JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Dusty space plasma diagnosis using the behavior of polar

mesopheric summer echoes during electron precipitation events

A. Mahmoudian1, A. Senior2, W. A. Scales3, M. Kosch4,5,6, M. T. Rietveld7

Abstract.The behavior of polar mesospheric summer echoes (PMSEs) during electron precip-

itation event (EPE) is investigated in this paper by including dusty plasma effects forthe first time. The observational data recorded with the VHF (224 MHz) and UHF (930MHz) radars at the European Incoherent SCATter Scientific Association (EISCAT) onJuly 10 and 11, 2012 is presented. The observed radar echoes show that the PMSEs areboth correlated and anti-correlated with the increased electron density associated withelectron precipitation events in the two consecutive days. The experimental observationsare compared with the numerical simulations of the temporal evolution of PMSE withdifferent background dusty plasma parameters during EPE. Specifically, the effect of dustradius, dust density, recombination/photoionization rates, photo-detachment current, andelectron density on the behavior of PMSE layer and the associated dust charging pro-cess in the course of electron precipitation events is studied. It is observed that the ra-tio of electron density fluctuation amplitude δne to the plasma density (ne) plays a crit-ical role in the appearance/disappearance of the layer. The simulation results revealedthat the existence of PMSE is mainly determined by dust radius and dust density. Thedusty plasma parameters associated with each event are estimated. The condensationnuclei of the ice particles such as proton hydrate clusters (H+(H2O)n) or Meteoric SmokeParticles (MSP) can be determined by employing the microphysical models along withthe dusty plasma simulations. This can resolve any discrepancy in the description of theobserved phenomena.

1. Introduction

The natural dusty plasma formed by the disintegrationof meteors appears in the atmosphere’s mesosphere regionbetween 50 and 90 km altitude. Climate change and humanactivity have caused decreasing mesospheric temperaturesand increasing water vapor content via increased methaneconcentration. Noctilucent clouds (NLC) occur in the coldpolar summer mesopause and are the direct visual manifes-tation of freezing of water vapor on the dust particles andformation of ice-coated meteoric dust particles. In-situ mea-surements using sounding rockets have shown deep depletionof electron density due to charging on mesospheric dust par-ticles (e.g. Reid, 1997; Havnes et al., 2001; Rapp, 2009;Robertson et al., 2009). Accumulation of free electrons onthe ice particles produces electron density structures, whichcause the reflection of radar waves. Polar Mesospheric Sum-mer Echoes PMSE are strong coherent radar echoes pro-duced by electron density fluctuations in the vicinity of po-lar mesopause and at the half the radar wavelength (Rapp

1Inter American University of Puerto Rico, BayamonCampus, PR, USA

2The Bradley Department of Electrical and ComputerEngineering,Virginia Tech, USA

3Independent Researcher, Lancaster, UK4Department of Physics, University of Lancaster,

Lancaster, UK5South African National Space Agency, Hermanus, South

Africa6Dept. of Physics and Astronomy, University of the

Western Cape, Bellville, South Africa.7EISCAT Scientific Association, Ramfjordmoen, Norway

Copyright 2018 by the American Geophysical Union.0148-0227/18/$9.00

and Lubken, 2004). The first VHF radar echoes from thehigh-latitude mesosphere were observed with the Poker Flatradar in Alaska (location 65.12◦ N, 147.43◦ W) (Ecklundand Balsley, 1981; Balsley et al., 1983). The PMSE havealso been observed in Antarctica (Halley station located at76◦ S, 27◦ W) with dynasonde at 28 MHz (Jarvis et al.,2005).

Solar occultation infrared measurements have confirmedthat the dust particles mainly consist of water ice in the sum-mer polar mesosphere (Hervig et al 2001, Eremenko, et al2005). Hervig et al (2009) reported the first measurements ofmesospheric smoke particles from a satellite. The formationof the dust particles in the Earth’s summer polar mesopauserequires water ice nucleation and condensation as describedby Rapp et al (2013). Water ice nucleation is possible from80 to 90 km above the Earth’s surface as the temperature inthis altitude range drops below the water vapor frost pointduring the summer. The nucleation process is likely to beof a heterogeneous nature involving water ice molecules at-taching to pre-existing nuclei. It has been proposed that thecondensation nuclei may include large condensation protonhydrate clusters, carbon particles (i.e. soot), sulfuric acids(volcanic ash), sodium bicarbonate and hydroxide, and me-teor smoke particles MSP with the latter being the mostlikely candidate. Extending the proton hydrate chain tolarge cluster sizes (H+(H2O)n, n >5) can quantify the effi-ciency of ionic nucleation of mesospheric ice particles. Whileionic nucleation is not feasible as a major mesospheric nucle-ation process, it can become efficient given moderate atmo-spheric variations as induced by gravity waves. It should benoted that the dusty plasma formation and existence in thepolar mesosphere is a very complicated that can be affectedby several parameters (Christon et al., 2017).

Formation of meteoric smoke particles happens afternear-complete ablation of meteoroids in the altitude rangeof 75-115 km and leads to particle sizes of 1–2 nm and den-sities of a few 1000 cm3 as stated earlier by Hunten et al.

1

X - 2 MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE

(1980). The critical radius for water ice particle nucleationunder typical mesospheric conditions is believed to be ≈ 1.3nm. These particles of meteoric origin are difficult to mea-sure and there is a relatively broad spread in the densitiesreported by various authors, which includes 101 to 103 cm3

(for rd =≈ 1nm). Gelinas et al (2005) reported the firstvalidation of the MSPs characteristics via sounding rocketin the tropical mesosphere. The measurements show thatthe charged population of these meteoric particles is of theorder of 100 cm3 and the uncharged population is 1000 cm3,which are in agreement with predictions by Hunten et al(1980). The flux of photons incident on the meteoric smokeparticle surface releasing photo-electrons and ultimately re-sulting in positive dust particles (Havnes et al., 1990; Rapp,2009). Therefore, photo-detachment current plays a criti-cal role in the charging process associated with mesosphericdust in the case of proton precipitation event.

