On the mechanism of the post-midnight winter NmF2 enhancements: dependence . . .

The mechanism of the NmF2 peak formation at different levels of solar activity is analyzed using Millstone Hill IS radar observations. The hmF2 nighttime increase due to thermospheric winds and the downward plasmaspheric fluxes are the key processes responsible for the NmF2 peak formation. The electron temperature follows with the opposite sign the electron density variations in this process. This mechanism provides a consistency with the Millstone Hill observations on the set of main parameters. The observed decrease of the nighttime NmF2 peak amplitude with solar activity is due to faster increasing of the recombination efficiency compared to the plasmaspheric flux increase. The E × B plasma drifts are shown to be inefficient for the NmF2 nighttime peak formation at high solar activity.


Introduction
Nighttime N m F 2 enhancements (pre-midnight and postmidnight) are a typical phenomenon for the mid-to lowlatitude F 2 -region which has long been observed both in N m F 2 and TEC (Arendt and Soicher, 1964;Evans, 1965Evans, , 1974Da Rosa and Smith, 1967;Titheridge, 1968Titheridge, , 1973Bertin and Papet-Lepine, 1970;Young et al., 1970;Tyagi, 1974;Davies et al., 1979;Kersley et al., 1980;Jakowski et al., 1986Jakowski et al., , 1991Balan and Rao, 1987;Joshi and Iyer, 1990;Jakowski and FoÈ rster, 1995). A morphological study by Mikhailov et al. (2000) of the N m F 2 nighttime enhancements on the latitudinal chain of the Eurasian ionosonde stations has revealed systematic variations with season and solar activity in the occurrence probability of the peaks, their amplitude and timing. In particular, the second (post-midnight) peak shows a well-pronounced seasonal variation in the occurrence probability with the peak to be more frequent in winter compared to summer both at solar minimum and maximum. The largest amplitudes of the peak take place in winter, the amplitudes being small for other seasons. The amplitude of winter N m F 2 enhancements is larger during solar minimum compared to solar maximum. There is a tendency for the amplitude to increase with latitude. A pronounced seasonal variation in the timing of the peak occurrence is also observed with winter peaks being later than summer ones.
The revealed morphological features require physical interpretation. Fluxes of thermal plasma from the plasmasphere into the nocturnal F 2 -region are considered as a commonly accepted mechanism to explain the eect (FoÈ rster and Jakowski, , 1988Jakowski and FoÈ rster, 1995). However, there are problems with model simulation of such nighttime N m F 2 increases as well as with its physical mechanism. The total¯ux required to produce the observed nighttime electron density increase was estimated to be 10 9 cm À2 s À1 by Davies et al. (1979) for winter solar minimum conditions. Jakowski et al. (1991) estimated necessary¯uxes as (3±5) Â 10 8 cm À2 s À1 for similar winter solar minimum conditions. More moderate¯uxes of the order of (1±2) Â 10 8 cm À2 s À1 are given by Bertin and Papet-Lepine (1970), Standley and Williams (1984), and Jain and Williams (1984). Direct observations at Millstone Hill (Evans, 1974(Evans, , 1975 gave plasmaspheric¯uxes of the order of 10 7 ±10 8 cm À2 s À1 with the most probable average nighttime value of 3 Â 10 7 cm À2 s À1 . Although the accuracy of nighttime observations is not high when electron concentration is low (Evans et al., 1978), it is dicult to consider large¯uxes as real, at least during low solar activity. The scatter mentioned in the required ux estimates re¯ects the dierence in the O ion recombination rates for the nighttime F 2 -region accepted by dierent authors. Our model calculations for the January 06±12, 1997, CEDAR period, (Mikhailov and FoÈ rster, 1999) have shown that the strong N m F 2 postmidnight enhancements observed at Millstone Hill can be explained with O plasmaspheric¯uxes equal to (1±2) Â 10 8 cm À2 s À1 in accordance with the Millstone Hill IS radar observations. The variety of nighttime N m F 2 variations observed during this period was shown to re¯ect the balance between plasma in¯ux and the total number of recombinations in the F 2 -region ionospheric column controlled by the linear loss coecient b c 1 N 2 c 2 O 2 . The eciency of recombination strongly decreases when the F 2 -layer is uplifted by the nighttime equatorward thermospheric wind and even moderate¯uxes of the order of (1±2) Â 10 8 cm À2 s À1 from the plasmasphere appear to be sucient to produce an essential enhancement in N m F 2 . Night-tonight variations was related in our approach with the plasma compression/decompression mechanism under the action of the observed E Â B drift moving plasma from higher L shells to lower ones and squeezing it into the F 2 -region. In contrast, Richards et al. (2000) when analyzing the same January 06±12, 1997, period came to the conclusion that the nighttime plasmaspheric heat ux variation drives the nighttime ionospheric density variation. However, they could not explain the reason for night-to-night plasmaspheric heat¯ux variation and their calculated nighttime¯uxes of O ions at 400 km are around 3 Â 10 8 cm À2 s À1 being by a factor of two larger than the observed ones.
