Joumal of Atmosphmic and Teweslrial Physics, Vol.42,pp.265-273 Pergamon Press Ltd. 1980. Printed inNorthern Ireland
!Seasonal difference in ionization
and height of FZ-layer caused by Neutrals at low latitudes
N. S. CHAUHAN, H. S. GURM
Department
and A. V. JANVE*
of Astronomy and Space Sciences, Punjabi University, Patiala-147002, India (Receiued 17 Apriit 1979; in revised form 20 September 1979)
Abstract-Simulation of seasonal anomaly based on a morphological study has been carried out for low latitudes, In the morphological study, summer-winter differences have been studied in the diurnal behaviour of foF2, hpF2 and in the strength of the equatorial electrojet for three low-latitude stations and for three different solar activity periods. Simultaneous examination of the equatorial electrojet strength, foF2 and hpF2 show that the seasonal differences cannot be ascribed to the corresponding differences in the magnitude of the electromagnetic drift. Solving the continuity equation at low latitudes for a high solar activity period and assuming increased atomic oxygen in winter (1.15 times) and increased moiecular oxygen and nitrogen in summer (1.15 times), it is concluded that the seasonal differences in the calculated foF2 are of the order of the observed seasonal differences (l-l.5 MHz), with the height of the F2-layer showing a trend similar to the observations. Furthermore, the observations from Alouette II as well as the theoretical studies show that seasonal anomaly is dominant only around the FZ-peak. Inclusion of a model neutral wind shows that the neutral wind opposes the for-mation of the seasonal anomaly.
WTRODWCITON
The anomalous increase in winter F2-region ionization compared to summer was pointed out by RISHBETH and SEW (1961). Besides the noon increase in the electron density in winter, the rate of increase of the electron density (dN/dt) in winter is also greater than that of the corresponding summer season and is known as the sunrise anomaly. Looking for seasonal differences at night, it was found that summer electron densities are greater than those of winter, indicating that the seasonal anomaly is a daytime phenomenon and should bear some relation to the sun. The seasonal anomaly in the F2-region electron density is stronger than the seasonal anomaly in the total electron content (TEC). This suggests that the anomaly is not uniform in the whole of the vertical column but is more dominant around the peak. Depressions in electron density in the F-region are associated with increased molecular abundances. For a mid-latitude station the loss coefficient, p, should change by 3: 1 to produce the observed changes in NmF2 (RISBEW and SETTY, 1961). At sunrise, the peak of production lies in the FZ-region. Losses and transport effects are quite small, dN]dt= Q (the production rate) i.e. the seasonal differences are directly reflected in the rate of change of the electron density. Changes in * Department of Physics, Saurastra University, Rajkot, India. 265
the density of the neutral gas upon which the production rate is dependent, are responsible for observed differences in dNldt. Taking the O/N, ratio at 130 km as 2.7 times greater in winter than in summer, RUSTER and KING (1973) have shown that for high solar activity the seasonal differences in the foF2 at Lindau (51”N) can be explained by a seasonal variation in the atmospheric composition. The seasonal differences in both altitude and electron density at the F2-peak for mid-latitudes were interpreted by MAO-Fou Wu and NEWELL (1972) as due to a 50% increase of the atomic oxygen during winter and a 50% increase of molecular oxygen and nitrogen during summer. However, ANDERSON and MATSUSHITA (1974) for low solar activity have interpreted the increase in winter electron density at Tucuman (dip angle, -22”) as due to a decrease in the ExB drift at the equator and to different seasonal neutral winds. We shall make a two pronged study: morphological and theoretical, including consideration of the role of the neutral winds. In the morphological picture we study both f&2 and hpF2 for low and equatorial latitudes along with the equatorial electrojet strength for three different periods of solar activity. The basic question is to what extent the electromagnetic effects and other dynamic effects account for the seasonal anomaly, which dominates which, and what is the effect of solar activity. The inference drawn from such a study will be used to
N. S. CHAUHAN, H. S. GURM and A. V.
266
simulate the actual seasonal anomaly. role of neutral wind will be assessed. 1.
