron content by analysing whis- tlers recorded at Tihani. He showed that the day to day filling of the plasmasphere after magnetic dis- turbances continues for several days, without exhi- biting saturation, with higher filling rates for lower values of average K,.

2.4. Electric field

The nose frequency derived from whistler spec- trograms specifies the path of whistler wave propa- gation in terms of L-value. Thus, measuring the nose frequency f;, for successively recorded whistlers, the variation of L with time in the equatorial plane is determined. Using the “frozen in field” concept, the plasma drift velocity derived from whistler data is related with the magnetospheric plasma drift caused by a large scale East&West electric field E. For dipolar magnetic fields, E is given by (Bernard, 1973 ; Block and Carpenter, 1974).

E = 2.07 x lO~‘ddlf3’ Vm-’ (4)

where ,fti is the whistler nose frequency measured in Hz. For &,/dt > 0, E is directed from East to West. In an active period (> 15 minutes), if a large number of whistlers are analysed then E can be determined with a precision of typically 0.1 mV mm’ (Carpenter et al., 1972; Sagredo et ul., 1973). The estimation of the E field is independent of the assumed electron distribution along the field lines. The whistler wave technique has been widely used to measured the East- West component of electric fields during substorm

Plasmaspheric parameters derived from whistlers

Table 2. Results of equatorial electric fields, E

501

Stations Results

Varanasi L = 1.07 0.24.3 mV mm’ westward field during post-midnight was observed at L = 2.1-2.7 (substorm). 0.1L0.3 mV mm’ westward field in the post-midnight sector is reported (substorm)

Nainital L = 1.12

Gulmarg L = 1.2

SofiaL= 1.6

Sanae L = 4.0

Siple L = 4.0

Siple L = 4.0

Eights L = 4.0

Eights L = 4.0

Roiberval L = 4.0

References

Singh, 1995

Khosa et al., 1982

0.3 mV mm’ eastward in pre-midnight and 0.330.5 mV mm’ westward in post-midnight sector at L = 1.12 is observed (substorm).

Khosa et al., 1982

0.1L0.5 mV mm’ westward in post-midnight at L = 1.12 and plasma drift towards smaller L-value is reported (substorm).

Mishra rt al., 1980

Substorm data show 0.3-0.7 mV mm’ eastward field in pre- midnight and 0.24.7 mV mm’ westward in post-midnight at L = 1.2.

Khosa et al., 1982

0.44-0.54 mV mm’ eastward field at L = 1.8&2.3 during Ralchovski, 1981 15:OO h < LT < 18:OO h is observed. Plasma drifted towards larger L values.

Westward field on quiet days during postnoon period vary as Lm4 in the equatorial plane. The variation confirms the ionospheric dynamo origin of this field.

Rash er al., 1986

0.1 mV mm’ westward field on quiet days at L = 4. The field Carpenter, 1978 varied as L 3’2, supported the concept that the observed electric fields originated in an ionospheric dynamo process. 0.2 mV mm’ eastward at L = 3.555.0 during Park, 1976 16:OO h < LT < 20:00 h is observed. It appeared during substorm onset within the accuracy of 10 min.

0.2 mV mm’ eastward in pre-midnight sector and 0.2- Park, 1978 0.6 mV m ’ westward in post-midnight sector during moderate substorms is observed. During quiet times, 0.05 mV rn-’ eastward field has been observed in the whole night time magnetosphere.

0.05 mV mm’ westward field during quiet periods at L = 3.5-5.0 Carpenter and Seely, 1976 and LT - 00.00 h is observed. 0.1-O. 15 mV mm’ westward fields at LT - 12:OO h are also reported.

