During several campaigns during the last 10 years, detailed in situ studies of electrons, positive ions, and charged aerosols have been performed by means of rocket borne instruments in the presence of Polar Mesophere Summer Echoes (PMSE) and Noctilucent Clouds (NLC). We have studied the correlation between the amount of charged aerosols present in the mesopause region and the PMSE echo power. We have also correlated the PMSE echo strength with the small-scale structure of electrons at the radar Bragg scale that are responsible for the echoes. We find that PMSE occur for rather small amounts of charged aerosols, with the number of electrons exceeding the number of charged aerosols. This is in contradiction with previous, mainly theoretical, studies predicting that PMSE only occur when the ratio between the aerosol charge number density and the number density of electrons is larger than about 1. We also find that there is a high degree of correlation between the PMSE echo power and the fluctuation intensity of electrons at scales comparable to half the radar wavelength. This confirms that variations in electron number density are responsible for the echoes, but does not explain the mechanism that creates the fluctuations.
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 A number of campaigns dedicated to the study of Polar Mesosphere Summer Echoes (PMSE) and Noctilucent Clouds (NLC) have taken place during the last 10 years. PMSE and NLC can be observed near the summer mesopause (80–90 km) when the temperature drops below 140–150 K [e.g., Lübken et al., 1996]. While NLC have been observed since 1884, PMSE were first observed in 1979 by the 50 MHz Poker Flat radar in Alaska [Ecklund and Balsley, 1981]. PMSE have, since then, been the subject to numerous theoretical and experimental investigations. It has been established that the echoes can be divided in two different classes: (1) turbulent and (2) non-turbulent. The turbulent type is, as the name suggests, related to neutral air turbulence and accounts for about 10–30% of all the observations [e.g., Lübken et al., 2002]. For most of the time, however, PMSE are observed in the absence of any variations in the neutral air. So far, it has not been possible to establish the mechanism that is responsible for the latter type of echoes, although numerous investigators have put forward a long list of theories. It is not the purpose of this paper to give a thorough review of these theories, the reader is referred to the paper by Cho and Röttger  and references therein for a more detailed description of the phenomenon. However, it is important to note that charged aerosols (ice particles) play a crucial role in these theories. It has also been confirmed by in situ measurements that such aerosols really exist [Havnes et al., 1996]. Recently, Rapp and Lübken  and Lübken and Rapp  have developed a model that quantitatively describe the charging process of aerosol particles and its consequences for the background plasma, i.e., electrons and positive ions. Parameters such as the ion/electron recombination rate α, the ion/electron production rate Q, the aerosol number density and the radii of the aerosol particles are taken into account. Applying this model to real data it has been possible to reproduce and interpret in situ measurements of electrons and ions during PMSE events. From observations as well as theoretical work we thus have firm evidence that charged aerosol particles exist as well as having a fairly good understanding of their interaction with the background plasma. In the companion paper by Rapp et al. , the importance of the size of the aerosols, not only their charge number density, for the creation of PMSE is investigated.
 It has been established, both by experimental and theoretical work, that aerosols have a significant influence on the charge balance of the upper mesosphere [e.g., Havnes et al., 1996; Blix, 1999a, 1999b; Cho and Röttger, 1997; Jensen and Thomas, 1991; Reid, 1990; Rapp et al., 2002]. However, it is still an open question which role the aerosols play in the creation process of PMSE. It has been shown that one of the most important effects of charged aerosols is to reduce the diffusivity of electrons [Cho et al., 1992; Rapp and Lübken, 2000; Rapp et al., 2002]. Cho et al.  also suggest that PMSE can be created only if the ratio Λ between the aerosol charge number density (ZaNa) and the electron density Ne is larger than about 1 (1.2 for negatively charged aerosols and 0.6 for positively charged aerosols). To test this hypothesis is the major task of this paper. In order to perform such a test, direct information about the aerosol charge number density and electron density is needed. Alternatively, assuming charge neutrality, one can calculate Λ from measurements of the positive ion and electron densities. In this paper we use both methods to derive Λ.
 In section 2 we describe the experimental methods applied in this study, i.e., in situ rocket experiments and ground-based VHF radar measurements. In section 3 we outline our method used to calculate the Λ factor from the in situ measurements and the uncertainty of the calculations. The results of using this method to four different cases are presented in section 4, and these results are discussed in further detail in section 5.