MORPHOLOGICAL
Finally,
Station
The low-latitude ionosphere is controlled by electromagnetic effects. Since there are no direct measurements of the vertical drift in the Indian sector, we shall consider the strength of the electrojet as a representative measure of the electromagnetic drift in the F-region (RASTOGI et al., 1972). Seasonal variations in the equatorial electrojet reversal times have been reported by BALSLEY (1970). In the morning hours there is a tendency for the reversals to occur earlier during the December solstitial seasons. In the evening, during June solstitial season, the reversals occur much sooner after sunset (- 1 h) than during the December solstitial season (~2: h). We consider three solar activity periods: very high 19581959 sunspot number 175, high 19681969 sunspot number 110, low 1963-1964 sunspot number 15. The summer season will be taken as the mean value of June and July months and the mean of December and the succeeding January months will be referred to as the winter season. Sample calculations with and without the inclusion of disturbed days show that the results are only 5-10% different in the two cases. Consequently, we have taken the mean of all the days for the respective seasons. If H denotes the horizontal magnetic field and the subscripts TR and AL refer respectively to Trivandrum (an equatorial station) and Alibag (a low-latitude station, geomagnetic latitude = 9.5”), then the equatorial electrojet strength Sd, is given by (KANE, 1973):
(I)
Sdr = HTR - HAL + Sq,,
where Sq,, is the quiet time value of the horizontal component of the magnetic field at Alibag. ASd, can be found by subtracting the mean value of Sd, for 0000-0500 LT i.e. ASd, = Sd,( t) - Sd, (average
value over 0000-0500
Table 1. Stations and locations
the
STUDY
LT)
(2)
ASd, is taken as a measure of the electrojet strength. We have chosen an equatorial station (Kodaikanal), a station at the crest of the equatorial anomaly (Ahmedabad) and a station away from the equatorial anomaly region (Delhi). For the above
JANVE
Kodaikanal Bombay Ahmedabad Delhi
Symbol
Geog. lat.
Mag. dip angle
KDK BMB AHM DLH
10.14”N 19.O”N 23.01”N 28.38”N
3.5”N 24.75”N 34.00”N 42.44”N
mentioned three solar activity periods plotted the seasonal electrojet strengths corresponding values of foFZ (Fig. 1).
we have and the
2. OBSERVATIONS
Except for the low solar activity period, 19631964, where the strengths of the equatorial electrojet for summer and winter are the same, the equatorial electrojet strength for summer is greater than that for winter and the difference increases with an increase in solar activity. Since the changes in foFZ are proportional to the changes in electrojet strength (RASTOGI et al., 1972), so from the viewpoint of the differences in the electrojet strength we should expect foF2 for summer to be greater than that for winter at low latitudes. For an equatorial station, the greater the strength of the electrojet, the greater would be the noon biteout effect in foF2. From the foF2 plots we note that the summer bite-out is greater than the winter bite-out for the corresponding solar activity period. Comparing the noon-time differences in foF2 for the equatorial station Kodaikanal, we find that for all solar activities, the differences in foF2 are insignificantly small though there are some kinks here and there. Around the crest of the equatorial anomaly, Ahmedabad, and outside the anomaly region, Delhi, winter foF2 for all three levels of solar activity is larger than the summer foF2 and furthermore there is a general trend for differences between summer and winter to increase towards high solar activity periods. Although the electrojet strength is weak in winter, foF2 around the crest of the anomaly (Ahmedabad) is nevertheless larger in winter, indicating the existence of some seasonal mechanism which is increasing foF2 in winter. The same mechanism seems to be also acting at Delhi. The other anomalous seasonal feature which is not much discussed in the literature is the sunrise anomaly. From Fig. 1 one can readily see that the rate of change of electron density in winter is larger than that in summer. Although Ahmedabad and Delhi clearly show the sunrise seasonal differences these features are obscure at Kodaikanal.
267
Seasonal difference in ionization and height of FZ-layer WINTER
SUMMER I~i~/‘l’l’l’!‘i~l~
‘l’i’l’lil’~‘~‘~‘~”
’ DLH
,’
‘\
,‘
’
\
‘..._
\
\
-.-
-
/ ,--\ /’
‘\
\ \
\
_ t
\
\_
I__
‘_.
\
__ 1958-59 - - - - 1968-69 ----1963-64
b-L 4
0
12
16
_I
20
LOCAL TIME HRS.