The time evolution of PMSE during perturbed atmo-spheric conditions such as enhanced electron density pro-vides a unique opportunity to measure the background dustyplasma parameters. Rapp et al. (2002) presented the firstinvestigation of PMSE dependence on background electrondensity during Solar Proton Event (SPE) and provided anestimation of the minimum and maximum electron densityrequired for the PMSE observation. The negative correla-tion (and anti-correlation) of VHF PMSE (224 MHz) and

Figure 1. Experiment conducted on July 10th, 2012a) electron density measured by EISCAT UHF radar b)EISCAT VHF radar and associated PMSE layer. Theblack rectangles labeled 1 and 2 indicate the regions ofPMSE.

enhanced electron density are attributed to the low dustdensity present within PMSE region. The increased elec-tron density can also modify the background ion chemistryin the mesosphere. The prominent changes in the cluster ioncomposition, appear in N+2 , N

+, O+2 and O+. As a result,

proton hydrates H+(H2O)n, may also be produced at loweraltitudes (70-85 km) and with densities ≈105 cm−3 throughthe fast O+2 chain. Another major candidate for conden-sation nuclei of mesospheric ice particles are large protonhydrates H+(H2O)n. The water cluster ions increase by afactor of 100 during solar proton event, while the transitionheight will shift downward about 6 km in comparison withquiet ionization condition. The previous study by Rapp etal. (2002) has shown that nucleation on large proton hy-drates during solar proton event is less likely due to Kelvineffect and large hydration numbers required.

Unlike the vast development of computational and theo-retical models as well as experimental observations of bothnatural and artificially modified PMSE over the past fewyears (Senior et al., 2014; Scales and Mahmoudian, 2016),there are still open questions in regards to the dust chargingprocess in the mesosphere. This paper presents the first clearvariation of VHF PMSE during EPE. The slow variationof background electron density during EPE in comparisonwith SPE, provides an excellent condition to measure dustyplasma parameters, study formation and extinction of dustparticles, and dust charging process. The main focus of thispaper is the changes in the PMSE strength due to back-ground electron density variation rather than HF heatingwhich modifies the background electron temperature (Te).

Figure 2. Repeated experiment on July 11th, 2012 a)electron density measured by EISCAT UHF radar b) EIS-CAT VHF radar and associated PMSE layer

MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE X - 3

This paper is organized as follows. The experimental ob-servations are presented in section 2. The computationalresults for the quiescent mesospheric condition and duringEPE with increased electron density by factors of 10 and 20are described in section 3. The discussion and conclusionare provided in sections 4 and 5.

2. Experimental Observations

The observations presented in this paper were recorded intwo consecutive days in July 2012. The experiments startedat 08:00 UT on July 10th and 11th, and lasted for 4 hoursin each day. The electron density in PMSE region was mea-sured by EISCAT UHF radar and the EISCAT VHF radarmeasured PMSE simultaneously. The electron density mea-sured by the UHF radar between 08:00 UT to 12:00 UT, onJuly 10, 2012 is shown in Figure 1a. Corresponding PMSElayer measured by VHF radar is shown in Figure 1b. Ac-cording to Figure 1a, two electron precipitation events areclearly seen on July 10th. The first electron precipitationoccurred from 08:00 to 08:45 UT and in the altitude ∼ 85km. The second event is observed over a longer time periodbetween 09:20 UT and 10:40 UT. This electron precipita-tion event extends to lower altitudes ∼ 80 km. Both casesshow a maximum electron increase of the order of 10-15 dur-ing the precipitation event. The VHF radar echoes (Figure2b) show an appearance of a weak PMSE subsequent tothe precipitation event at 08:45 UT, and near the maximumelectron density enhancement region ∼ 89 km (marked withblack rectangle labeled 1). The second PMSE occurs rightafter the long-period precipitation event and is located ina lower altitude range of 87-88 km. This case shown withblack rectangle labeled 2, stays for about 20 min and is muchstronger than the case 1. The amount of energy depositedby the precipitation is quiet small even though the electronspectrum is hard. The electron temperature most likely isclose to the neutral temperature (Tn). Considering the back-ground electron density (ne) of the order of 2×109 m−3, thene enhancement ratio associated with PMSE is estimated tobe about 10 based on the observations shown in Figure 1.It should be noted that some weak and scattered PMSE isobserved from 09:30–10:30 UT.

Figure 2 represents the similar experimental observationscarried out on July 11, 2012. In this case, a continuous

Figure 3. Proton flux measured by the GOES 13 satel-lite showing quiet geomagnetic condition during the ex-periments on July 10 and 11, 2012.

electron precipitation event is detected between ∼08:00 UTand 12:00 UT. The precipitation event expands to lower al-titudes below 85 km. The simultaneous PMSE formationextends from 83 km to 88 km and persisted for more thantwo hours. Unlike the earlier experiment on July 10, obser-vations on July 11 show the coincidence of PMSE formationand electron precipitation. The electron density accumula-tion in PMSE region is not expected, at least not for the in-tegration time of the radars. The VHF radar data-recordinginterval used in this experiment is 4.8 s. It should be notedthat the HF transmitter was operating during this experi-ment with the heating cycle was 24 s on, 156 s off on bothdays. The integration time used in this study in order toresolve the heating cycles is complicated. The integrationtime of the radar observations presented in Figures 1 and2, are 24 s, 153.6 s, 4.8 s, 19.2 s, 4.8 s, and 153.6 s. Thisarrangement is chosen to cover most of heating cycles. Thisis repeated for other heating cycles. This is due to the highrecombination rate because of the high collision frequency.According to Figure 2a, ne ∼2× 109 m−3 is considered forthe background plasma in the absence of EPE. The elec-tron density increases of the order of 10 (∼ 2×1010 m−3)in the PMSE altitude range 83–85 km from 08:00 to 08:20UT. This period is marked with cases 1 and 2. A strongerelectron precipitation event is observed from 08:50 to 11:30UT with a maximum electron density of 5×1010 m−3 (in-creased by a factor of ∼20). This period is shown in case3. The electron precipitation altitude extends to 80 km incase 3. Two weak events are also observed 12:30 to 12:35UT (case 4) and 12:50 to 13:00 UT (case 5). The electrondensity enhancement ratio within PMSE region is estimatedto be ∼5 in these two cases.

The appearance and weakening of PMSE shows differentbehavior as the background electron density changes. Thecases denoted by 1–5 show the correlation of enhanced back-ground electron density and VHF radar echoes appearance.This is mainly due to the increased background electron den-sity above the threshold level (as well as electron densityfluctuation amplitude) to scatter radar signal. The totalelectron density enhancement along with the radar echo in-tensity can be used to estimate the charging rate, and sizeand density of dust particles.