0.2 mV mm1 eastward field between 07:00-12:OO LTand Saxton and Smith, 1989 westward field between 15:00-22:00 h LT is reported. The fields were thought to be due to ionospheric dynamo. The electric field induced by a rapidly decaying storm time ring Wang and Kim, 1972 current is in good agreement with that deduced from whistler duct studies.

periods as well as during quiet times (Carpenter and Stone, 1967 ; Park and Carpenter, 1970 ; Carpenter and Akasofu, 1972 ; Carpenter et al., 1972 ; Block and Carpenter, 1974 ; Rycroft, 1974 ; Carpenter and Seely, 1976; Park, 1976, 1978 ; Carpenter, 1978 ; Andrews et al., 1978 ; Andrews, 1980 ; Mishra et al., 1980 ; Khosa et al., 1982; Lalmani, 1984; Rash et al., 1986; Saxton and Smith, 1989; Singh, 1995). The main results are summarised in Table 2. From this table it is evident

that the quiet time electric fields usually lie between 0.05 mV m-’ and 0.15 mV me’, whereas, during sub- storm periods, fields up to 0.7 mV mm’ are observed. The fields during the post-midnight period are usually westward and are associated with cross-l inward drift of plasma.

Carpenter (1978) using whistler data recorded on four consecutive magnetically quiet days (4-7 July 1973) estimated a westward electric field of

502 R. P. Singh, A. K. Singh and D. K. Singh

0.1 mV mm ’ at L = 4 and argued that the electric field decreased as L-“‘. The data strongly supported the concept that the observed electric fields originated at middle to low latitudes, apparently in an ionospheric dynamo process (Carpenter, 1978 ; Saxton and Smith, 1989). The estimated electric field is based on the assumption that the geomagnetic field is dipolar, which is valid as long as the ring current is weak and magnetic conditions quiet. During storm sudden commencements, substorm expansion and recovery phases, there is a deviation from the dipolar nature of the geomagnetic field and, hence, systematic errors in the estimation of electric field are introduced. Block and Carpenter (1974) have discussed this problem at length and have shown that

where K, = 0.94 x lO~“‘THz-‘. In the above equation the second term is a correction to the estimated field. Block and Carpenter (1974), assuming a nearly dipolar fieldno potential fields and a uniform tem- poral change in the geomagnetic field at the equator, showed that the corrected field simply involves a reduction in scale of the order of 40% from the uncor- rected value. Contrary to this, the model calculations of Wang and Kim (1972) revealed that the electric field induced by a rapidly decaying storm time ring current is in good agreement with that deduced from whistler duct studies. This implies that no correction is required. A similar conclusion was reported by Singh (1995) using whistler data recorded at Varanasi.

2.5. Duct properties

The propagation of whistler waves in the ducted mode along geomagnetic field lines reveals the wavy structure of the ionization density in the mag- netosphere (Storey, 1952 ; Smith, 1960, 1961 ; Singh, 1993). Although, the direct verification of duct struc- ture has yet to be made, there are ample direct (Smith and Angerami, 1968 ; Cerisier, 1974 ; Park and Carp- enter, 1970 ; Carpenter et al., 198 1 ; Koons, 1989) and indirect (Somayajulu and Tantry, 1968 ; Angerami, 1970 ; Park, 1970 ; Hayakawa and Iwai, 1975 ; Ondoh, 1976; Hayakawa et al., 1983 ; Lalmani, 1984; Wang and Wang, 1984 ; Singh et al., 1994) evidences to sug- gest the existence of ducts. The morphology of the ducts, in particular their size and relative enhancement of electron density are not very well known at present (Cerisier, 1974; Strangeways, 1981a, b; 1982). Infor- mation about the duct width is derived by measuring the diffuseness of the whistler trace (Somayajulu and Tantry, 1968 ; Singh et al., 1996) whereas duct lifetime

is determined from the dispersion analysis and power spectrum analysis of occurrence data (Okuzawa et al., 1971 ; Shimakura et al., 1991 ; Singh, 1995). Table 3 summarizes information about duct width, duct life- times and enhancement factors.

Duct lifetime usually varies between 30 minutes and 2 hours, although duct lifetime can be as high as 4 hours (Shimakura et al., 1991) and 1 to 2 days (Tanaka and Hayakawa, 1973). Somayajulu et al. (1972) and Singh et al. (1994) have discussed the formation, growth and decay of additional ducts during magnetic storm periods. They showed that while it might require 30 minutes or less for a duct to form it takes 3 hours to grow to its full size. Okuzawa et al. (1971) suggested that duct formation and decay occur much more rapidly (within 30 minutes) and that the cycle of formation and decay is continuous. Further, it has also been suggested that a number of ducts may exist simultaneously. Ducts occupy a relatively small vol- ume (-0.01%) in the magnetosphere (Burgess and Inan, 1993).