Fig. 1. Observed diurnal variation of foF2, the critical frequency of F2-layer and Sd,, the electrojet strength for winter and summer season of 1958-1959, 1968-1969, 1963-1964 at Kodaikanal, Ahmedabad and Delhi. Some interesting results are given by the hpF2 plots shown in Fig. 2. It is to be pointed out that hpF2 and hmF2 differs in magnitude only and qualitively there is no difference between the two even at fow latitudes (cf. CHANDRA et ai., 1973). Since we are interested only in the relative summer-winter differences in the height of the layer rather than in their absolute values, the choice of hpF2 parameter as a measure of height
should not be misleading. Unfortunately, complete winter and summer data for all three solar activity periods are available only for Ahmedabad. Daytime data for 1958-1959 only are available for Delhi. Other equatorial stations in the Indian zone e.g. Tiruchirapalli and Trivandrum also do not have complete data. For Ahmedabad, the summer values of the daytime hpF2 are higher than winter daytime values
24
268
N. S. CHAUHAN, H. S. GURMand A. V. JANVE AUMEDABAD
Fig. 2. Observed diurnal variation of hpF2, the height of maximum ionization for winter and summer seasons of 1958-1959,1968-1969,1963-1964 at Ahmedabad.
far all three solar activity periods (Fig. 2). There is a general increase in the value of hpF.2 for the high solar activity period. Another feature to note is the sudden increase of hpF2 at 0500-0600 LT in winter. In summer this effect is negligibly small. There is no increase in winter foF2 for the corresponding increase of hpF2. Only a small winter increase in foF2 during the low-solar activity period around 0200-0300 LT is observed (Fig. 1). During 1958-1959, for Delhi, the seasonal noontime difference in hpF2 is about 60-80 km (larger in summer), for Ahmedabad 40-60 km and for Tiruchirapalli the seasonal difference is insignificant. For other solar activities the trend is similar. To illustrate the above morphological inferences, we have plotted N(h) profile from the experimental data of Alouette II for the year 1969 (Fig. 3). It is interesting to note that apart from the seasonal differences in the electron densities and the height of the F2-layer, the electron densities are larger in winter only near the FZ-peak. The seasonal anomaly disappears at higher altitudes. We shall discuss this aspect further in Section 4. It may be concluded that in winter, apart from an increase in foF2 there is a decrease in the height of the layer. The increase in height of the layer in
Fig. 3. N(h) profile from Alouette II. S (geomag. lat. 17.2”, long. 140.42”) for summer (S) 30 May 1969, at 1324LT. W (geomag. 17.0”, long. 140.42”) for winter (W) 11 December 1969 at 1330 LT.
summer suggests that the loss coefficient might have increased, and the increase in foF2 in winter implies that the production rate might have increased. It further implies that in winter the atomic oxygen should increase thereby increasing the production rate and in summer the molecular gases (0, and N,) should increase thereby decreasing
269
Seasonal difference in ionization and height of F24ayer foF2 and raising the height of the layer as a consequence . Any hypothesis which may be invoked needs to explain the above seasonal change in the electron density as well as the change in the height of the layer. 3. THEORETICAL. STUDY
Electromagnetic effects are dominant at lowlatitude region but we need to consider whether these effects are responsible for the observed seasonal differences. We also need to consider the role of the seasonal circulation of neutrals in the formation of the seasonal anomaly. Bearing in mind the results of the morphological study (just discussed) we shall estimate the change in densities of the neutrals and the corresponding changes in hmF2 and foF2. Neutral winds contribute significantly to the dynamics of the ionosphere but at present there exist no measured values of seasonal neutral winds at low latitudes. We can incorporate the summer and winter neutral winds in the continuity equation and examine their effects on the seasonal anomaly. The plasma continuity equation is
$&-L-V.
(NV)
where P is the production rate, L is the loss rate and N is the electron density. The divergence term contains the contribution from ExB drift, ambipolar diffusion and neutral winds, The continuity equation is solved by the method discussed in CHAUHAN and GURM (1979) for the latitudes of Delhi, Ahmedabad and Kodaikanal with the following parameters: 1. Only high solar activity conditions are considered. -The solar activity conditions are taken similar to those of the year 1958-1959 with 10.7 cm solar flux given by 220 x 10-zzW mm2 Hz-‘. It has been assumed that the solar activity remains constant for summer and winter months. 2. From ExB drift measurements made by WOODMAN (1970), it is evident that the vertical drift in summer is more than the vertical drift in winter. This is also noticeable in the ExB curves given by ANDERSON and MATSUSHITA (1974). Figure 1 shows that the electrojet strength is higher in summer than in winter for high solar activity. In the absence of any measured value of the Ex B drift, the maximum value of the ExB drift velocity for summer has been taken to be 20 ms-‘, for winter 19ms-’ and its variation with time of day is taken to be simple harmonic with a daytime maximum at 1200 LT.