Figure 3 shows the proton flux measured by the GOES(Geostationary Operational Environmental Satellite) 13satellite that shows a quiet geomagnetic condition duringexperiments on July 10 and 11, 2012. The technical defini-tion of an SPE is when the 10 MeV flux exceeds 10 cm−2

s−1 sr−1, the dashed horizontal line in the plot, which itfell below on 2012-07-09. Although there may have beensome residual enhancement of the electron density due tosolar protons on 2012-07-10, it would be weak. The radardata also show no such activities. Another characteristicof solar proton precipitation is that it tends to vary veryslowly in time. Therefore, the strong and rapidly-changingenhancements in electron density shown in the radar data inFigures 1 and 2, are entirely due to energetic electron precip-itation. This is of internal magnetospheric origin-electronswhich have drifted around from substorm injections in thenight-side and is very common at this time of day.

3. Numerical Model

The first 1-D unmagnetized model that employs a hybridapproach with fluid electrons and ions and particle-in-cellMonte Carlo Collision (PIC-MCC) dust particles and allowsfor flexibility in incorporating dynamical charging models forthe dust as well as dust mass distributions, is used in thisstudy (Scales, 2004; Chen and Scales, 2005; Mahmoudianand Scales, 2011; Senior et al., 2014). This model is capa-ble of simulating the time evolution of the electron density

X - 4 MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE

irregularities, which corresponds to the radar echoes in allfrequency bands associated with polar mesospheric clouds(PMSE) and for all background dusty-plasma parameters.The simulations are corresponding to the coherent radarscattering and fluctuations in dust-plasma are assumed tobe at half the radar wavelength. The electron density fluctu-ations ultimately result in the observed backscattered radarsignals. The initial uncharged dust is taken to have an ir-regular density of the form

nd(x) = nd0

(1 +

δndnd0

sin (2πmx/l)

)(1)

where nd0 is the undisturbed dust density, δnd is the dustdensity irregularity amplitude which is set to 0.2 in the sim-ulation, m is the irregularities mode number and l is thesystem length in this model. The radar reflectivity is propor-tional to the electron density fluctuations amplitude in thewavenumber domain (δne(k)) (Royrvik and Smith, 1984).Scales (2004) has shown that for the sinusoidal perturba-tions used in this model, the radar reflectivity η(k) ∝ δn2e,where δne is the electron density irregularity amplitude.

The one-dimensional mesospheric irregularity model isused in this study for the formation and the time evolu-tion of associated PMSE irregularities in the altitude rangearound 85 km. At this altitude region the plasma densityne0 = ni0 = 2×109 m−3. The plasma temperature is typ-ically Te = Ti = 150

◦ K; therefore the electron thermalvelocity is vthe ∼105 m/s. The ion mass is mi = 50 mp(O+2 ), where mp is the proton mass. The ions are highlycollisional with νin ≈ 105 Hz (Mahmoudian et al., 2011).The density irregularities are assumed to have a wavelengthof ∼ 64 cm, which corresponds to the radar frequency ∼ 230MHz. The photoionization/recombination rates in the equi-librium is Pi = Li = αne0ni0, α ∼ 10−12 m3s−1 and for typi-cal mesospheric parameters. The production/recombinationtimescale is of the order of 100 s which is comparable to theion charging time. Several parameters in the simulationsincluding dust charge density to the background electrondensity zdnd/ne, δn

2e (corresponding to radar echoes), and

ne are used in this study. The photo-detachment current in-cluded in the charging model is described here (Mahmoudianet al., 2017). The time variation of charge on dust particlesbased on continuous Orbital-Motion Limited OML approach(Bernstein and Rabinowitz, 1959) can be written as follows:

dQdt

= Ie + Ii + IP (2)

where Ie, Ii, and IP are the electron and ion current on eachdust particle, and photodetachment current, respectively.Assuming negatively charged dust, photo-detachment cur-rent can be approximated by (Rosenberg, 1996)

IP,Zd0 = −πr2dαexp(qeφd/KTp), (4)

where rd is the dust radius, K is the Boltzmann constant,and φd is dust floating potential. In Eq. (3) and (4), theparameter α is α = qeJpQabYp where qe, Jp, Qab, Yp, andTp are the electron charge, photon flux, photon absorptionefficiency, photoelectron yield, and average photoelectron

temperature. Previous studies have estimated solar pho-ton flux Jp to be of the order of ∼1.5×105 photon cm−2 s−1for hν ∼4-5 eV and the absorption efficiency Qab ≈ 1 (e.g.Brasseur and Simon, 1981). Photoelectron yield Yp can alsobe estimated using Yp = C(hν −W )2, with C = 0.01/(eV )2(Rapp and Lubken, 1999). Qab is assumed to be ∼1 for2πrd/λ > 1, where λ is the wavelength of the incident pho-tons (Shukla and Mamun, 2002). Calculations by Rapp(2009) indicate that photo-detachment current is importantfor sufficiently small radii (1 nm) and metallic compounds(e.g. Fe2O3 , SiO). The average photoelectron temperatureTp is assumed to be ∼ 400Te (Mahmoudian et al., 2017).The previous studies have shown that MSP present in themesosphere may be positively charged due to photoemissionby solar UV radiation (Rosenberg and Shukla, 2002). Rosen-berg et al., (1996) provided an estimation of photo-emissioncurrent for UV intensity of 8-9 eV photon.

The ratio of dust charge density zdnd to the backgroundelectron density ne determines the amplitude of the elec-tron density fluctuations. This parameter will be critical forbackscattered radar signal to be above the threshold andPMSE to be observable using radars. Therefore, the ele-vated ne during EPE, dust density, and dust radius willdetermine the strength of the backscattered radar signal.The simultaneous increase in electron attachment onto dustparticles (ne decrease) and enhancement of zdnd will causestronger radar echoes. The charging of electrons onto thedust particles will reduce the ambipolar diffusion of electrondensity fluctuations which results in long-lasting PMSE.Unlike the previous study by Cho and Kelley (1992) thatsuggests 50% of electrons need to be bound to dust parti-cles in order to observe PMSE, our study shows that withmuch lower dust density and radius the PMSE should beobserved. Previous in-situ rocket measurements and simul-taneous PMSE observations have shown PMSE presence forzdnd/ne > 0.05 (Rapp et al., 2002 and references therein).