2. Experimental Methods
2.1. Plasma Probes
 The two types of rocket payloads used in the study presented in this paper, TURBO (Turbulence Bonn Oslo) and MIDAS (Middle atmosphere Investigations of Dynamics And Structure), are constructed to identify spatial structures by means of different electrostatic probes. Three types of probes have been used in this study: (1) a positive ion probe (PIP) mounted in the front of three of the payloads measuring variations in positive ion density; (2) a combined neutral and electron probe (CONE) mounted in the rear of all the payloads; and (3) a charged aerosol detector (DUSTY) mounted in the front of one of the payloads. If a small scale structure is detected first by the front and then by the rear probe, with a time delay corresponding to the distance between the probes along the velocity vector divided by the velocity, we feel confident that the structure is real and not caused by some instrumental disturbance such as variations of payload potential due to ionization by dust impact [Blix and Thrane, 1993]. The technical layout and specifications of the probes can be found in Blix et al. , Giebeler et al.  and Havnes et al. . The most important characteristics of the probes relevant to this work are given in Table 1.
Table 1. Important Parameters of the Plasma Probes Used in This Study
2.2. VHF Radars
 During the launches reported in this paper, three different VHF radars were used. The most important characteristics of these radars are given in Table 2. The EISCAT VHF radar is located at Ramfjordmoen, close to the city of Tromsø, about 130 km from Andøya Rocket Range (ARR). EISCAT was in operation during all the launches reported in this paper, measuring in vertical position at all times. The ALOMAR-SOUSY radar was located within a kilometer from ARR, and was used during the launches in 1994, and gave, for the first time, local information about PMSE structures in nearly the same volume as probed by the rockets. In 1998, the new ALWIN radar replaced SOUSY and has since then intensively studied PMSE structures every summer. ALOMAR-SOUSY as well as ALWIN measured in vertical as well as off-zenith. For consistency, we have used the vertically measured profile in all cases.
Table 2. Technical Parameters of the VHF Radars Used in This Study
 The amount of charged aerosols present in the polar summer mesosphere can be described by the parameter Λ defined as the ratio:
where ∣Za∣ is the mean aerosol charge, Na the aerosol number density and Ne the electron number density. Λ can also be calculated from accurate calculations of the ion (Ni) and electron (Ne) number densities. Λ can then be derived from the expression:
where we have assumed charge neutrality and negatively charged aerosol particles. If we assume positively charged aerosol particles instead, we get the same expression as (2) but with apposite sign (Λ = 1 − Ni/Ne). Therefore, applying (2) in all cases we see that a negative value for Λ implies positive aerosol particles. We will consequently use (2) in this paper. Ni and Ne can be derived from the measured ion and electron currents, but knowledge of the effective cross-section of the probes is necessary. In most cases, it is difficult to determine these with the necessary accuracy. However, one can circumvent this problem in the following way.
 The theory for the capture of electrons and ions by different types of probes is relatively complicated and it is not our task to review this theory in detail. Instead we refer to the works of Sagalyn et al. , Smiddy and Stuart , and the Ph.D. work of Folkestad . There, it is shown that the current to a spherical collector (as in our case) is given by the current to a stationary sphere (I0 = πr02eNVt; r0 is the spheres radius, N the plasma density and Vt the thermal speed of the species in question) multiplied by a correction factor that depends upon the thermal speeds of the ions and electrons as well as the speed of the payload (probe) through the ionosphere. For ions the payload velocity is 3–4 times larger than the thermal speed and for electrons the thermal speed is 70–80 times the payload velocity. In the latter case the correction factor is for all practical purposes 1. The correction to the ion data is consistently less than 5–10%, i.e., a factor of 0.9–0.95. In the simplest case we can therefore derive the following relations between the electron and ion number densities and the measured currents:
Here, A and B represent the calibration factors for the electron and ion number densities. It is these parameters that are difficult to determine. R1 = 3.2 cm and R2 = 5 cm are the geometric radii for the electron and ion probe, respectively. Vte is the electron thermal velocity and VR the rocket velocity. Vte has been calculated based on measurements of the temperature by the CONE experiment. Λ has only a meaning when charged aerosols are present, so below an aerosol layer, we can assume that Ne = Ni. Using (3a) and (3b) we can then derive the following relation between the calibration factors A and B:
In the following, this ratio is called C. This “relative normalization factor” depends only upon measured quantities. Determining C in a region with no aerosols (e.g., just below an aerosol layer), we can apply the experimentally determined C to the measurements inside the layer. From (2), (3a), (3b), and (4), we finally find the following expression for Λ:
This expression again only involves measured quantities. The most important parameters in (5) are the ion and electron currents. The velocities change only little with height, although we have used the actual values in our calculations of Λ. In Figure 1 we show, as an example, the measured ion and electron currents in the height region 80–90 km on upleg for the SO-MI-05 flight (see Table 3). We have, for this flight, normalized the ion and electron densities at a height close to 81.5 km, giving C = 0.62. The same procedure has been applied to the other two flights where we have utilized this method.