3. The value of ‘b’ in the expression for the diffusion coefficient (cf. equation (14) in CHAUHAN and GURM, 1980) is taken to be equal to 4.1 x 10” cm-’ set-’ both for summer and winter. 4. For summer months, declination of the sun So is taken to be +23.5” and for winter months -23.5”. 5. The seasonal differences in the composition in the Jacchia’s density model are incorporated through the changes in declination of the sun. However the variation in the O/O2 and the O/N2 ratio so produced are not significant to account for the seasonal differences in foF2. Delhi and Ahmedabad show seasonal differences in foF2 of the order of l-l.5 MHz while at Kodaikanal the differences are insignificant (Section 2). Thus in an attempt to explain the summer-winter differences in foF2 at Ahmedabad and Delhi, we have increased O2 and Nz by 1.15 times in summer and 0 by 1.15 times in winter at the lower boundary (120 km) of the Jacchia’s density model (Table 2). No seasonal change in composition at Kodaikanal is assumed. It may be mentioned that there is a general agreement between the assumed seasonal variations in the chemical composition in the present modelling (Table 2) and those found with the help of mass spectrometer and incoherent scatter observations by HEDIN et al. (1977a, b)
Table
[Ol P&l [%I
2. Seasonal concentration neutrals used (X mm3)
of
the
Summer
Winter
9.8 x 10n 4.37 x 10” 7.24 x 1016
1.13 x 10” 3.8 x 10” 6.3 x 1016
Taking the lower boundary of the densities as given in Table 2, the computed height variations in O/O, and O/N* ratios at 1200 LT for both seasons are shown in Fig. 4. The values of the O/O, and the O/N* ratios given by Jacchia’s model do not vary significantly with season and the curves corresponding to the Jacchia’s model lie between those shown in Fig. 4. 6. The production rate and the temperature formulation are adjusted to account for the effect of the sun’s declination. 7. Because of the lack of observations, the meridional component of the neutral wind is most difficult to model. This is especially true at low latitudes. Consequently we have chosen a very
270
N. S. CHAUHAN,
H. S. GURM and
A. V. JANVE
-P - -- -- WINTER
700-02
-
SUMMER
700
E500 Y : Y Y 300
0 T
2
,
I I I
, I'
2' I' I' ,' /' / ,I'
/' 100 v 0.1
I,
LflllLlflllll,l
LAI.1 I-O
IO
L
LLI
,
I,
i
/
1
,
I
1
Lll
-3 IO2
II 3
RATIO
Fig. 4. Seasonal height variations in O/O, (upper section) and O/N, (lower section) assumed in the calculations at 1200 LT.
Fig. 5. Models of seasonal neutral wind at Kodaikanal, Ahmedabad and Delhi. The negative velocity is away from the equator.
4. RESULTS
in which the meridional wind is symmetric about the geographic equator during both of the solstitial periods. The speed does not vary with the altitude and the phase is independent of latitude. In reality, the atmospheric pressure gradient should not be symmetric about geographic equator during solstices (JACCHIA, 1970). The meridional component U, varies approximately as sine function of twice the geographic latitude 0, (CHAUHAN and GURM, 1980) simple
/
model
U, = U, Sin (20, - Go)[cos (4 - &) - T]
(4)
where U, = - 70 m/s, &, = 1400 LT, T = 0.3 and a0 = +23.5”, positive sign for summer and negative for winter. The seasonal trend of the model of the neutral wind computed from equation (4) shown in Fig. 5 is similar to the winds computed from pressure gradient consideration by GEISLER (1967) and those deduced by AMAYENC and VASSEUR (1972) from incoherent scatter observations.
AND
DKXUSSION
Transport of the neutrals occur as a result of difference in heat input. The fact that the sunlight heats up the F-region is known from the day-night variations and the solar tlux correlations (JACCHIA, 1965). Temperatures in summer exceed those of winter only by 50-90°K as compared to 400°K change from day and night in the F-region. Hence it appears that there is a constant movement of heat from the summer to the winter hemisphere by processes such as circulation. The global circulation based on the theory of convection proposes that the solar heating which occurs mainly in the lower ionosphere induces upwelling of air rich in molecular species over the summer hemisphere and settling of air rich in atomic oxygen over the winter hemisphere. Even if the circulation reaches no higher than 120 km (i.e. to the turbopause), the changes in the composition will be transmitted to higher altitudes in the ionosphere through ditIusion. The seasonal circulation in the thermosphere from summer to winter is not as strong as the diurnal circulation in which it is embedded, which makes it more difficult to detect observationally.