The computational results for the background meso-spheric parameters in the quiet mesospheric condition arepresented in Figure 4. It should be noted that the irregular-ities reach the steady state after 200 sec. The dust radius rdis varied from 2 nm to 20 nm, and dust densities nd/ne0 =200%, 100%, 50%, 20% are considered. According to thecharging model, 20 nm dust particles can collect two elec-trons on average. As can be seen in Figure 4a, the electrondensity reduces about 90% for dust particles larger than 10nm and nd/ne0 = 100%. For smaller dust particles (rd ∼2 nm), the reduction in electron density is about the same(< 20%) for nd/ne0 = 100%, 50%, and 20%. The criti-cal parameter of zdnd/ne0 in mesospheric dusty plasma thatdetermines the strength of VHF PMSE (224 MHz) is shownin Figure 4b. According to this figure, the dust charge den-sity to background plasma density is below the thresholdlevel (0.05) for nd/ne0 = 20% and rd =2 nm. As the dustradius increases to 20 nm, zdnd/ne0 increases to 1.4. An-other critical aspect of the dusty plasma within PMSE, thathas been overlooked in previous studies, is the variation ofthe amplitude of the electron density fluctuations δne as thedusty plasma parameters vary. A comparison of δn2e shownin Figure 4c, which corresponds to the backscatter radarsignal amplitude. This figure indicates that measuring thedust charge density zdnd normalized to ne is not sufficientto assess the background mesospheric parameters. Althoughzdnd/ne0 increases to 100 and for nd/ne0 = 100% and 50%(Figure 4b), the corresponding radar echoes (∝ δn2e) ap-proach zero (Figure 4c). The maximum amplitude of δn2efor nd/ne0 = 200%, 100%, 50%, and 20% occurs at rd =4 nm, 6 nm, 9.5 nm, and 15 nm, and for both δnd/nd0 =0.2. The maximum amplitude of fluctuations (radar echoes)reach 9.61, 9.57, 9.5, and 9.35 log10 m−3, for nd = 4×109,2×109, 109, and 4×108 m−3, respectively. Therefore, whilethe required condition zdnd/ne > 0.05 for dust densities100%, 50%, and 20% is satisfied, the radar echoes (∝ δn2e)

MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE X - 5

are very weak and may be below the threshold level of VHFradar detection. These values for δnd/nd0 = 0.5 are 10.9,10.82, 10.82, and 10.6 log10 m−3, for nd = 4×109, 2×109,109, and 4×108 m−3, respectively. According to observa-tions presented in Figures 1b and 2b, no PMSE is observednear 10.5 log10 Ne m

−3 which is in agreement with the nu-merical results presented in Figure 4.

Figures 5 and 6 represent similar parameters includingthe electron density variation due to charging onto dust par-ticles (ne/ne0 %), zdnd/ne, and δn

2e for the elevated back-

ground electron density by a factor of 10 and 20 (ne =2×1010 m−3 and 4×1010 m−3, respectively). Two values ofdust density fluctuation amplitude δnd/nd0 of 0.2 and 0.5,and dust density nd = 4×109 m−3, 2×109 m−3, and 109m−3 are considered in these two figures. Figures 5 showsthat the threshold level of zdnd/ne = 0.05 for PMSE to beobserved by VHF radar is satisfied for rd > 4 nm (nd =4×109 m−3), rd > 8 nm (nd = 2×109 m−3) and rd > 15nm (for nd = 10

9 m−3) in the case of ne = 4×1010 m−3.According to Figure 6, this condition for increased ne by afactor 20 is rd ∼ 5 nm (nd = 4×109 m−3), rd > 10 nm (nd =2×109 m−3), and rd > 17 nm (nd = 109 m−3).

The variation of recombination/photoionization rates isconsidered in order to study the long-lasting electron pre-cipitation events (case 3 in Figure 2b) as well as short periodEPE (Cases 1, 2, 4, and 5 in Figure 2b). As can be seenin Figure 7, the electron density reduces to the value nearthe natural condition in short period events (α =10−12 m3

s−1). The difference between the long and short EPE eventsis mainly prominent for larger dust radius and higher dustdensities.

A complete assessment of the required conditions forPMSE observations includes the exact measurements of nd,rd, ne, as well as photoionization/recombination rates, andcharging characteristics of dust/ice particles. Therefore, thePMSE existence, time evolution, and strength can be em-ployed to provide an estimation for nd, rd, and dust chargingcharacteristics.

4. Discussion

The behavior of PMSE during background electron den-sity enhancement and active geomagnetic condition mayhave a great potential as a diagnostic for dusty plasma pa-rameters within PMC as well as the formation of ice particlesin the polar mesosphere. The main focus of this section isto compare the computational results with the experimen-tal observations in order to develop a remote sensing tech-nique to characterize and measure natural dust layers in thenear-Earth space environment. The following sections willinvestigate the time evolution of PMSE layers observed onJuly 10 and 11, 2012 and presented in Figures 1 and 2.

4.1. Event 1: July 11, 2012

Case 1 & 2: T These two events show the formationof a weak PMSE layer 83–84 km associated with electrondensity enhancement by a factor of 10 (ne ∼ 2×1010 m−3).As shown in Figure 4, δn2e (backscattered VHF radar signal)in the natural mesospheric conditions is small and decreasessignificantly as the background dust density nd reduces. Theexpected radar echoes are 10.87 and 10.7 log10 Ne m

−3.Therefore, non-existence PMSE during natural mesosphericcondition is mainly due to the high nd present in this re-gion. A close comparison with Figure 5b shows that thereare three parameter regimes for which the required conditionof zdnd/ne > 0.05 for the PMSE observation will be satis-fied in the enhanced ne condition by a factor of 10. Theseparameters for δnd/nd0 = 0.5 are (nd = 4×109 m−3 andrd > 4 nm), (nd = 2×109 m−3 and rd > 8 nm), or (nd =109 m−3 and rd > 15 nm). The small values of δn

2e shown in

Figure 5c, validates the weak PMSE observed in cases 1 and2. According to Figure 5c, these values correspond to theradar echoes ∼ 11.3 log10 Ne m−3, which is comparable tothe observed radar echoes (Figure 2b). It should be notedthat the values of radar echoes associated with δnd/nd0 =0.2 are of the order of 10 log10 Ne m

−3, which is much weakerthan the observed radar echoes. Appearance of PMSE in thecourse of a very short EPE in cases 1 and 2, and comparisonbetween the value of the estimated radar echoes in the nat-ural mesospheric condition and enhanced electron densityby a factor of 10 (10.7–10.87 and ∼ 11.3 log10 Ne m−3, re-spectively), validate the computational results and that thethreshold level of VHF PMSE is reached.