Our aim here is the further analysis of the physical mechanism responsible for the N m F 2 nighttime enhancements using Millstone Hill IS radar observations. Among many features of the N m F 2 nighttime enhancements revealed by our morphological study (Mikhailov et al., 2000), the dependence of the winter post-midnight N m F 2 peak amplitude on solar activity will be analyzed.

Morphology of the American sector
It was stressed by Mikhailov et al. (2000) that the results of dierent morphological studies of the N m F 2 nighttime enhancements in various longitudinal sectors were controversial to a great extent. This may be due to either real longitudinal dierences in the occurrence of this eect, or may re¯ect dierences in the method of analysis used. As we are considering Millstone Hill observations, an additional morphological study was made for the American sector. All available ionosonde f o F 2 observations at Boulder (40:0 N, 254.7 E, L 2:3) were analyzed for the years of solar maximum (1957± 1959, 1968±1970, 1979±1981, 1989±1990) and solar minimum (1953±1954, 1964±1965, 1975±1976, 1985± 1986) using the same method as was applied to the Eurasian sector by Mikhailov et al. (2000). The selected years correspond to the periods around solar maxima and minima of the last four solar cycles. The presence of nighttime peaks was checked in N m F 2 daily variations for the years in question. The absolute minimum was searched in N m F 2 values within the period after sunset to 02 LT, and this value was called N min . The amplitude of the peak, N peak =N min and the local time of its occurrence were found for each case. A plateau of 2±3 N m F 2 hourly values was referred to as a peak with its maximum in the middle of the plateau. Several maxima are possible after midnight. Therefore, the largest postmidnight maximum was found and treated as the peak. Only quiet days with Ap 12 were analyzed to exclude storm eects, although nighttime N m F 2 increases are frequent during storm periods. The results of the postmidnight (second) peak occurrence are given in Fig. 1 for Boulder.
In general the results are similar to those obtained for the Eurasian sector by Mikhailov et al. (2000). There is a well-pronounced seasonal dependence in the occurrence probability of the peak. As with the Eurasian sector the peak is most frequent in winter (November± February, 70±80% of all quiet days), the summer probability being about 40%. Seasonal dierences are larger in the Eurasian sector, (80±90% and 10±30%) for winter and summer periods, respectively. It should be stressed that the seasonal pattern is the same regardless the solar activity. This contradicts the results of Jakowski et al. (1991) for Havana, Cuba, who found an inversion of the seasonal pattern with the largest peak occurrence in summer at high solar activity. Similar to the Eurasian sector, the winter nighttime enhancements are the largest with amplitudes being higher during solar minimum (Fig. 1, bottom). The mechanism of this solar activity dependence for the peak amplitude is analyzed below. Like the Eurasian sector there is a clear dependence in the timing of the peak: winter peaks are later in local time than equinoctial and summer ones (Fig. 1, middle panel). This also contradicts the results of Jakowski et al. (1991) who revealed no seasonal variations in the timing of the peak occurrence during solar minimum and are an inverse to our results showing seasonal dependence during solar maximum with summer peaks to be the latest. Perhaps additional analysis is needed for lower-latitude stations (close to Havana, Cuba) in the American sector to clear up the reason for these dierences.
Summarizing the results of the morphological study we may conclude, that there are no substantial dierences between the Eurasian and the American sectors in the post-midnight peak occurrence at least for stations with L-parameter close to 3. This is important for the further analysis of the Millstone Hill (L 3:13) observations. We must be sure that cases of nighttime N m F 2 enhancement chosen for the analysis re¯ect the typical situation for the given geophysical conditions.