271
Seasonal difference in ionization and height of F24ayer WINTER
SUM14ER i”l”i”l”l”:“l’~ (7
“lj’l’/l’//‘(//‘/I.‘,l T
OLH
Fig. 6. Computed diurnal variations of foF2, the critical frequency of F24ayer for summer and winter season (F10,7= 220 units) at Kodaikanal, Ahmedabad and Delhi.
Figure 6 shows that the diurnal variation of foF2 in summer and winter seasons due to the combined effect of the seasonal changes in composition introduced (cf. Table 2) plus the usual changes in the neutral concentration and the production rate occurring as a result of change of declination of the sun in Jacchia’s formulation. At Ahmedabad, on the crest of the anomaly, the winter value of foF2 is greater than the summer value by about l1.5 MHz, though the vertical drift in winter is less than that in summer. It implies that of the two competing mechanisms, ExB drift, which decreases foF2 and due to changes in composition which increases foF2, the latter prevails over the former. In summer, the atmosphere is more molecular hence the losses must increase which dominate the gain in the ionization because of the increased vertical drift. The changes in foF2 conforms to the study made in Section 2. At Delhi, which lies outside the equatorial ano6
maly region, the seasonal changes in composition increases the winter foF2 and this agrees with the study made in Section 2. At Kodaikanal, the changes are inconclusively small. Another factor which confirms the present modelling is the increase of the height of the FL?-layer in summer and the decrease in winter (Fig. 7). The equatorial station Kodaikanal does not show much seasonal change in the height of the F2-layer, as such it is not plotted in Fig. 7. The seasonal movement of the layer implies that in winter as the electron density (NmF2) increases due to enrichment of atomic oxygen, the peak height (hmF2) decreases, while in summer hmF2 increases, as NmF2 decreases due to an increase in 0, and NZ. This is consistent with the observations (cf. Section 2) that hpF2 in winter is lower than that in summer. An important feature to be noticed is that the electron density variations are sensitive to changes in the composition of the neutral atmosphere only
272
N. S. CHAUHAN,H. S. GURM and A. V. JANVE
ELECTRON
DENSITY
i(d2
G3 >
Fig. 7. Computed changes in electron density profile at 1200 LT for Ahmedabad and Delhi. around the F,-peak. This happens because both the production and the recombination rates lose their importance at the higher altitudes where diffusion is dominant. The seasonal difference in the declination of the sun causes the difference in the sunrise time both for summer and winter. The night-time ionization in winter falls to lower values compared to the summer values (Fig. 1). Both these effects combined together should produce a higher rate of increase of the electron density in winter compared to summer. The present theoretical results do not show this sunrise feature though from the morphological study (cf. Fig. 1) we notice distinctly different morning rates of increase of the electron density at Delhi and at Ahmedabad. Rusrnx and KING (1973) simulated the seasonal anomaly at mid-latitudes by solving coupled equation for four species (0’, Oz’, N,+ and NO*), but the observed sunrise differences were not reproduced though the disagreement is not as bad as m the present case. It seems that the inclusion of accurately measured time and duration of maximization of E X B, which exerts a considerable influence upon the sunrise seasonal differences, may help a closer simulation of these features. Secondly, the non-linear contributions from the loss rates and the neutral winds may also play a significant role at morning hours. Seasonal changes in the equatorial electron densities have been pointed out by RAJARAM and
RASTOGI (1977). The emphasis is more on equinoctial values rather than on summer-winter differences. It appears that the differences in the depth of the noon-time biteout, morning and afternoon peak of biteout, are related to the differences in vertical lifting of plasma rather than to any other process. From the present study (Section Z), we cannot draw any conclusion about the equatorial seasonal differences. For such a study, good quality of data along with an exact measurement of the magnitude and the shape of the EX B drift is needed. The seasonal differences in foFZ at Delhi are more than that at Ahmedabad. Furthermore, for mid-latitudes, the seasonal differences in composition are about three to four times more than the present differences (RUSTER and KING, 1973). For a closer agreement between the theoretical modelling and the morphological results at Delhi, the winter increase of 1.20 times instead of 1.15 times would have been better. This is further justified from the consideration that because of seasonal circulation of the neutrals, the deposition of atomic oxygen increases towards higher latitudes (50-60”). In practice the increase of atomic oxygen in winter, and of the molecular oxygen and the nitrogen in summer by equal amounts may not be true since the response of different neutrals to the seasonal temperature variation will be different. In the absence of any precise measurement of the seasonal concentration of the neutrals, the present modelling appears to be satisfactory. Within the aforementioned limitation, it may be concluded that the seasonal behaviour of the height and the electron density of the F2-layer at lowlatitude is well explained in terms of composition changes. The electromagnetic effects are unable to produce the observed seasonal behaviour.