Table 3. Rocket Flights and Radar Measurements With Simultaneous In Situ Measurements of Electron Density (Ne), Ion Density (Ni), and Aerosol Charge Number Density (Na)
Date and Time
Radar and Frequency
01.08.93 01:46 UT
EISCAT 224 MHz
28.07.94 22:39 UT
ALOMAR SOUSY 53.5 MHz
12.08.94 00:53 UT
ALOMAR SOUSY 53.5 MHz
17.06.01 00:05 UT
ALWIN 53.5 MHz
Ne, Ni, Na
3.1. Uncertainty Analysis
 At this point we find it necessary to give an estimate of the uncertainty in the derivation of Λ. We have used two different methods to determine Λ, i.e, (1) from electron and positive ion measurements and (2) from electron and charged aerosol particle measurements. These methods depend on the following factors: (a) errors using the approximate formulas 3a and 3b (probe theory), (b) uncertainties in the measured currents, (c) assuming a constant factor C = B/A through the PMSE layer; uncertainties induced by a change in payload potential, (d) ram and wake effects of the supersonically moving payload, (e) uncertainties in temperature used to determine the thermal velocity of electrons.
 The two expressions relating the measured electron and ion currents to the electron and ion densities given by equations 3a and 3b are good approximations to the real situation as already discussed above. For all practical purposes, no correction to equation 3a is necessary. The correction to the ion data is consistently less than 5–10%. Hence, the effect of this correction factor is that the calculated Ni is reduced, indicating that Λ is also reduced (see equation 2). It must further be mentioned that for electrons extensive testing of the probe has been performed in a plasma chamber at the Norwegian Defence Research Establishment. Here, the plasma density and the pressure were changed, in a controllable manner, and the probe carefully calibrated. In the flight version, with an attractive potential of 6 V, the effective radius of the probe was reff = 6 ± 0.1 cm. This is what we have used in all cases where an absolute estimate of the electron density is needed (e.g., for ECT-02).
 Uncertainties of the measured currents have been determined in the laboratory by comparing the output from the probe as a result of a known and precise input (current) source. These calibrations have shown that the probe electronics is accurate within 2% except for the smallest currents the probe can measure where the uncertainty increases to 5%.
 A constant factor C through the PMSE layer means that we assume that e.g., the payload potential does not change significantly within the layer. This potential has shown to be negative in all the cases we discuss in this paper: During one of the flights (SO-MI-05), the payload potential was actually measured, although not through the entire layer. The measured value was −2.8V, and it did not vary for a height interval of about 3 km in the upper part of the PMSE layer. In the other three cases we can infer that the payloads must have been negatively charged due to the fact that the ion and electron densities (determined with equations (3a) and (3b) and the plasma chamber calibration mentioned above) below the PMSE layer were different from each other though charge neutrality would require equal number densities of both species. The calculated ion density was always larger by a factor of 2–5 than the electron density, indicating that the effective area of the probe was larger (by the same factor) than the geometric cross section. This means that an attractive potential (for ions) must have been present on the outer grid of the ion probe that is also the payload potential because this grid is electrically connected to the skin of the payload. To a first approximation, a potential will be screened over distances of about the Debye-length of the plasma. This is about 1–2 cm in the upper mesosphere. Thus, an increase (or decrease) of the potential by e.g., 0.5 V will only have minor importance for the detection of ions or electrons since the payload was already charged before entering the layer. The increase (or decrease) of payload potential should only result in a change of effective radius of the probe that is much less than the Debye-length, i.e., much less than 1 cm. This gives a relative uncertainty of less than 5–10% due to a change in payload potential. It must again be noted that if the payload potential becomes more negative than assumed (assumption C=const.) when passing through the PMSE layer, we overestimate Ni and consequently overestimate Λ.