Hayakawa (1990) estimated an enhancement factor AN, = IO-15% of whistler ducts at medium latitudes on the basis of the properties of the Earth-ionosphere waveguide propagation of whistlers after their iono- spheric transmission. Sonwalker et al. (1994) have reported the first direct evidence of a magnetospheric duct at L = 2.94 while studying whistler wave signals transmitted from the Khabarovsk transmitter (15.0 kHz, geomagnetic latitude 48 N, geomagnetic longitude 135 ’ E) and observed on the COSMOS 1809 satellite. The duct width at the equator was - 367 km and AN, - 10-l 3%. They measured the wave fields inside the ducts and showed that the duct end points could extend down to at least - 1000 km. The other satellite measured results are : duct width D - 400 km near L = 3.0 (Smith and Angerami, 1968) D = 223- 230 km and AN,. = 622% for L = 4.14.7 (Ang- erami, 1970) D = 68-850 km and AN, = 1040% for L = 3.1-3.5 (Scarf and Chappell, 1973) D = 630- 1260 km and AN, d 30% between L = 4.0 and L = 5.0 (Carpenter et al., 1981), and D = 500 km and AN, - 40% (Koons, 1989). Clilverd et al. (1996) have recorded whistler mode signals simultaneously at Faraday, Antarctica (65” S, 64” W) and Dunedin, New Zealand (46” S, 171” E) that have propagated in the same duct after transmission from a single VLF trans- mitter operated by US Navy. To explain the observed power, the cross-sectional area of the duct is assumed to be 1 x lo9 m2 (Dowden and Adams, 1993 ; Burgess and Inan, 1993). Vero et al. (1997) analysing whistlers recorded at Tihany, Hungary and geomagnetic pul- sations recorded at Nagycenk observatory (L -2) have discussed similarities and differences between

Plasmaspheric parameters derived from whistlers

Table 3. Results related with plasmaspheric ducts

503

Station Results References

Varanasi L = I .07 Power spectrum analysis of the whistler data yields 70-80 min Singh, 1995 as duct life time. Simultaneous presence of a number of ducts is also proposed The data analysis also yields 50 min for the growth/decay of ducts.Khosa ef al., 1983

Gulmarg L = 1.2 It takes much less than 30 min for duct formation. Duct grows Somayajulu and Tantry, 1968 to its full size within 3 hours and it may persist for 2-3 days, The duct width for 5 kHr varies from 15 to 25 km for normal days and from 40 to 180 km for magnetically disturbed days. Duct width during magnetic storm period (8 February 1986) lie Singh et al., 1996 in the range of 5&200 km.

Power spectrum analysis yields duct lifetimes of the order of 1 h. Rao and Lalmani, 1975

Duct lifetime is of the order of 50 min. Electric field plays dominant role in duct formation which is found to be - 0. l- 0.7 mV mm’.

Lalmani, 1984

Gulmarg Nainital

Gulmarg

Nainital Varanasi

Moshiri L = I .6 Spectrum analysis of the data yields cyclic occurrence of whistler Simakura et al., 1991 ducts of 2 h and 4 h.

Moshiri L = I .6 Ducts are formed in less than 1 h and they may persist for the Hayakawa et al., 1983 same time period. The distribution of occurrence data suggests successive growth and decay of ducts.

Kagoshima L = I .22The apparent lifetimes of ducts are found to be l-2 h. Hayakawa et al.. 1981 Ohgata L = 1.25

Moshiri L = 1.6

Sakusima L = 1.28

Okinawa L = 1.12

Ceduna Austraha L = 1.93

Sanae Halley Duct life as short as 30 min is reported and its constraints on L = 4.24 duct formation mechanism is discussed.

