Plasmaspheric parameters as determined from whistler spectrograms: a review

Journal

Pergamon

of Amospher;r

and

Solar-Trrwsrnal

PII : Sl364-6826(98)00001-7

Ph>srcs, Vol. 60, No. 5, pp. 495-50X, 199X c’ 1998 ElsewerScienceLtd 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

1997, and accepted 19 Drcember

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.

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 resonance 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 geomagnetic 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 propagating in the Earth-ionosphere waveguide. This mechanism also explains the observed high dispersion of some whistlers recorded at low latitudes. 2. The propagating whistler waves interact with energetic 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

1. INTRODUCTION The electromagnetic waves generated during return strokes of lightning discharges over a wide frequency range under suitable conditions penetrate the ionosphere 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 convective 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 propagation and about the medium. Some of these assumptions 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. 495

496

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

is violated only for a wave frequency near the electron gyrofrequency. Usually the ground-received whistler wave frequency is less than half the minimum 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

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 exploitation of whistler spectra recorded at low, mid and high latitude ground stations. The parameters discussed 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.

dw Q = dk 2. RESULTS AND DISCUSSION

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 >.ffHe, where .L, fHp and f are the electron plasma frequency, electron gyrofrequency and wave frequency, respectively. However, in the estimation of electron temperature, we have relaxed this condition and have considered wave propagation 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 fied as spectra containing : 1. 2. 3. 4.

waves can be classi-

initiating sferics and nose frequencies. nose frequencies. initiating sferics but no nose frequencies, and 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 Carpenter, 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).

The form of whistler dynamic spectra is determined by the group delay time of the whistler wave propagating at different frequencies from the source to the receiver. The magnetospheric parameters are derived by determining the nose frequency&, the corresponding 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 geomagnetic latitude of the station, fp is the plasmafrequency (proportional to the square root of the electron density n), ,&, is the equatorial electron gyrofrequency,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 L=-

9.56 (2) .fJi$

where,f;,,,

is measured

in kHz. Thus, measuring

the L

497

Plasmaspheric parameters derived from whistlers value by using a direction finder (or any other technique), 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 considering 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 proportional to geomagnetic field), or diffusive equilibrium 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 modified 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. In Table 1, the recent results of equatorial electron densities derived from whistler analyses are summarised. 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 density sharply increases as the L value decreases. The average electron density derived from whistlers recorded at Tihani (Hungary) and Siple (Antarctica) are superimposed on each other, and show electron density 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 = 34). 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-

tler analysis (Tarcsai et al., 1989). At low L-values (L < 2) there is an increasing tendency to underestimate 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 ionospheric path, assuming that the maximum contribution comes from the F,-layer of the ionosphere. Usually part of the sub-ionospheric path at low latitudes 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. 2.3. Totul electron content along uflux

tube

Considering the field aligned propagation of whistlers, the electron density distribution along the geomagnetic field line is evaluated and used to estimate the total electron content in a flux tube of unit crosssectional 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 elecfron content with L-values derived from whistlers recorded 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 magnitude, 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

Station

electron

density,

Results

Varanasi

L =

References

1.07 The electron density linearly decreases from 5 x 10’ crnm3 at

Singh,

L = 2.1 to 1 x lo3 cme3 at L = 2.7 during magnetic storm periods (8-9 March 1991). 5.2 x lo4 cm-’ at L = 1.07 (during magnetic storm) on 19 March 1977. Nainital

L = 1.12

Gulmarg

L = 1.2

SofiaL=l.6

Tihany

Singh et al., 1993

Singh et al., 1993; Lalmani et al., 1992 Khosa et al., 1990; Lalmani et al. 1996

7.3 x IO4 cm-’ at L = 1.2 (during 1986

Singh et al., 1993

magnetic

storm) on 6 February

x IO3 cm-3

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

Panska

Ves

neq decreases

Poitiers

Riga,

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

L = 2.8

1995

6.8 x IO4 cm-’ at L = 1.12 (during magnetic storm) on 25 March 1971. 3 x 103-3 x 10’ cmm3 at L = 1.63.3 for whistlers recorded on 18-19 April 1971 during quiet periods.