 Ram/wake effects can be studied by comparing differences in the measured currents on upleg and downleg of the flights. Since the electrons are much more mobile than the ions, we should expect the differences to be larger between upleg and downleg for ions. This is confirmed by observations. The measured electron currents in the 80–90 km height region are always very similar, while the measured ion current on average seems to be larger on upleg where the positive ion probe is located in the front and thus in the ram position of the payload. In addition, the ion data show more modulations caused by spin and nutation of the payloads on downleg. We have therefore chosen to only use the upleg data for the determination of Λ. For the single case where the charge number density (ZaNa) was actually measured (flight ECT-02), we also use only upleg data since the particle detector can only properly work if located in the ram of the payload. A further question in this context is if all the particles present were measured by the probe. Horányi et al.  have shown that for ice particles larger than 5nm, the detection efficiency is ∼95%. Lübken et al.  analyzed the particle measurements during flight ECT02 with the aid of a microphysical model of the charging of aerosol particles in the mesopause region and concluded that the particle radii were ∼8 nm, i.e., larger than 5 nm. Uncertainties in the derivation of absolute values of ZaNa from flight ECT02 should therefore be small (∼5%).
 Uncertainties in the thermal velocity of electrons are caused by uncertainties in the temperatures determined from the CONE experiment. These temperatures are derived from an integration of absolute densities which are obtained with an accuracy of ∼2% [Rapp et al., 2001]. Hence, also the relative error in temperatures is ∼2% resulting in an absolute uncertainty of ∼3 K for altitudes between 80–90 km. Since the temperature enters the thermal velocity as a square root only, the uncertainty of the thermal velocity is about 1%.
 To summarize, we conclude that our derived values of Λ are correct within an uncertainty of 25% even under worst case assumptions. Note, in addition, that the error analysis presented above hints at the fact that we have generally overestimated Λ, i.e., that the true values of Λ were even smaller than presented in our study. This result thus supports our main conclusion, i.e, that Λ appears to be much smaller than expected from current theoretical work. We have, in addition, chosen to use upleg data only to calculate Λ because we regard the ion probe data to be most reliable for this part of the flights.
4. Observational Results
 In this paper, data from four flights of the TURBO and MIDAS payloads have been used. Table 3 summarizes the most important characteristics of these flights. During the first flight, the EISCAT 224 MHz radar located close to Tromsø, about 130 km from Andøya, was used to measure PMSE. During the other 3 flights, the local SOUSY or ALWIN 53.5 MHz radars were used to monitor the PMSE situation. Also listed in Table 3 are the most important parameters measured by the respective payloads and relevant for this study. In the following we will present the results from each flight separately.
4.1. Electron Density Fluctuations
 In order to receive echoes from the mesosphere, electron number density fluctuations at the Bragg scale, i.e., half the radar wavelength, of the probing radar are necessary. For a 50 MHz radar this corresponds to a spatial scale of 3 m. In addition to calculate the parameter Λ discussed in section 3 and compare the results with the radar measurements, we also calculate the density fluctuations at the Bragg scale. We compute the power spectrum of the measured density fluctuations and determine the fluctuations at the Bragg scale by reading out the associated power density. As an illustration, we have calculated the power spectrum at two different heights on the upleg of flights ECT-02. The result is shown in Figure 2. The left panel of this figure shows the spectrum inside a PMSE layer, while the right panel shows a typical spectrum outside a PMSE layer. As can be seen, the difference between the calculated power at the Bragg scale (in this case 2.8 m) is more than 2 orders of magnitude. The actual electron density fluctuations can easily be calculated from the following relation:
Here, ΔNe/Ne is given in % and P(f) is the power density at a frequency corresponding to the radar Bragg scale. Two orders of magnitude in power correspond therefore to a factor of 10 in absolute density fluctuations. Much larger differences than this have been observed, but the present case illustrates the effect of enhanced fluctuations at the Bragg scale nicely. This method of determining the density fluctuations has been applied to the four cases we study in further detail below.
4.2. Flight SCT-06
 This payload was launched as part of a rocket salvo during the SCALE campaign from Andøya Rocket Range in July/August 1993. The payload carried the PIP sensor in front and the CONE sensor in the rear and measured Ni and Ne on upleg as well as on the downleg part of the flight. The EISCAT radar used to study the PMSE structure during the flight has a Bragg scale of 67 cm. Due to the sampling rate of the electron density measurements onboard SCT-06, it is not possible to calculate the density fluctuations at exactly the Bragg scale of the radar. We have therefore calculated the electron density fluctuations at a scale corresponding to half the sampling rate. During the passage of the observed PMSE layer this is about 80 cm. The results are shown in the left panel of Figure 3 together with the observed radar profile at the time of flight. As can be seen, the EISCAT radar shows a double layer structure centered at around 85 km and 87.2 km, respectively. During the upleg part of the SCT-06 flight, the measured electron density drops below the sensitivity limit in the center of the lower layer. It is therefore impossible to measure any electron density fluctuations inside this layer. However, below the peak the in situ measurements show an increased fluctuation level corresponding to the lower ledge of the layer. The upper layer does not seem to be observed in situ. The reason for this may be the horizontal difference between the ground-based and the in situ measurements (about 150 km). Generally, the agreement between the fluctuation level observed on upleg and downleg agree, although not in detail. The increased fluctuation level observed above 86 km on downleg is the result of a plasma instability and has nothing to do with PMSE.