Belsk L = 2.25

Wellington L = 2.15

Duct belt localized at L close to L = 2.7 has been observed. Krainski, 1977

Most of the whistlers propagated along ducts localized at Stuart, 1977 L = 2.2663.6. Propagation is favoured at larger L during winter time and at smaller L during equinox period.

Campbell Island Scott Base L = 34.27

Temporal movement of the ducts have been demonstrated. The simultaneous presence of few ducts at the same latitude is also seen.

Whistler observation during and after the storm period suggests Tanaka and Hayakawa, 1973 duct life of the order of l-2 days. Duct width for the enhancement factors of 0.25 and 0.5 varies between 25 and 200 km.

Duct life is of the order of 2 h. Numerical computation suggests Ondoh et al., 1979 (A N/N) of the -0.27 for whistler trapping which may be produced by 0.29 mV m -’ electric field. Duct formation and decay is a cyclic phenomenon. The whistler ducts extend downward below the height of maximum ionospheric electron density for the low latitude ground whistlers.

Nakamura, I993

Mid latitude ducts are characterized either by the ducts lying at Takahashi et al., 1993 the same latitude or by a sheet like structure including some structures acting as ducts. The duct separation in the meridional direction is - 500 km.

Hansen P/ crl., 1983

504 R. P. Singh, A. K. Singh and D. K. Singh

whistler ducts and geomagnetic L-shells and have con- cluded that whistler ducts and geomagnetic field line shells are closely connected with each other within the magnetosphere. Takahashi et al. (1993) have also discussed the similarity in structure and extent of whis- tler ducts and L-shells.

The normal spectrogram of a whistler when ana- lysed by a matched filtering technique produces dynamic spectra with higher resolution in both fre- quency and time and usually many fine structure com- ponents are seen (Lichtenberger et al., 1991 ; Hamar et ul., 1992). These results indicate the existence of a number of fine structure ducts within a broader duct. Based on a ray tracing study, Strangeways (1982) showed that rays first trapped in the main duct at low altitude may be further trapped within fine structure enhancements at higher altitudes. From ray tracing calculations for normal whistlers observed at L = 4, Strangeways (1991) concluded that the ducts should have considerable fine structure which results in tigh- ter (second-degree) trapping in the equatorial region and that the enhancement factor should increase by about an order of magnitude along their path length from low altitude to the equatorial plane. Laird (1992) suggested that the fine structure seen in the whistler spectrum could be due to multi-mode propagation inside the duct.

ation or propagation effects. Guthart (1965), includ- ing the effect of thermal electrons in the group velocity, evaluated the change in whistler spectra rec- orded at Eights (L = 4) near the upper cutoff fre- quency and estimated the magnetospheric electron temperature - 1.7 eV (- 2 x IO6 K). Analysing whis- tlers recorded at Sanae (L = 4) McChesney and Hughes (1983) showed that the temperature increased from 1500 K at L = 3 to 3000 K just inside the plas- mapause. Comparing theoretical and experimental whistler dispersion curves in the vicinity of plas- mapause, Kobelev and Sazhin (1983) obtained elec- tron temperatures in the range 7-19 eV, depending upon the model of electron density distribution along the field lines used in the computations. considering thermal corrections to the group delay time and using diffusive equilibrium models (DE-l, 2, 3,4), Sazhin et al. (1990, 1993) analysing whistlers recorded at Halley (L = 4.3) estimated the electron temperature to be below 4 eV and showed its dependence on the choice of electron distribution model. The possible error in the temperature was of the order of or larger than the value of the temperature itself. The above method is based on the fact that the thermal corrections to group delay time are largest at frequencies close to the upper cut-off frequency and negligible elsewhere (Sazhin et al., 1992).