Case 3: The time period 3 from 08:50 to 11:00 UTshows the strongest PMSE layer with persistent intensityduring EPE, which correlates well with the electron pre-cipitation altitude. The lower layer formed in the altituderange 83–86 km consists of larger particles. The electrondensity increases by a factor of 15 to 20 throughout thiscycle (ne = 4×1010).

The layer at altitudes closer to mesopause with lower tem-perature may compose of smaller ice particles and higherdensities. The formation of ice particles starts at mesopausealtitude where the temperature reaches its minimum. Asthe ice particles grow through water ligand accumulation,they will settle at lower altitudes due to the action of grav-ity. The descending in the altitude of this layer between9:50-10:00 UT and 10:30-10:50 UT may also confirm thishypothesis. The delay in the appearance of this layer couldbe due to a high ratio of nd/ne. This figure shows that theVHF radar echoes reach a maximum amplitude of 12 log10Ne m

−3. A close comparison with the results presented inFigure 6c and for electron density enhancement by a factorof 20, shows that the condition of radar echoes in the or-der of 12 log10 Ne m

−3 can be satisfied for one parameterregimes. According to the computational results shown inFigure 6, the expected radar echoes of the amplitude of 12log10 Ne m

−3 occurs at rd = 10 nm (nd = 4×109 m−3), andfor δnd/nd0 = 0.5. The computational results also show thatthis condition is satisfied for rd > 20 nm (for nd = 2×109m−3), and for δnd/nd0 = 0.5. Therefore, by taking intoaccount the typical mesospheric conditions, the two param-eter sets of (rd ∼ 10 nm, nd = 4×109 m−3, δnd/nd0 = 0.5)is more probable parameters to reproduce the experimen-tal observations shown in Figure 2b and case 3. Anotherimportant feature of the computational results presented inFigure 6 is that the radar echoes of 12 log10 Ne m

−3 satisfiedvery close to the other requirement of zdnd/ne of 0.05 oc-curs (Figure 6b), which is estimated based on in-situ rocketmeasurements and simultaneous VHF PMSE observationson the ground.

According to Figure 2b, a secondary PMSE layer startsto develop at a higher altitude range around 87 km at 09:50UT and extends to lower altitudes around 86.5 km. Thislayer is composed of smaller ice particles and larger densi-ties. The delay in appereance also justifies the slow chargingprocess due to smaller charging timescale (Mahmoudian etal., 2011). Based on the simulation results presented in Fig-ure 6, the existence of this layer will require nd >∼ 6–8×109m−3 for smaller dust particles (rd ∼ 2 nm). The formationof PMSE in higher altitude range 87-88.5 km which corre-sponds to the smaller dust particles may show a clear sig-nature of newly formed ice cloud with a smaller size (< 3nm) that are exposed to enhanced electron density and getcharged. Another feature to point out is the variation ofPMSE strength between 9:30-9:50 UT is due to the satura-tion of dust particles and enhancement of ne which resultsin lower radar reflectivity. The disappearance of PMSE af-ter EPE could be due to the photo-detachment process ofelectrons from dust particles and recombination with the

X - 6 MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE

background ions. This effect could also be as a result of iceparticles destroyed by collision with MSP (< 0.2 nm). Asproposed by Rapp et al. (2002), the decay of PMSE canalso be explained in terms of the evaporation of ice particlesas a result of Joule heating.

Figure 7 shows the variation of zdnd/ne and radar echoeswith and without photo-detachment current as well as thevariation of recombination rate by a factor of 20. As canbe seen, the effect of photo-detachment current and pres-ence of positive dust particles on the required threshold ofzdnd/ne = 0.05 for VHF PMSE observations and the as-sociated radar echoes is significant. According to the com-putational results, the minimum dust radius for satisfyingzdnd/ne = 0.05 condition increases between 4–6 nm, whichis much larger than the typical dust particles present in thePMSE region. The effect of photo-detachement current onthe associated radar echoes shown in Figure 7b is substan-tial. This effect is more prominent for larger dust particles.Another parameter that is investigated in Figure 7, is the ef-fect of recombination/photoionization rates enhancement bya factor of 20. This is applicable for long-lasting precipita-tion event. The changes produced on the minimum dust ra-dius requirement for PMSE observation is ∼ 0.5 nm. The es-timated backscattered signal amplitude remain unchanged.Therefore, the effect of recombination/photoionization ratedon the expected VHF PMSE is very small.

Rapp et al. (2002) argued that the positive correlationof PMSE and electron density enhancement implies a lowerlimit in electron density. They have also postulated thatlong-lasting geomagnetic disturbances may increase abso-lute ne such that leads to irregularities decrease below thethreshold and cause decay of PMSE. This is considered asthe upper electron density limit. This paper shows that thecorrelation of the VHF PMSE presented in Figure 2b andthe elevated ne during long EPE from 8:50-9:30 UT and10:10-11:10 UT could be due to a wide range of parametersassociated with a mesospheric dusty plasma such as ne, nd,and rd.

Case 4 & 5: The cases 4 and 5 show a similar trend tothe cases 1 and 2, with the electron density enhancement ofthe order of ∼5×ne0. A close comparison between Figures5 and 2 indicates that in the case of lower ne enhancement,the required conditions for the PMSE existence should besatisfied with lower dust densities and smaller dust particles.Therefore, as the electron density increases above the sat-uration level of dust particles, the electron density fluctua-tion amplitude increases correspondingly. As discussed, thisis mainly due to the dust particles charged up by free elec-trons, which produce a footprint in the background electrondensity. The appearance of PMSE layer in such a short EPEconfirms that δn2e were very close to the required thresholdof VHF PMSE observation (∼ 11.3 log10 Ne m−3). Thisis in agreement with the numerical simulations presented inFigure 4c and 5c, corresponding to the natural and enhancesne by a factor of 10, respectively.

4.2. Event 2: July 10, 2012

Figure 1b shows the VHF PMSE during several EPEpresent on July 10, 2012 from 08:00 to 12:00 UT. The twodistinct PMSE events are depicted by case 1 and 2. Theanti-correlation of the observed VHF PMSE and the en-hanced electron density could be attributed to the very lowdust density in the region. The observed echoes are veryclose to mesopause altitude where the condition favor theformation of ice particles as the temperatures reaches itsminimum. As can be seen both VHF PMSE occur afterthe electron precipitation event is ended. The scattered andweak echoes between 09:30 to 10:30 UT could be due to en-hanced random fluctuations within enhanced plasma regionrather than dust charging process.