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

L = 1.8

neq

Ralchovski,

Tarcsai

1976

et al., 1988

Tarcsai,

1985

Jiricek & Tarcsai,

(1977)

Corcuff

1980

et al., 1977

Kerguelen Eights Hebrides Kerguelen

Belgrano

L = 3.38 L = 3.7

L= 2

Siple, L = 4

Chilbolton

at L = 3.3 (Scotland)

Rycroft,

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

at

Corcuff

1973 and Corcuff,

1982

L = 4.5

Halley L = 4.3

Stanford

3.3 x 10’ cm-’ has been observed

L = 2.4

South Uist L = 3.4

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 increasing L from 2.5 to 6.0.

from lo1 to 10’ cm-j

Hamar

1980

et al., 1992

Park et al., 1978

with

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

Lester and Smith,

with

Park,

1973

Mathur

and Rycroft,

1972

Mathur Plasmapause is observed at L = 5.0, tzeqdecreases 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.

and Rycroft,

1972.

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

from 10’ to

Plasmaspheric

parameters

derived from whistlers

499

m-

‘E 1oooc s

I

1.2

I

1.8

1.4

I

/

2.8

2.8

1

1.8

2

2.2

2.4

I

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)

+

1.2

1.4

t

1.6

t

1.8

2

2.2

2.4

2.6

2.8

3

3.2

L-VALUE Fig. 2. Variation

of electron

content

(electrons

cmm2 tube-‘)

in a flux tube with L-Value

3.4

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 structures 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 electron 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 transported 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 plasmasphere 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 electrons 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 beacon 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’ near L = 2.5 during quiet electrons cm-’ set’ 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 network 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 varying, 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 variation of the total electron content by analysing whistlers recorded at Tihani. He showed that the day to day filling of the plasmasphere after magnetic disturbances continues for several days, without exhibiting saturation, with higher filling rates for lower values of average K,. 2.4. Electric field The nose frequency derived from whistler spectrograms specifies the path of whistler wave propagation 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 EastWest component of electric fields during substorm

Plasmaspheric

parameters

derived

Table 2. Results of equatorial Stations Varanasi

Nainital

Gulmarg

SofiaL=

electric fields, E References

Results L = 1.07

L = 1.12

L = 1.2

1.6

501

from whistlers

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

Singh,

was

Khosa et al., 1982

sector is

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). 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

Khosa et al., 1982

Substorm data show 0.3-0.7 mV mm’ eastward field in premidnight and 0.24.7 mV mm’ westward in post-midnight at L = 1.2. 0.44-0.54 mV mm’ eastward field at L = 1.8&2.3 during 15:OO h < LT < 18:OO h is observed. Plasma drifted towards L values.

1995

Ralchovski,

1981

larger

Sanae L = 4.0

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

Siple L = 4.0

0.1 mV mm’ westward field on quiet days at L = 4. The field 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 16:OO h < LT < 20:00 h is observed. It appeared during substorm onset within the accuracy of 10 min.

Carpenter,

Park,

1976

0.2 mV mm’ eastward in pre-midnight sector and 0.20.6 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.

Park,

1978

Eights L = 4.0

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

Carpenter

Roiberval

0.2 mV mm1 eastward field between 07:00-12:OO LTand westward field between 15:00-22:00 h LT is reported. The fields were thought to be due to ionospheric dynamo.

Saxton

The electric field induced by a rapidly decaying storm time ring current is in good agreement with that deduced from whistler

Wang and Kim, 1972

Siple L = 4.0

1978

Eights L = 4.0

L = 4.0

and Seely, 1976

and Smith,

1989

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 substorm 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 temporal 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 uncorrected 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 magnetosphere (Storey, 1952 ; Smith, 1960, 1961 ; Singh, 1993). Although, the direct verification of duct structure has yet to be made, there are ample direct (Smith and Angerami, 1968 ; Cerisier, 1974 ; Park and Carpenter, 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 suggest 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). Information 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 lifetimes 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 volume (-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 ionospheric 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 = 223230 km and AN,. = 622% for L = 4.14.7 (Angerami, 1970) D = 68-850 km and AN, = 1040% for L = 3.1-3.5 (Scarf and Chappell, 1973) D = 6301260 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 transmitter 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 pulsations recorded at Nagycenk observatory (L -2) have discussed similarities and differences between

Plasmaspheric Table 3. Results Station

parameters

related with plasmaspheric

ducts References

Results

Varanasi

I .07

L =

Gulmarg

1.2

L =

503

derived from whistlers

Singh, Power spectrum analysis of the whistler data yields 70-80 min 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

1995

ef al., 1983

It takes much less than 30 min for duct formation. Duct grows 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 in the range of 5&200 km.