The various duct formation mechanisms are: (a) electric field mechanism, (b) electron precipitation mechanism, and (c) protonosphere-ionosphere coup- ling mechanism. Out of these the most probable mech- anism is that involving localized electric fields which produces an E x B drift of flux tubes. Park and Hel- liwell (1971) showed that an electric field of 0.1 mV mm ’ in the equatorial plane near L = 4 can modulate the plasma, giving rise to enhancements and depressions of density of the order of 5% in 30 minutes. These enhancements are large enough to trap whistler waves. The source of the electric field could be a thundercloud electric field (Park and Dejnakarintra, 1973), or the electrostatic polarization field in the ionosphere due to an unsymmetrical wind, etc. Park and Helliwell ( I97 I) have suggested thundercloud electricity as a possible source of electric fields in the magnetosphere to produce irregularities.

3. CONCLUSION

2.6. Electron temperature

The results relating to electron density, electric field and morphological feature of ducts are summarised in Tables l-3. In addition, some results related to the total electron content in a flux tube, down- ward/upward transport of flux, electron temperatures, etc., are also discussed. The estimation of electron temperature based on thermal correction faces some problems due to the omission of some terms which are of same magnitude as the thermal correction (Sazhin et al., 1992). Further, the uncertainty of the models of the electron density distribution along field lines causes uncertainty in the estimation of electron temperature (Sazhin et al., 1993). Hence the whistler technique in its present form is not suitable for elec- tron temperature measurements in the plasmasphere. Theoretical and experimental developments have to be made before the technique could be used.

Considering the upper cutoff frequency of the nose The duct lifetime, duct width and enhancement fac- whistler to be due to thermal attenuation, Scarf (1962) tors are also summarised. Information about duct and Liemohn and Scarf (1962, 1964) attempted to structure and its distribution in the magnetosphere is determine the electron temperature. The method was lacking. Matched filtering techniques may give some not widely used because it is difficult to distinguish information about fine structure of the ducts. More whether the upper cutoff was due to thermal attenu- studies are required in this direction. Whistler mode

Plasmaspheric parameters derived from whistlers 505

propagation through a complex duct structure should be carried out to understand the fine structure spec- trum of whistler waves obtained from the matched filtering technique.

technique is essential so that the magnitude of the error could be decreased.

The electron density derived from whistler measure- ments compares well with direct rocket/satellite measurements. The study of latitudinal/longitudinal distribution of electron density and its long term vari- ations using rockets/satellites becomes financially and technically improbable, whereas the same can be stud- ied very readily by whistler measurements using a network of stations equipped with identical equip- ment spread over a range of latitudes and longitudes. The temporal evolution of fluctuations in the ion- ization density of the plasmasphere and its finer struc- tural details can be studied by improving the registering and analysis techniques of whistler waves. At low latitudes, arrival directions and polarization measurements are essential : efforts should be made in this direction.

The total electron content in a flux tube and its time development yields the upward/downward movement of ionization flux, which provides a tool to study the coupling of ionosphere and plasmasphere. Plasma flows between the ionosphere and plasmasphere are of importance as most of the ionization in the plas- masphere originates in the ionosphere, whilst down- ward flows of plasma may contribute to the maintenance of the nocturnal ionosphere (Bailey et al.. 1987). Experimental measurements seem to be lag- ging behind theory and model computations in the study of the interchange of cold plasma between the ionosphere and the plasmasphere. Coupling fluxes have mainly been inferred from incoherent scatter observations (Evans. 1975) topside soundings and satellite beacon measurements (Poulter et a/., 1981a, b). As compared to these methods, whistlers represent an inexpensive and most effective method for obtain- ing coupling electron fluxes and hence the study of ionosphere-plasmasphere coupling. Coordinated work at a chain of stations spread over a range of latitudes and longitudes is required to have a complete picture of plasmasphere dynamics.

The electric field is an important parameter in the study of the coupling of the ionosphere and the plas- masphere. Out of various techniques developed to measure plasmaspheric electric fields, the whistler wave technique, based on cross-l plasma drifts in the equatorial plane, has been widely used to evaluate the East-West component of electric fields. In this method, only information about the Whistler path is required, the longitudinal position within the viewing area is unimportant. The error involved is of the same order as the existing field and hence a refinement of

Acknowledgements-The authors are grateful to Department of Science and Technology (DST). Government of India for partial financial support through a research project. We are grateful to the referees for their fruitful and critical sugges- tions.

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