4.3. Past PMWE observations during SPE:

The previous study by Kirkwood et al. (2002) has shownthe enhanced radar echoes between 50-80 km altitude in the

winter mesosphere by the 52 MHz ESRAD radar and dur-ing electron precipitation events. The PMWEs are seen ina wide range of background electron densities but limited tothe ratio of negative ions to free electrons (∼ 100). The lownumbers of enhanced PMWE in the presence of SPE couldbe due to the different charging characteristics of dust parti-cles within PMWE region. It should be noted that water-icedust particles are less likely to be candidates for dust as thetemperatures in the winter mesosphere are too high. Thecomputational results presented in this paper can be appliedto PMWE observations.

5. Conclusion

Dusty space plasma diagnosis associated with polar meso-spheric clouds (PMC) is investigated using the behaviorof polar mesospheric summer echoes (PMSE) during elec-tron precipitation event. The two consecutive day observa-tions of PMSE using 224 MHz VHF radar at EISCAT dur-ing electron precipitation event (EPE) on July 10 and 11,2012 have been presented. The Virginia Tech dusty plasmacomputational model capable of simulating the time evo-lution electron density fluctuation in the presence of nat-ural mesospheric dust layers and the corresponding radarechoes (PMSE) in different frequency bands is employed inthis study. The effect of several parameters including dustradius rd, dust density nd, recombination/photoionizationrates, on background plasma on the associated radar echoesis investigated. It has been shown for the first time thatthe dust density and dust radius limit within PMSE regioncan be understood by studying the evolution of radar echoesincluding existence of PMSE layer, duration of the echoes,correlation with EPE, as well as the strength of the backscat-tered signal. While electron density plays an important in(δne)

2 corresponding to the radar echoes, the results pre-sented in this paper show that the PMSE strength is mostlygoverned by background dusty plasma parameters such asdust radius and dust density.

A comparison of the PMSE observations during short pe-riod EPE with elevated electron number densities ∼2×1010(10ne0 background electron density) reveals the existence ofice particles in the polar summer mesopause region aboutnd > 4×109 m−3 and rd > 2 nm. A comparison of thenumerical simulations in the natural mesospheric conditionsand the enhanced electron density by a factor of 10 showsthat the minimum requirement of δnd/nd0 = 0.5, which isbased on the past VHF PMSE observation and simultaneousin-situ rocket measurement, is satisfied for the nd = 4×109m−3 and rd > 4 nm. The estimated radar echoes are ∼ 10.8and 11.3 in the natural and enhanced ne conditions, respec-tively. This validates the appearance of VHF PMSE duringshort EPE. The long-lasting PMSE enhancement correlatedwith EPE on July 11, 2012, imposes a lower limit of nd >∼8×109 m−3 and rd >∼ 2 nm. The computational resultsassociated with radar echoes of 12 log10 Ne m

−3 revealedthe conditions of nd = 4×109 m−3 and rd ∼ 10 nm. Consid-ering that this layer appreas in the lower altitudes (83–85km) validates the numerical results which impose a mini-mum dust radius of 10 nm for VHF PMSE observations.The secondary PMSE layer formed at higher altitude rangeof 86.5–88 km is composed of smaller ice particles. The de-lay in the formation of this layer is due to the slow chargingprocess of small dust particles. The numerical simulationsrequire a much higher dust densities (6–8×109 m−3 and rd ∼2 nm) for VHF PMSE observations in this altitude range andwith a strength ∼ 12 log10 Ne m−3. The weak VHF PMSE

MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE X - 7

observed on July 10, 2010 show anti-correlation with the el-evated electron density due to EPE. This was attributed tothe very low dust density present in this region. The nega-tive correlation between electron density enhancement andradar echoes is due to the limited amount of dust particlespresent in the region. In summary, the dusty plasma sim-ulations will be sufficient to interpret the PMSE behaviorduring EPE or solar proton event (SPE) and can lead tosignificant diagnostics of the dust layer.

The model predicts a stronger PMSE ∼ 1 log10 Nem−3 for long-lasting EPE in comparision with short pe-riod EPE, which is consistent with the experimental obser-vations. This validates the diagnostic information resultedfrom the comparison of the PMSE variation during EPEwith the computational results. The variation of recombi-nation/photoionization rates by a factor of 10 may intro-duce 0.1–0.5 nm difference in the minimum required con-dition (zdnd/ne = 0.05) to observe VHF PMSE, which isnegligible. This effect on the associated radar echoes is neg-ligible. The disappearance of PMSE is explained of threepossible processes including photo-detachment of electronsfrom dust particles and recombination process, collision withsmall MSP, and ice particle evaporation due to Joule heat-ing.

The condensation of nuclei of the ice particles such asproton hydrate clusters (H+(H2O)n) or meteoric smoke par-ticles (MSP) can be determined by employing microphysi-cal simulations. This can resolve the discrepancy in thedescription of the observed phenomena. The possibilitiesof combining the Virginia Tech dusty plasma model withNCAR WACCM/CARMA (Whole Atmosphere CommunityClimate Model/Community Aerosol and Radiation Model)to develop a large aperture radar simulator for dusty spaceplasma in the near Earth space environment is currentlyunder investigation. In this approach the background meso-spheric parameters will be incorporated in the micro-physicssimulations in order to derive the ice/dust density profileand dust size distribution, which will be imported to thedusty plasma model for corresponding radar echoes calcula-tions. To provide a better explanation of the PMSE duringactive geomagnetic event and use this as a naturally modi-fied mesospheric condition, the new EISCAT 3D interferom-etry capability will be implemented in the future in orderto develop a remote sensing technique for the backgroundmesospheric parameters.

Acknowledgments. This work was partially supported byNational Science Foundation (NSF). The EISCAT is an in-ternational association supported by research organizations inChina (CRIRP), Finland (SA), Japan (NIPR and STEL), Norway(NFR), Sweden (VR), and the United Kingdom (NERC). Thedata presented in this paper can be downloaded from the EIS-CAT online database at https://www.eiscat.se/scientist/data/

References

Balsley, B. B., Ecklund, W. L., and Fritts, D. C.: VHF echoesform the high-latitude mesosphere and lower thermosphere:observations and interpretations, J. Atmos. Sci., 40, 24512466,1983.