Millstone Hill observations
Nighttime N m F 2 enhancements are most pronounced during winter conditions. This is the outcome of the morphological study as reviewed in the previous section. Solar activity dependence of the peak amplitude is clearly seen in the observations (Fig. 1, bottom). Therefore, three January nights with Millstone Hill IS radar observations were chosen for the analysis. Solar minimum conditions are presented by January 08, 1997, (F 10:7 71:3, F 10:7 73, Ap 8) earlier analyzed by Mikhailov and FoÈ rster (1999), medium activity by January 24, 1993, (F 10:7 104:8, FS=134.2, Ap 10), and high solar activity by January 27, 1990, (F 10:7 232:2, F 10:7 200, Ap 4), where F 10:7 is a 3month average of the F 10:7 index. Figure 2 gives the observed N m F 2 and h m F 2 nighttime variations for the dates in question. In accordance with the results of our morphological analysis the largest (by a factor of 4) N m F 2 enhancement takes place at solar minimum on January 08, 1997, the amplitude of the N m F 2 enhancement is around 2.3 on January 24, 1993, for solar medium activity and is around 1.25 only at solar maximum on January 27, 1990.
The observations selected were made using dierent modes. The time step was 2.5-min on January 08, 1997, a 5-min step on January 27, 1990, and a 20-min step on January 24, 1993. A``chirp correction'' of À15:36 ms À1 was applied to the V z observations on January 27, 1990, while V z values were initially corrected for the other two days. A sucient number of observations on January 08, 1997, enabled us to calculate median plasma¯uxes with SD each 15 min using a 0.5 h gate running interval, but individual N e and V z observations were used for the other two days. The calculated plasma¯uxes are compared to the observed ones at 365 km, 406 km, and 425 km for January 08, 1997, January 24, 1993, and January 27, 1990 respectively. The choice of these heights was due to the following reasons. The level should be chosen high enough to avoid recombination eects, but the accuracy of V z measurements strongly decreases with height. The main amount of recombinations takes place around and below h m F 2 and the experimental V z show a large scatter and are unreliable above (depending on solar activity) 400±450 km. These factors speci®ed the choice of the levels.

Method of calculations
The applied method includes two steps. First we ®nd the thermospheric neutral composition and temperature for daytime hours to correct the MSIS-83 model values if such a correction is required. Then using these correction factors we normalize the MSIS-83 model for the nighttime hours. Usually this correction is not large for quiet time periods analyzed here. The self-consistent method to derive thermospheric parameters from IS radar observations is described by Mikhailov and Schlegel (1997) with later modi®cations given by Mikhailov and FoÈ rster (1999). The main idea of the method is to ®t a theoretical N e h to the observed one and thus to obtain a self-consistent set of the main aeronomic parameters: neutral composition [O], [O 2 ], [N 2 ], temperature T n h, vertical plasma drift W, and total EUV solar ux. All the parameters mentioned are responsible for the formation of the N e h pro®le in the daytime F 2 -region. The theoretical model of the mid-latitude F-region used in this method is described by FoÈ rster et al. (1995). It takes into account transport process for O ( 4 S) and photo-chemical processes only for O ( 2 D), O ( 2 P), O 2 (X 2 P), N , N 2 and NO ions in the 120±620 km height range. Vibrationally excited N 2 eects are not taken into account explicitly in the Hill N m F 2 and h m F 2 variations for the three January nights at different levels of solar activity model. It was shown by Mikhailov and Schlegel (2000) that recent laboratory measurements of the O + N 2 reaction rate constant by Hierl et al. (1997) could be recommended for F 2 -region model calculations in the 850±1400 K temperature range. For lower temperatures the McFarland et al. (1973) temperature dependence may be used for this rate constant. This is important for nighttime solar minimum conditions as was shown by Mikhailov and FoÈ rster (1999). A dependence of solar EUV¯ux on solar activity is taken from the twocomponent model by Nusinov (1992) with further modi®cations made by Nusinov et al. (1999). The model is used to calculate the photo-ionization rates in 35 wavelength intervals (10±105 nm). The photo-ionization and photo-absorption cross sections are obtained mostly from Torr et al. (1979). Observed electron concentration at 620 km is used as the upper boundary condition to solve the continuity equation for O ( 4 S). At the lower boundary O ( 4 S) is presumed to be in a photo-chemical equilibrium. We use the stationary form of the continuity equation for daytime hours, therefore, only periods of relative stability in N m F 2 and h m F 2 around noon are used for the analysis. Observed T e h and T i h pro®les are used in the calculations. Collisions of O ions with neutral O, O 2 , N 2 and NO , O 2 , N 2 , N ions are taken into account. All O ion collision frequencies are taken from Banks and Kockarts (1973 ] values, T ex and the shape parameter S to specify the MSIS T n h pro®le as well as a factor for the total EUV solar¯ux from the Nusinov (1992) model. No special constraints are laid on the searched parameters. The temperature at 120 km, T 120 is formally added to the list of searched parameters as it was found that the method worked better if the MSIS T 120 value was freed. Minimizing D logN e h obs =N e h cal 2 in the 160±550 km height range, we ®nd the set of thermospheric parameters in a selfconsistent way.