 In the right hand panel of Figure 3, we show the result of calculating Λ using the procedure outlined in section 3. Not shown in the figure are data below 84 km and above 88 km which are hampered with large spin modulations in the lower part and a change in the calibration factor at the upper part due to changes in the ion composition (from water cluster ions to molecular ions). The latter manifests itself through a gradient in the measured ion and electron densities. Data from these heights are from outside the PMSE layer and have therefore no influence on our derivation of Λ. In the lower layer (i.e., 84.7–86 km) our data show that Λ ≥ 1, in accordance with the theory put forward by Cho et al. .
4.3. Flight ECT-02
 This payload was launched as part of a salvo during the ECHO campaign in July/August 1994. During this campaign, the local SOUSY VHF radar was used for the first time in combination with instrumented sounding rockets to study the PMSE structure in the same volume at the same time. As for the SCT-06 flight, we have calculated the electron density fluctuations as close to the radar Bragg scale (2.8 m) as possible. The results for the upleg part of the flight are shown in the left hand panel of Figure 4 together with the observed radar profile at the time of flight. As can be seen, the general agreement between the electron density fluctuations and the radar profile is excellent, especially for upleg. The fluctuations observed on downleg are plotted for comparison purposes and show that the PMSE layer extends over a horizontal distance of about 50 km and that the main features are generally the same on upleg and downleg.
 In the right hand panel we have again calculated the parameter Λ. During this flight, the payload carried the DUSTY aerosol detector from the University of Tromsø [Havnes et al., 1996] and direct measurements of the aerosol charge number density were possible for the first time. We have used these data together with the calculated electron density from the CONE experiment to determine Λ directly by (1). The resulting Λ-profile is shown in the right hand panel of Figure 4. As can be seen, the variations of Λ are much larger for this flight as compared to the SCT-06 flight. The height region covered by PMSE is also broader as compared to the SCT-06 situation. The most interesting result is the observation that Λ ≤ 1 for most of the PMSE height region. The exceptions are for heights corresponding to the heart of the upper layer around 87.5 km and close to 85.5 km. Here, it is interesting to note that there seems to be an anti-correlation between the very large Λ-values and the observed electron fluctuation level: both altitude ranges with Λ ≫ 1 correspond to a local minimum in ΔNe/Ne. In the lowest region, the electron density was practically zero. This anti-correlation would have been even more pronounced if we had converted the fluctuations from relative to absolute density variations. A rough estimate of the background density at the heights in question gives a value of the order of 5 × 109 m−3, while the density inside the layer was less than 109 m−3. The minimum of about 0.03% at 87.5 km corresponds therefore roughly to an absolute fluctuation of 3 × 105 m−3. The fluctuation outside the layer is about 2 × 107 m−3, more than a factor of 50 larger. However, this is simply an observational fact and is not important for the main task of this paper: the determination of Λ.
4.4. Flight ECT-12
 The ECT-12 payload was launched into a relatively weak PMSE layer located between 85 km and 87 km. As for the ECT-02 flight, this payload was launched as part of the ECHO campaign in summer 1994. Figure 5 shows, in the left hand panel, the observed electron density fluctuations for both upleg and downleg of the flight as well as the observed PMSE profile. The electron density fluctuations on upleg show a small increase co-located in height with the PMSE maximum at about 86 km. On downleg the layer seems to be broader, but the peak is located at almost the same height (about 0.5 km lower).
 The calculated Λ profile for this flight is shown in the right hand panel of Figure 5 and shows that Λ < 1 at all heights. It peaks at a value of 0.3 around the maximum of the PMSE layer. The ECT-12 observations therefore confirm that PMSE can be observed for very small values of Λ.