Brasseur, G., and P. C. Simon, Stratospheric chemical and ther-mal response to long-term variability in solar irradiance, J.Geophys. Res., 86, 7343-7362, 1981.

Bernstein, I.B., and Rabinowitz I.N. (1959), Theory of electro-static probes in a low density plasma Phys. Fluids 2 11221

Chen, C., and W. A. Scales (2005), Electron temperature en-hancement effects on plasma irregularities associated with-charged dust in the Earths mesosphere, J. Geophys. Res., 110,A12313, doi:10.1029/2005JA011341.

Cho, J. Y. N. and Kelley, M. C.: Enhancement of Thomson scat-ter by charged aerosols in the polar mesosphere: measurementswith a 1.29-GHz radar, Geophys. Res. Lett., 19, 10971100,1992.

Christon, S. P., Hamilton, D. C., Plane, J. M. C., Mitchell,D. G., Grebowsky, J. M., Spjeldvik, W. N., Nylund,S. R. (2017). Discovery of suprathermal ionospheric ori-gin Fe+ in and near Earth’s magnetosphere. Journal ofGeophysical Research: Space Physics, 122, 11,17511,200.https://doi.org/10.1002/2017JA024414

Ecklund, W. L. and Balsley, B. B.: Long-term observations of thearctic mesosphere with the MST radar at Poker Flat, Alaska,J. Geophys. Res., 86, 77757780, 1981.

Eremenko, M. N., S. V. Petelina, A. Y. Zasetsky, B. Karlsson,C. P. Rinsland, E. J. Llewellyn, and J. J. Sloan (2005), Shapeand composition of PMC particles derived from satellite re-mote sensing measurements, Geophys. Res. Lett., 32, L16S06,doi:10.1029/2005GL023013.

Gelinas, L. J., K. A. Lynch, M. C. Kelley, R. L. Collins, M. Wid-holm, E. MacDonald, J. Ulwick, and P. Mace (2005), Meso-spheric charged dust layer: Implications for neutral chemistry,J. Geophys. Res., 110, A01310, doi:10.1029/2004JA010503.

Havnes, O., de Angelis, U., Bingham, R., Goertz, C. K., Morfill,G. E., and Tsytovich, V.: On the role of dust in the summermesopause, J. Atmos. Terr. Phys., 52, 637643, 1990

Havnes O. and Brattli A. and Aslaksen T. and Singer W. and Lat-teck R. and Blix T. and Thrane E. and Trim J. (2001), Firstcommon volume observations of layered plasma structures andpolar mesospheric summer echoes by rocket and radar, Geo-phys. Res. Lett., 28, 1419–1422

Hervig, M. E., R. E. Thompson, M. McHugh, L. L. Gordley, J.M. Russell III, and M. E. Summers (2001), First confirmationthat water ice is the primary component of mesospheric clouds,Geophys. Res. Lett., 28, 971–974.

Hervig, M. E., Gordley, L. L., Stevens, M. H., Russell, J. M.,Bailey, S. M., and Baumgarten, G.: Interpretation of SOFIEPMC measurements: Cloud identification and derivation ofmass density, particle shape, and particle size, J. Atmos. So-lar. Terr. Phys., 71, 316330, doi:10.1016/j.jastp.2008.07.009,2009.

Hunten, D. M., R. P. Turco, and O. B. Toon (1980), Smoke anddust particles of meteoric origin in the mesosphere and strato-sphere, J. Atmos. Sci., 37, 1342 1357.

Jarvis, M. J., M. A. Clilverd, M. C. Rose, and S. Rodwell(2005), Polar mesosphere summer echoes (PMSE) at Halley(76 S, 27 W), Antarctica, Geophys. Res. Lett., 32, L06816,doi:10.1029/2004GL021804.

Kirkwood, S., Barabash, V., Belova, E., Nilsson, H., Rao, N.,Stebel, K., Osepian, A., and Chilson (2002), P. B.: Polar meso-sphere winter echoes during solar proton events, Adv. Pol. Up.Atmos. Res., 16, 111125.

Mahmoudian, A., W. A. Scales, M. J. Kosch, A. Senior,and M. Rietveld (2011), Dusty space plasma diagnosis us-ing temporal behavior of polar mesospheric summer echoesduring active modification, Ann. Geophys., 29, 21692174,doi:10.5194/angeo-29-2169-2011.

Mahmoudian, A., A. R. Mohebalhojeh, M. M. Farahani, W. A.Scales, and M. Kosch (2017), Remote sensing of mesosphericdust layers using active modulation of PMWE by highpowerradio waves, J. Geophys. Res. Space Physics, 122, 843856, doi:10.1002/2016JA023388.

Rapp, M., and F. J. Lubken, Modeling of positively chargedaerosols in the polar summer mesopause region, Earth PlanetsSpace, 51, 799 807, 1999.

Rapp, M., Gumbel, J., Lubken, F.-J., and Latteck, R. (2002): D-region electron number density limits for the existence of po-lar mesosphere summer echoes, J. Geophys. Res., 107 (D14),doi:10.1029/2001JD001323, 2002.

Rapp, M. and F.J. Lubken (2004), Polar mesosphere summerechoes (PMSE): Review of observations and current under-standing, Atmos. Chem. Phys., 4, 26012633.

Rapp, M., Charging of mesospheric aerosol particles: the roleof photodetachment and photoionization from meteoric smokeand ice particles, Annales Geophys. 27, 24172422, 2009.

Rapp M, Strelnikova I, Li Q, Engler N, and Teiser G., (2013),Charged Aerosol Effects on the Scattering of Radar Wavesfrom the D-Region, Climate and Weather of the Sun-EarthSystem (CAWSES), Chapter 19 (doi:10.1007/978-94-007-4348-919)

X - 8 MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE

Reid, G. C. (1997), On the influence of electrostatic charging oncoagulation of dust and ice particles in the upper mesosphere,Geophys. Res. Lett., 24(9), 1095 1098.

Robertson, S., et al. (2009), Mass analysis of charged aerosolparticles in NLC and PMSE during the ECOMA/MASS cam-paign, Ann. Geophys., 27, 12131232.

Rosenberg, M., J. Vac. Sci. Technol., Ion-dust streaming stabili-ties in processing plasmas, 14, 631, 1996

Rosenberg, M., and P. K. Shukla, Dust-acoustic-drift wave insta-bility in a space dusty plasma, J. Geophys. Res., 107(A12),1492, doi:10.1029/2002JA009539, 2002.