Thermospheric parameters thus found are used to normalize the MSIS-83 model for nighttime hours. A non-stationary continuity equation for O ions is solved in the 150±500 km height range. Molecular NO and O 2 ions are considered to be in chemical equilibrium. The H ions contribution may be ignored below 500 km for the conditions in question (Antonova et al., 1992;MacPherson et al., 1998). Model T e h from Brace and Theis (1981) and T i h from Banks and Kockarts (1973) pro®les are normalized at 300±400 km (depending on solar activity) by the observed values. Smoothed experimental h m F 2 values are kept by vertical plasma drift during the calculations. The pro®le N e h observed at 0300 UT is used as the initial condition and the O ion ux at 500 km ± as the upper boundary condition. This ux is varied to ®t the observed N m F 2 variations.

Calculations
The results of the thermospheric parameters determination for the daytime hours are given in Table 1 and they are compared there with the corresponding MSIS-83 values. Daytime observations on previous days (January 23 and January 26) are used to ®nd the correction factors for the following nights of January 24 and January 27. The correction is not large as it is seen from Table 1. Such a correction of nighttime values by the daytime ones seems to be reasonable as we consider quiet time conditions. The results of our calculations are given in Figs. 3±5 for the three nights in question. The ®gures give smoothed observed N m F 2 and h m F 2 variations, Millstone Hill estimates of neutral temperature in comparison with the used one, and the observed O ion¯uxes compared to the calculated ones. Squares (bottom panels) are¯uxes at the chosen heights obtained with the boundary¯uxes required to match the observed N m F 2 variations. The boundary¯uxes are generally close to those shown at the selected heights as the recombination is not very ecient above the F 2 -layer maximum. Calculations were also made with constant boundarȳ uxes (dashes in the ®gures). Millstone Hill estimates of T n were not available to the authors for January 08, 1997, therefore we used observed T i values which are very close to T n for the conditions in question.
The model calculations (Figs. 3±5) show that N m F 2 nighttime enhancements can be described with the O ion¯uxes close to the observed ones at dierent levels of solar activity. This allows us to analyze the physical mechanism of the N m F 2 enhancement.

Basic mechanism
Despite the variability in the post-midnight N m F 2 peak occurrence, it is possible to specify the basic mechanism responsible for the nighttime N m F 2 peak formation. This mechanism comprises the following. Downward plasma velocity (V z < 0) means H eff > H p in the topside ionosphere. 2. The starting point of the process is the increase in the meridional (equatorward) thermospheric wind velocity maximizing soon after midnight (e.g., Buonsanto and Witasse, 1999) which uplifts the F 2 -layer. The F 2 -layer elevation (Figs. 3±5) due to the enhanced vertical plasma drift W strongly decreases the eciency of recombination in the F 2 -layer especially at low solar activity when the thermosphere is cold (Fig. 3) and the corresponding linear loss coecient b c 1 N 2 c 2 O 2 becomes very small. For instance, on January 08, 1997, the loss coecient b in the F 2 -layer maximum was as small as 1:4 Â 10 À5 s À1 around 07 UT. 3. With strongly decreased recombination even moderate plasmaspheric¯uxes of the order of 1 Â 10 8 cm À2 s À1 provide a sucient plasma in¯ux to start the electron concentration enhancement in the F 2 -region. 4. The N e increase results in the T e decrease due to plasma cooling in the whole F 2 -region. This process is clearly seen in N m F 2 and T e variations (Figs. 3, 5 and 6). 5. The electron temperature decrease results in H p decrease Eq.
(3) and further downward plasma velocity, the V z increase as the dierence between H eff and H p becomes larger Eq.