5. EFFECT OF NE-
WINDS
A few attempts have been made to study the role of neutral winds in the formation of seasonal anomaly. The F-region seasonal anomaly is supposed to be caused by composition changes in the neutral gas but the meridional winds have a modulating effect on the seasonal F-region behaviour. STUBBE (1975) found that the neutral wind enhances the seasonal anomaly for high solar activity at midlatitude but reduces it at low latitudes. FOT low solar activity period MAO-F• U WV and NEWELL (1972) concluded that the neutral winds are not responsible for the formation of the F-region seasonal anomaly, though the winds can seriously alter
Seasonal
difference
in ionization
the F,-peak height. ANDERSON and MATSUSHITA (1974) have tried to explain the seasonal differences at low-latitudes without invoking composition changes. In their neutral wind models the summer values of the wind speed are more than the winter values which is in contradiction with hoFu Wu and NEWELL (1972) and STUBBE (1975). MAYR and MAHAJAN (1971) interpreted the daytime higher peak heights in summer compared to those in winter at Puerto Rico as due to an equatorward wind in summer and to a poleward wind in winter. We consider a neutral wind blowing poleward during daytime and equatorward during the nighttime both in summer and winter (Fig. 5). It thus reduces the electron density during daytime by forcing the plasma to diffuse along the magnetic field lines and increase the electron density at night by moving the plasma up the field lines. This is evident from Fig. 6 for both summer and winter. In winter, the differences in foF2 with and without the inclusion neutral wind are more than the corresponding differences in foF2 in summer (Fig.
and height of F2-layer
6). In other words the neutral wind has suppressed the electron density more in winter compared to summer. Because the magnitude of the neutral wind increases with latitude, the formation of the seasonal anomaly will be hindered to a maximum extent at Delhi and to the least extent at Kodaikanal. We may conclude that neutral wind opposes the formation of seasonal anomaly. In practice the role of neutral wind on seasonal anomaly may not be as simple as pictured here. The variation of the neutral wind speed as well as the phase might bear a complex relation with solar activity, latitude etc. Since the seasonal anomaly is seen at and below the F,-peak, the simultaneous solution of the neutral wind equation and the plasma continuity equation may lead to some interesting results. Acknowledgements-The authors are grateful to various friends and colleagues both at Patiala and at the Physical Research Laboratory, Ahmedabad for numerous discussions. The data used from the different sources are gratefully acknowledged. One of the authors (N.S.C.) is grateful to CSIR and his university for providing financial support for this research work.
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A~~IAYENC P. and VASSEURG. ANDERSON D. N. and MATSUSHITAS. BALSLEV B. B. CHANDRA H., RAJARAMG. and RASTOGI R. G. CHAUHAN N. S. and GURM H. S. GEISLERJ. E. HEDIN A. E., SALAH J. E., EVANS J. V., REBER C. A., NEUTON G. P., SPENCER N. W., KAYSER D. C., ALCAYDE D., BAUER P., C~GGER L. and MCCLURE J. P. HEDIN A. E., REBER C. A., NEWTON G. P., SPENCERN. W., BRINTON H. C. and MAYR H. G. JACCH~AL. G. JACCHIAL. G. KANE R. P. MAO-F• U Wu and NEWELL R. E. MAYR H. G. and MAHAJAN K. K. RAJARAMG. and RASTOGI R. G. RASTOGI R. G., CHANDRA H., SHARMA R. P. and RAJARAMG. RISHBETHH. and Sorry C. S. G. K. RUSTER R. and KING J. W. STUBBEP. W~~DMAN R. F.
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