Royrvik, O., and L. G. Smith (1984), Comparison of meso-spheric VHFradar echoes and rocket probe electron concen-tration measurements,J. Geophys. Res., 89, 9014.

Scales, W. (2004), Electron temperature effects on small-scaleplasma irre-gularities associated with charged dust in theEarths mesosphere, IEEETrans. Plamsa Sci., 32, 724.

Scales, W.A. and Mahmoudian, A. (2016), Charged dust phenom-ena in the near Earth space environment, Reports on Progressin Physics, Vol 79, No 10, http://dx.doi.org/10.1088/0034-4885/79/10/106802.

Senior, A., A. Mahmoudian, H. Pinedo, C. La Hoz, M. T. Ri-etveld, W. A. Scales, and M. J. Kosch (2014), First modulationof high-frequency polar mesospheric summer echoes by radioheating of the ionosphere, Geophys. Res. Lett., 41, 53475353,doi:10.1002/2014GL060703.

Shukla, P. D., and A. A. Mamun (2002), Introduction to DustyPlasma Physics, Inst. of Phys., Bristol, U. K.

Corresponding author: Alireza Mahmoudian (alirezam@vt.edu)

2 4 6 8 10 12 14 16 18 20rd (nm)

0

10

20

30

40

50

60

70

80

90

100

ne/n

e0 (

%)

ne = 2×10

9 m

-3

nd/n

e0 = 20%

nd/n

e0 = 50%

nd/n

e0 = 100%

nd/n

e0 = 200%

(a)

2 4 6 8 10 12 14 16 18 20rd (nm)

0.01

0.05

0.1

1

10

100

1000

zdn

nd

/ne(lo

g)

ne = 2×10

9 m

-3

(b)

2 4 6 8 10 12 14 16 18 20rd (nm)

9.7

10.17

10.47

10.65

10.77

10.87

10.95

(δ n

e)2

lo

g1

0 m

-3

ne = 2×10

9 m

-3

nd = 10

9 m

-3

nd = 2×10

9 m

-3

nd = 4×10

9 m

-3

nd = 4×10

8 m

-3

10.55

δ nd/n

d0 = 0.5

δ nd/n

d0 = 0.2

10.38

10.47

10.25

10.07

9.77

9.3

(c)

Figure 4. Variation of polar mesospheric summer echoes(PMSE) during quiescent mesospheric conditions withdust radius and dust densities a) steady-state electrondensity relative to the background electron density b)dust charge density relative to background plasma den-sity c) Steady-state plasma density in the presence of dustparticles. The unit is calculated for the dust density of100%. For dust densities (nd/ne0) 200%, 50%, and 20%,the values should be adjusted by +0.3, -0.3, and -0.7,respectively.

MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE X - 9

2 4 6 8 10 12 14 16 18 20rd (nm)

20

30

40

50

60

70

80

90

100

ne/n

e0 %

ne = 2×10

10 m

-3

nd = 4×10

9 m

-3

nd = 2×10

9 m

-3

nd = 10

9 m

-3

δ nd/n

d0 = 0.5

δ nd/n

d0 = 0.2

(a)

2 4 6 8 10 12 14 16 18 20rd (nm)

0.01

0.05

0.1

0.6

zdn

d/n

e (

log

)

ne = 2×10

10 m

-3

(b)

2 4 6 8 10 12 14 16 18 20rd (nm)

10.3

11.3

11.6

11.77

11.9

12

12.07

(δ n

e)2

lo

g1

0 m

-3

ne = 2×1010 m-3

11.68

11.6

11.5

11.3

11.2

10.9

9.9

(c)

Figure 5. Variation of polar mesospheric summer echoes(PMSE) with dust radius and dust densities during EPEand for enhanced ne = 2 × 1010 m−3 a) steady stateelectron density relative to the background electron den-sity b) dust charge density relative to background plasmadensity c) Steady-state plasma density in the presence ofdust particles. The units on the left is calculated forthe dust density 4×109 m−3 and δnd/nd0 = 0.5, and theunits on the right corresponds to δnd/nd0 = 0.2. For dustdensities nd = 2×109 and 109 m−3, the values should beadjusted by -0.3 and -0.6, respectively.

X - 10 MAHMOUDIAN ET AL.,: DUST CHARGING PROCESS IN SPACE

2 4 6 8 10 12 14 16 18 20rd (nm)

40

50

60

70

80

90

100

ne/n

e0 %

ne = 4×10

10 m

-3

(a)

nd = 4×10

9 m

-3

nd = 2×10

9 m

-3

nd = 10

9 m

-3

δnd/n

d0 = 0.5

δnd/n

d0 = 0.2

2 4 6 8 10 12 14 16 18 20rd (nm)

0.001

0.01

0.05

0.1

0.3

zdn

d/n

e (

log

)

ne = 4×10

10 m

-3

(b)

2 4 6 8 10 12 14 16 18 20rd (nm)

11

11.6

11.9

12.07

12.2

12.3

12.38

(δn

e)2

lo

g1

0 m

-3

ne = 4×10

10 m

-3

10.6

11.2

11.68

11.5

11.8

11.9

11.98

(c)

Figure 6. Variation of polar mesospheric summer echoes(PMSE) with dust radius and dust densities during EPEand for enhanced ne = 4×1010 m−3 a) steady-state elec-tron density relative to the background electron densityb) dust charge density relative to background plasmadensity c) Steady-state plasma density in the presenceof dust particles. The units on the left is calculated forthe dust density 4×109 m−3 and δnd/nd0 = 0.5, and theunits on the right corresponds to δnd/nd0 = 0.2. For dustdensities nd = 2×109 and 109 m−3, the values should beadjusted by -0.3 and -0.6, respectively.

2 4 6 8 10 12 14 16 18 20rd (nm)

0.001

0.01

0.05

0.1

1

zdn

d/n

e lo

g

ne = 4×10

10 m

-3

(a)

2 4 6 8 10 12 14 16 18 20rd (nm)

11.3

12

12.3

12.47

12.6

12.7

12.77

12.84

(δ n

e)2

lo

g1

0 m

-3

ne = 4×10

10 m

-3

nd = 4×10

9 m

-3

nd = 10

9 m

-3

nd = 2×10

9 m

-3(b)

increased recombination/photoionization rates by 20

α = 0.1

α = 0

Figure 7. Similar to Figure 6 including theeffect of photo-detachment current and recombina-tion/photoionization rate by a factor of 20.