(2). This downward V z increase is also seen in the Millstone Hill observations (Fig. 6). 6. The downward V z increase provides additional plasma in¯ux to the F 2 -region resulting in further electron density increase and so on. This is a selfsupporting avalanche type process forming the N m F 2 peak. A similar self-supporting process takes place with respect to the electron temperature leading to a steep decrease in T e as was considered by Mikhailov and FoÈ rster (1999) for the January 06±10, 1997 CEDAR period. 7. The process stops when the equatorward V nx starts to decrease later in time with a corresponding h m F 2 lowering. The F 2 -layer plunges back into the high recombination region, N m F 2 starts to decrease and the described process reverses. This inversion is clearly seen in Figs. 3±6 with the decreasing N m F 2 , increasing T e and decreasing of O ¯u x. The maximal down-ward¯ux strictly coincides in time with the peak in N m F 2 variation as it is a product of V z and N e , both maximizing around this time. 8. According to this mechanism there should be always a delay of the N m F 2 peak with respect to the h m F 2 variation. The N m F 2 peak is to form on the slope of the lowering h m F 2 , the feature often mentioned by the authors (Evans, 1974;Mahajan and Saxena, 1976;Davies et al., 1979;Jakowski et al., 1991). However, it should be stressed that the beginning of the h m F 2 lowering only stops and inverses the process of the N m F 2 increasing. Therefore, it only determines the timing of the N m F 2 peak, but is not responsible for the mechanism of N m F 2 increasing. This was also mentioned by Mikhailov and FoÈ rster (1999).

Dependence on solar activity
According to the results of the morphological study the most pronounced solar activity eect is the decreasing of the peak amplitude with solar activity (Fig. 1). Let us analyze the results of model calculations which reproduce the observed N m F 2 variations for the three January nights belonging to dierent levels of solar activity. The mechanism of the N m F 2 nighttime enhancement is based (as discussed already) on the balance between the total plasma in¯ux from the plasmasphere and the total number of recombinations in the F 2 -region. Table 2 gives speci®c (total divided by the time interval) plasma in¯ux to the F 2 -region and speci®c number of recombinations as well as their ratio for the three nights in question. Table 2 shows that both the speci®c plasma in¯ux and the speci®c number of recombinations increase with solar activity, but the recombination increases faster, therefore their ratio decreases. This explains why the amplitude of the N m F 2 nighttime peak decreases with solar activity. The peak value of the downward¯ux increases by a factor of 4 when we pass from solar minimum (Fig. 3) to solar maximum (Fig. 5) conditions. This increase is mostly due to a general increase in the electron density at high solar activity while the vertical velocities V z are close to each other for the two nights (Fig. 6). On the other hand, the recombination eciency increases by a factor of 10 on January 27, 1990, compared to January 08, 1997 (Table 2). This is due to the following. At solar minimum the thermosphere is cold (T ex % 700 K, Fig. 3) while the vertical plasma drift is large (W % 60 m s À1 ), therefore, the F 2 -layer is located in the area with low recombination, the linear loss coecient b c 1 N 2 c 2 O 2 is 1:4 Â 10 À5 s À1 in the F 2 -layer maximum around 07 UT. At high solar activity on January 27, 1990, (Fig. 5) the neutral temperature is high (T ex % 1050 K) while the vertical plasma drift is rather small (around 25 m s À1 at 08 UT) and the F 2 -layer turns out to be in the relatively high recombination area (b m 5:3 Â 10 À5 s À1 at 08 UT). Therefore, available plasmaspheric uxes can produce only small N m F 2 peaks at solar maximum conditions. The crucial point in this solar activity dependence is the decreased equatorward neutral wind which keeps the F 2 -layer in the high recombination area at high solar activity. Such a dependence of the nighttime V nx on the solar activity level was revealed at Millstone Hill by Buonsanto and Witasse (1999). Although the described mechanism of the nighttime N m F 2 enhancement implies a time varying O ion boundary¯ux, the results of model calculations with a constant plasmaspheric¯ux may be interesting as authors usually give estimates of an average¯ux required to explain the observed N m F 2 enhancements. During low (Fig. 3) and moderate (Fig. 4) solar activity small plasmaspheric¯uxes around 1 Â 10 8 cm À2 s À1 are sucient to produce a noticeable N m F 2 enhancement (dashes in Figs. 3, 4) due to the low recombination eciency. An interesting point is that the unchanged boundary¯ux gives the same timing of the peak as with the time varying¯ux. This tells us that the timing of the peak is controlled mainly by the h m F 2 temporal variation, that is by V nx and thermospheric parameter variations. At high solar activity on January 27, 1990, much stronger¯uxes of about (7±8) Â 10 8 cm À2 s À1 are required to produce any noticeable N m F 2 peak (Fig. 5,  Fig. 6. Observed downward plasma velocity and electron temperature variations for the analyzed nights of solar minimum (January 08, 1997) and maximum (January 27, 1990) conditions. Solid smooth curves are polynomial least squares approximations of the observed variations which illustrate the nighttime peak N m F 2 formation mechanism (see text) dashes, top) as the recombination is rather strong (see earlier). Therefore, dierent estimates of the required plasmaspheric¯ux which can be found in publications, may partly re¯ect dierent solar activity conditions analyzed by the authors.