Somayajulu

Gulmarg Nainital

Power spectrum

Rao and Lalmani,

Gulmarg

Duct lifetime is of the order of 50 min. Electric field plays dominant role in duct formation which is found to be - 0. l0.7 mV mm’.

Lalmani,

1984

Simakura

et al., 1991

analysis

yields duct lifetimes of the order of 1 h.

and Tantry,

1968

Singh et al., 1996

1975

Nainital Varanasi Moshiri

L =

I .6

Spectrum analysis of the data yields cyclic occurrence 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 same time period. The distribution of occurrence data suggests successive growth and decay of ducts.

of whistler

Kagoshima L = I .22The apparent lifetimes of ducts are found to be l-2 h. Ohgata L = 1.25 Temporal movement of the ducts have been demonstrated. simultaneous presence of few ducts at the same latitude is also seen. Moshiri

L = 1.6

Hayakawa

et al., 1983

Hayakawa

et al.. 1981

The

Whistler observation during and after the storm period suggests 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.

Tanaka

Duct life is of the order of 2 h. Numerical computation suggests (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.

Ondoh

Ceduna Austraha L = 1.93

Mid latitude ducts are characterized either by the ducts lying at 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.

Takahashi

Sanae Halley

Duct life as short as 30 min is reported and its constraints duct formation mechanism is discussed.

Hansen

L = 4.24

Belsk L = 2.25

Duct belt localized

Sakusima

Okinawa

L = 1.28

L = 1.12

Wellington L = 2.15

Campbell Island Scott Base L = 34.27

on

at L close to L = 2.7 has been observed.

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

L = 2.2663.6.

and Hayakawa,

et al., 1979

Nakamura,

Krainski, Stuart,

I993

et al., 1993

P/ crl., 1983

1977 1977

1973

504

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

whistler ducts and geomagnetic L-shells and have concluded 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 whistler ducts and L-shells. The normal spectrogram of a whistler when analysed by a matched filtering technique produces dynamic spectra with higher resolution in both frequency and time and usually many fine structure components 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 tighter (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. The various duct formation mechanisms are: (a) electric field mechanism, (b) electron precipitation mechanism, and (c) protonosphere-ionosphere coupling mechanism. Out of these the most probable mechanism is that involving localized electric fields which produces an E x B drift of flux tubes. Park and Helliwell (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. 2.6. Electron temperature Considering the upper cutoff frequency of the nose whistler to be due to thermal attenuation, Scarf (1962) and Liemohn and Scarf (1962, 1964) attempted to determine the electron temperature. The method was not widely used because it is difficult to distinguish whether the upper cutoff was due to thermal attenu-

ation or propagation effects. Guthart (1965), including the effect of thermal electrons in the group velocity, evaluated the change in whistler spectra recorded at Eights (L = 4) near the upper cutoff frequency and estimated the magnetospheric electron temperature - 1.7 eV (- 2 x IO6 K). Analysing whistlers 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 plasmapause. Comparing theoretical and experimental whistler dispersion curves in the vicinity of plasmapause, Kobelev and Sazhin (1983) obtained electron 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).

3. CONCLUSION

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, downward/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 electron temperature measurements in the plasmasphere. Theoretical and experimental developments have to be made before the technique could be used. The duct lifetime, duct width and enhancement factors are also summarised. Information about duct structure and its distribution in the magnetosphere is lacking. Matched filtering techniques may give some information about fine structure of the ducts. More studies are required in this direction. Whistler mode

Plasmaspheric

parameters

propagation through a complex duct structure should be carried out to understand the fine structure spectrum of whistler waves obtained from the matched filtering technique. The electron density derived from whistler measurements compares well with direct rocket/satellite measurements. The study of latitudinal/longitudinal distribution of electron density and its long term variations using rockets/satellites becomes financially and technically improbable, whereas the same can be studied very readily by whistler measurements using a network of stations equipped with identical equipment spread over a range of latitudes and longitudes. The temporal evolution of fluctuations in the ionization density of the plasmasphere and its finer structural 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 plasmasphere originates in the ionosphere, whilst downward flows of plasma may contribute to the maintenance of the nocturnal ionosphere (Bailey et al.. 1987). Experimental measurements seem to be lagging 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 obtaining 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 plasmasphere. 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

derived from whistlers

505

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

of the

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 suggestions.

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