4.5. Flight SO-MI-05
 This flight was performed during the recent SOLSTICE campaign that took place at Andøya Rocket Range in June 2001. We have, as for the previous flights, calculated the electron density fluctuations at the Bragg scale of the probing ALWIN VHF radar (2.8 m). The results are shown in the left hand panel of Figure 6, together with the observed PMSE profile at the time of flight. SO-MI-05 was launched during a very strong PMSE event covering the height range 81 km to 91 km. This is the broadest PMSE we have ever launched a payload through. Generally the fluctuations are observed in the same height range as the radar, but there is a lot of structure in the electron density data that are not revealed by the radar. The upleg and downleg fluctuation data are also different. As one might expect, since the distance is shortest, the agreement is best between the upleg in situ data and the radar. The horizontal distance between the upleg and downleg parts of the flight is approximately 30 km and the time difference between the observations is about 130–140 s at PMSE heights. The ALWIN radar did not show any significant differences over this time interval, which implies that the differences we see in the electron data between upleg and downleg corresponds to spatial rather than temporal variability in the PMSE.
 The result of the Λ calculation is shown in the right hand panel of Figure 6. One can immediately see that Λ ≤ 1 for an extended height range. Λ is larger than 1 only in the upper part of the layer close to 87–88 km. SO-MI-05 did also carry a charge detector onboard. However, due to flow conditions, the best results from this instrument are from the downleg part of the trajectory. A separate paper by Smiley et al.  deals with the results from this instrument and the most important conclusion is the indication of negatively charged aerosol particles as we find in our study. The uncertainty in the derived charge number densities is between 5 × 108 and 109 m−3, while the derived values are less than 109 m−3, except for heights close to 90 km where it is about 2 × 109 m−3. A rough estimate of Λ gives values in the range 0–0.5 taking the uncertainty into account. This is in agreement with our derivation of Λ using electron and ion data.
5. Discussion and Conclusion
 The purpose of this work is to check if experimental data is consistent with the model of Cho et al.  of electron diffusion in the presence of charged aerosols. According to this model, it is necessary that the amount of charged aerosols must exceed a certain threshold with respect to electrons in order to reduce the diffusivity of the electrons. Cho et al.  considered negative as well as positive aerosols and showed that the parameter Λ discussed in sections 3 and 4 must exceed 1.2 (0.6) for negative (positive) aerosols to achieve a significant reduction of the electron diffusivity. As pointed out by Cho et al.  themselves, the model in its present form is relatively simple. Only one type of positive ions and a single size of aerosols are for example taken into account. In the real atmosphere, a number of positive ions are present, especially in the lower part of the PMSE region with water cluster ions. One should also implement a distribution of aerosol sizes, e.g., a log-normal distribution as a simple, but possibly important, extension of the parameter space. The most important result of Cho et al.  is that, for some value of Λ, the diffusivity of electrons is reduced and small scale density variations may therefore be present. However, the actual value of Λ for which this reduction takes place is not clear due to the simplification of the model discussed above. We have in section 4 presented observational evidence showing that small-scale electron density fluctuations can be present in cases where the aerosol charge number density is much smaller than the electron density.
 In this paper, we present height profiles of Λ showing that Λ can be less than 1. This is an interesting observation, and must have consequences for possible theories put forward to explain the creation/existence of PMSE. To further investigate the behavior of Λ, we have made a statistical analysis of our calculations presented in section 4. We have binned Λ in three intervals: (1) 0–0.5; (2) 0.5–1.0 and (3) >1.0. The results are shown in Table 4. As can be seen, for all the cases we discuss in this paper, between 55% and 100% of the height region covered by PMSE is associated with Λ values less than 0.5. We find that Λ > 1 for between 0 and 30% of the height region covered by PMSE.
Table 4. Lambda Values Calculated for the Four Flights Used in this Study
 In the accompanying paper by Rapp et al. , the importance of the size of the aerosols in addition to their number density is investigated. These authors suggest a “proxy” for the existence of PMSE. It is assumed that the radar reflectivity is proportional to the charge number density times the square of the aerosol radius. In the case studied by Rapp et al. , the proxy does a very good job in recreating the profile observed by the radar. This shows that the picture we have of PMSE is indeed very complicated and we must be cautious in drawing too strict conclusions based on either simplified theoretical investigations or a limited number of in situ observations.
 From the experimental results presented in this paper we therefore draw the following conclusions: (1) The electron diffusivity is reduced in such a way that plasma density fluctuations at scales of meters or less are created for very small levels of charged aerosols; (2) More work, especially theoretical and model investigations, is needed in order to resolve details of the interaction between charged aerosols and the ionospheric plasma.
 This work was supported under grant 115980/431 from The Research Council of Norway and under DLR-grant 50 OE 9802.