Vertical plasma drift (due to thermospheric wind) should be strong enough to provide a sucient h m F 2 increase and uplift the F 2 -layer from the high recombination area. Figure 7 shows the case for January 28, 1990 (Ap 7) with a small h m F 2 excursion. The observed O ion¯ux (Fig. 7, bottom) was around 4 Â 10 8 cm À2 s À1 which is insucient to produce any noticeable N m F 2 enhancement at high solar activity (see earlier). A small h m F 2 increase along with small plasma in¯ux produced only a small plateau in the N m F 2 variation around 07 UT. The basic mechanism described does not fully work in this case: only a small T e decrease at 0630 UT without any increase in the downward plasma velocity is seen (see Fig. 6).

Electric ®elds eects
Electric ®elds can produce a horizontal plasma transport under the action of the E Â B plasma drift. Thus they may contribute to the nighttime N m F 2 enhancement (Standley and Williams, 1984;Jain and Williams, 1984). Electromagnetic E Â B plasma drift measurements at Millstone Hill are available for the January 27±28, 1990, period analyzed. The components of the ion drifts parallel (V par ) and perpendicular to the magnetic ®eld in the northward/upward direction (V pn ) at 350 km are Fig. 7. An example of undeveloped nighttime N m F 2 enhancement on January 28, 1990 due to small h m F 2 excursion and relatively small plasmaspheric in¯ux insucient to produce a noticeable N m F 2 enhancement at high solar activity. Solid smooth curves are polynomial least squares approximations of the observed variations  Fig. 8. Despite the geomagnetical quite time periods considered, strong surges in V pn are seen for both nights. A well-pronounced anticorrelation between the two drift components takes place. This eect was discussed earlier by Buonsanto and Foster (1993); Buonsanto (1994) and Buonsanto and Holt (1995) as well as in the references therein. Due to this anticorrelation ionospheric plasma moves in approximately horizontal direction. This motion may result in an additional horizontal plasma in¯ux where there are suciently large spatial gradients in the electron concentration. A major eect may be expected from the meridional plasma transfer due to the zonal electric ®eld while zonal plasma transfer is much less ecient (e.g. Standley and Williams, 1984). The meridional plasma in¯ux to the ionospheric column may be estimated as follows: Millstone Hill (U 55 ) is located on the equatorward wall of the main trough during nighttime, therefore a considerable grad (TEC) of the order of (2±4) Â 10 4 cm À2 cm À1 may be expected (Buonsanto, 1995;Leitinger et al., 1999). Average values of V pn 20 ms À1 and V par À20 ms À1 may be taken throughout the whole time interval 03±11 UT for January 27, 1990 (Fig.  8). This gives a horizontal plasma velocity of V x V pn sin I À V par cos I % 26 m s À1 with the Millstone Hill inclination I 70 . The resultant plasma in¯ux Fh is around (5±10) Â 10 7 cm À2 s À1 depending on the assumed latitudinal grad (TEC). This is much less compared to the speci®c plasmaspheric in¯ux for this date ( Table 2). The peak values of V pn 80 m s À1 and V par À50 m s À1 (Fig. 8) give V x % 90 m s À1 and this could result in a considerable plasma in¯ux comparable with the plasmaspheric one. However the duration of these surges of velocity are too short (about 1 h) to provide any noticeable changes in the electron density. The characteristic horizontal scale is more than 1000 km for the observed latitudinal grad TEC and with the V x of 90 ms À1 the required characteristic time of such V pn upsurges should be about 3 h i.e. much longer than the observed one. The inclusion of such a horizontal plasma transport with the observed V pn and V par variations to the model con®rmed the low eciency of this process. Therefore, the main source of plasma to provide the N m F 2 nighttime enhancement is the downward¯ux from the plasmasphere. The same conclusion was obtained by Jain and Williams (1984) by analyzing the St. Santin nighttime observations.

Discussion
The proposed mechanism of the winter nighttime N m F 2 enhancement formation based on the analysis of our model calculations is consistent with the Millstone Hill observations on the set of main parameters. The observed N m F 2 enhancements observed at dierent levels of solar activity are reproduced quantitatively in our model calculations with O ¯u xes close to the observed ones. The N m F 2 peak occurrence on the slope of the decreasing h m F 2 usually mentioned in publications is explained within the scope of this mechanism. The mechanism explains also the observed maximum in the downward plasma velocity V z (and in the O ¯u x, correspondingly) coinciding in time with the N m F 2 peak. In this mechanism the electron temperature variation is dependent on the electron density variation contrary to the approach by Richards et al. (2000), where the plasmaspheric heat¯ux variation drives the nighttime ionospheric density variation. Electron density and temperature are known to be tightly related likè`h orse-and-cart'', but in each case it should be speci®ed exactly where the``horse'' is and where the``cart'' is. According to observations nighttime N m F 2 enhancements are closely related to the h m F 2 increases. No N m F 2 enhancement during quiet time periods has been revealed yet without a corresponding increase in h m F 2 , while the opposite is possible if the plasmaspheric¯ux is insucient (Mikhailov and FoÈ rster, 1999). The h m F 2 increase is produced by the enhanced equatorward thermospheric wind regularily observed in the nighttime F 2 -region (e.g. Buonsanto and Witasse, 1999 and references therein). This F 2 -layer uplift strongly reducing the recombination eciency, along with usually existing plasma in¯ux from the plasmasphere is the starting point of the nighttime N m F 2 increasing mechanism. The electron density increase is followed by the electron temperature decrease and corresponding increase in the downward plasma velocity (and¯ux) resulting in further N e increase an so on. Such T e and V z variations do take place in the Millstone Hill observations (Fig. 6). Therefore, the electron density variation is primary with respect to the electron temperature variation in the scope of the nighttime N m F 2 increasing mechanism. This is dierent from the mechanism of summer evening N m F 2 enhancement noted by Evans (1965Evans ( , 1974, and Eccles and Burge (1973) which results from a collapse of the F 2 -layer when the electron temperature decreases at sunset. This produces a strong surge of downward plasma¯ux into the F 2 -region (Evans, 1974), which along with the F 2 -layer uplifting produces a well-pronounced evening N m F 2 enhancement (Eccles and Burge, 1973). In this case the electron gas cooling is the primary process with respect to N e variations.
In case of the nighttime N m F 2 enhancements the electron temperature may demonstrate various types of variation, but they are always linked to the N e variations, the latter being linked to the h m F 2 variations (see earlier). Nighttime h m F 2 variations are known to be due to thermospheric wind and electric ®eld as well as to thermospheric parameter variations, but not to electron temperature. Within the scope of the mechanism considered the N m F 2 peak occurrence and its timing are mostly determined by V nx variations, producing the corresponding h m F 2 variations. In case of an undeveloped h m F 2 increase no N m F 2 enhancement is observed (Fig. 7). The other side of the mechanism is the plasma in¯ux from the plasmasphere. These¯uxes are (1±2) Â 10 8 cm À2 s À1 at low and moderate solar activity and up to (7±8) Â 10 8 cm À2 s À1 at solar maximum. It should be stressed that these estimations were made inside the F 2 -region below 450 km where a comparison with the observations was possible while the plasma-spheric¯uxes are generally smaller in the upper ionosphere. This is due to a slight variation of the plasma velocity with altitude during nighttime hours (Evans, 1971), therefore the¯ux should decrease with height (e.g. Evans, 1974). With regard to the solar activity dependence of the plasmaspheric¯ux it should be kept in mind that vertical plasma velocities are about the same throughout the solar cycle and the plasmaspheric ux increase up to (7±8) Â 10 8 cm À2 s À1 is mostly due to the general increase in the electron density during solar maximum.
The electric ®eld eects were shown to be small at high solar activity on January 27±28, 1990 although the observed V pn variations were rather strong despite the quiet geomagnetic conditions. Due to the strong anticorrelation between V pn and V par plasma moves mostly in the horizontal direction, therefore this motion does not contribute to the h m F 2 variations and does not help in producing the N m F 2 increase via this channel. The timeaveraged horizontal velocity provides a horizontal plasma in¯ux which is much less than the in¯ux from the plasmasphere.
There is a question concerning the plasma compression/decompression mechanism which allowed us to explain night-to-night N m F 2 variations during solar minimum in January 1997 (Mikhailov and FoÈ rster, 1999), but is not seen to be ecient during solar maximum in January 1990. This may be due to the dierent plasma ®lling of the magnetic¯ux tubes in these two cases. According to Krinberg and Tashchilin (1982) the saturation time is T s % 0:17 Â L 4 days. With L 3:13 for Millstone Hill, this gives T s % 16 days for such a¯ux tube. With regard to the January 06±12, 1997 CEDAR period, the last geomagnetic disturbance was two weeks before on December 23, 1996. This is a time interval which is close to T s for this magnetic tube which should be practically ®lled in this case. Therefore, plasma moving under the action of E Â B drift from higher L shells to lower ones should be squeezed into the F 2 -region providing a sucient in¯ux to produce the observed N m F 2 enhancement. Due to low recombination eciency during solar minimum (see earlier) the required¯uxes are rather moderate (1± 2) Â 10 8 cm À2 s À1 which are comparable with¯ux squeezed into the F 2 -region under this compression mechanism (Mikhailov and FoÈ rster, 1999). The other period of January 27±28, 1990, took place immediately after a prolonged disturbed period and the magnetic tube should be emptied to a great extent. It may be considered that the plasma compression mechanism under the E Â B drift is not ecient for such magnetic ux tubes.

Conclusions
The main results of our analysis are the following. 1. A morphological study of the post-midnight N m F 2 peak occurrence on Boulder ionosonde observations has shown no substantial dierences between the Eurasian and the American sectors at least for stations with L % 3. There is a well-pronounced seasonal dependence in the occurrence probability of the peak. Similar to the Eurasian sector, the peak occurs most frequently in winter (November±February 70±80% of all quiet days), while the summer probability is about 40%. The seasonal pattern is about the same regardless of the level of solar activity. Also similar to the Eurasian sector, the winter nighttime enhancements are the largest with amplitudes being larger during solar minimum and with winter peaks being later in local time than the equinoctial and the summer ones. These morphological ®ndings contradict the results of other authors who analyzed this eect in the American sector earlier.
2. The mechanism of winter nighttime N m F 2 enhancements was considered using Millstone Hill IS radar observations. This mechanism provides consistency with the observations on the set of main parameters. The primary and necessary step in this mechanism is the h m F 2 increase due to the equatorward thermospheric wind maximizing soon after midnight and lifting the F 2 -layer from the high-recombination area. The downward plasmaspheric¯ux which always exists during nighttime hours, starts the N m F 2 increasing process. The electron temperature follows with the opposite sign of the electron density variations in this process. This is a self-supporting avalanche-type process leading to an increase in the downward plasma velocity. The related enhanced plasma in¯ux results in the N m F 2 increasing. The decrease in the thermospheric wind velocity stops and inverses this process forming the N m F 2 peak.
3. The amplitude of the N m F 2 enhancement re¯ects the balance between plasma in¯ux and the eciency of recombination in the F 2 -region. Both speci®c plasma in¯ux and speci®c number of recombinations increase with solar activity, but the recombination increases faster. The peak value of the downward¯ux increases by a factor of 4 while the recombination eciency increases by a factor of 10 when we pass from solar minimum to solar maximum conditions. This explains the decrease in the amplitude of the N m F 2 peak with solar activity. The crucial factor in this solar activity dependence is the decreased equatorward neutral wind during high solar activity which keeps the F 2 -layer in the high recombination area.
4. The E Â B plasma drift appears to be inecient for the N m F 2 nighttime peak formation. On one hand, it has a small eect on the h m F 2 variation due to strong anticorrelation between V pn and V par resulting mainly in the horizontal plasma transfer. On the other hand, this horizontal velocity provides a horizontal plasma in¯ux which is much smaller compared to the in¯ux from the plasmasphere. A similar conclusion on small E Â B drift eects was obtained by Jain and Williams (1984) who analyzed the St. Santin nightime observations. 5. The plasma compression/decompression mechanism which was useful to explain the night-to-night N m F 2 variations during solar minimum in January 1997, obviously did not work during high solar activity in January 1990. Dierent plasma ®lling of the magnetic ux tubes in these two cases is proposed as a plausible explanation.