Numerical Analysis of Artificial Electron Heating Effects on Polar Mesospheric Winter Echoes

Abstract—In this paper,an analytical model is used to analyze the modulated polar mesospheric winter echoes(PMWE).The winter parameters were introduced to simulate the effects of different parameters during the artificial electron heating of PMWE.The important role of the charged dust particle in the creation of PMWE is confirmed again.It is found that during the heating of PMWE,the increases of the dust size,dust charge,electron temperature,initial electron density,and ion-neutral collision frequency cause the increase of the electron density irregularity,and hence the PMWE strength.However,with increasing the dust density,the electron density irregularity and the PMWE strength decrease.

1.Introduction

The phenomenon of radar echoes observed in the mesopause region during the summer in the polar latitude range (80 km to 90 km) is called polar mesospheric summer echoes (PMSE)[1].Noctilucent clouds (NLC) occur at the lower edge of PMSE,with a comparatively greater dust size.Recently,a new method of mesospheric dust analysis is presented[2].Atmospheric and solar parameters affected the properties of NLC differently[3].Latteck and Bremer showed the positive correlation of PMSE with the solar radiation and geomagnetic disturbance[4].The theoretical explanations of the PMSE origin,dust particle size,charge number,and irregular structure of the dusty plasma and its corresponding dynamics are not yet fully understood.A corresponding phenomenon of PMSE formed due to nanometer size particles of meteoric origin has also been observed in winter in the polar latitude range (55 km to 80 km) and is called polar mesospheric winter echoes (PMWE)[5].PMWE is rarer and much weaker than PMSE.No greater attention has been paid to it,therefore the main features and physical mechanism of it are not clear[6].The nature of PMWE is recently investigated with medium-frequency (MF) and Program of the Antarctic Syowa mesosphere-stratosphere-troposphere/incoherent scatter (PANSY) radars,operating at well separated frequencies of 2.4 MHz and 47 MHz,respectively[7].The spectra of the received signal were analyzed by using the tri-static observation of PMWE with the European Incoherent Scatter (EISCAT) very high frequency(VHF) radar[8].Using numerical simulation in the source region of PMWE/PMSE,the fluctuation in the plasma,dust density,and electric field has been studied[9].During high frequency (HF) heating,PMWE intensity shows a small recovery and an increase of about 15% after the heating has been switched off[10].Using the VHF radar,the electron temperature was estimated around 5 times greater than the neutral or ion temperature during the heating-on period[11].These effects are the results of electrons charging onto dust due to HF heating.Because of the electrons attachment,the dust particles are charged negatively[11].These observations show that the active modulation of PMWE due to the enhanced electron temperature depends upon mesospheric smoke particles around PMWE altitudes.The first active modulation experiment of PMWE was performed using the VHF (224 MHz) radar with a 10-s heating cycle,and observed 93% suppression of the signal strength[12].The same experiment as shown in [12]was performed for a relatively large heating cycle (20 s on and 160 s off) and presented 50% suppression of turnon and turn-off PMWE overshoot[13].

Havnes and Kassa modeled the effects of PMWE heating experiments[14].By neglecting the finite diffusion time-scale and considering the Boltzmann approximation,this model was not perfect and was limited to low dust densities,small dust sizes,and small wavelengths.On the other hand,to simulate the temporal evolution of modulated PMSE,the models in [15]and [16]work well for all the Braggs wavelengths[15],[16].The numerical simulation model of artificial electron heating effects on PMWE as well as on PMSE[14],[15]is an effective diagnostic tool.Based on the PMSE analytical model with the parameters in the polar winter mesosphere,we can find one new analytical way to analyze the effect of powerful HF radio waves on PMWE.

In this article,the temporal variation of PMWE during the heating-on period is analyzed using the analytical model.In order to understand the physics behind the creation of PMWE,the variations in dusty plasma parameters during heating are analyzed and discussed.

2.Experimental Observations

The observations shown in Fig.1 were carried out on October 24,2006 by the EISCAT VHF radars.In this experiment,the VHF radar was run with the arc_dlayer_ht mode.The range of the VHF radar is from 60 km to 140 km.The height and time resolution is 300 m and 2 s,respectively.Incoherent scatter measurements with the EISCAT radars are normally analyzed in terms of electron number densities or“apparent” electron number densities.However,in our case,the EISCAT tool “The Grand Unified Incoherent Scatter Design and Analysis Program”(GUISDAP) is used for the analysis of raw data.The term “apparent electron density” is used to clarify the fact that the signal does not result from the real electron density but due to the coherent scatter of PMWE which adds to the incoherent scatter.Such derived apparent electron number densities are then converted into volume reflectivities.

Fig.1.Epoch average of PMWE measured by the EISCAT VHF radar.Color bar indicates volume reflectivity in m–1.Vertical lines indicate the heating-on period.

In Fig.1,the radar echoes at PMWE altitudes are represented by the volume reflectivity (“backscatter cross section per unit volume”) which is obtained by using the relation:

HereηandNeare the volume reflectivity and apparent electron density,respectively.Whereasσis the half cross section of an electron (σ=4.99×10?29m2).In Fig.1 the epoch analysis is performed for four heating cycles corresponding to time from 11:32:42 UT to 11:44:42 UT,because these cycles correspond to obvious PMWE.Fig.1 clearly shows that during the heating-on period the PMWE intensity decreases significantly.

Fig.2.Temporal evolution of PMWE for the same four heating cycles shown in Fig.1 heating on between the vertical dashed-dotted lines.

In Fig.2,the PMWE response to HF heating for the same four cycles of Fig.1 is shown.It is clear that the PMWE intensity decreases just after the heating switchon at 20 s.During the heating-on period,the PMWE intensity shows great variation in strength.Just after the heating switch-off at 40 s,the PMWE intensity quickly increases but its strength is much smaller than the PMSE overshoot[17].

3.Analytical PMWE Model

Launching radio waves from the ground to heat the PMSE/PMWE source region increases the temperature of dusty plasma.At the beginning of heating experiments,its switch-off was found when the heating starts,the PMSE signal strength is weakened significantly.After the heating switch-off,the temperature gradient of electrons in the dusty plasma increases,consequently leading to stronger radar echoes.It is quickly realized that radio wave heating can be used to diagnose the dusty plasma parameters in the PMSE/PMWE region.Recently,it is shown that in the ionosphere,the direction of electromagnetic wave propagation can be measured from the ground based transmitter[18].

In addition,experiments also show that the radio wave energy changes the distribution of electron density of the target area,thereby artificially achieving an overall change in the ionospheric properties.The electron density irregularity is destroyed by diffusion due to radio wave heating.In previous numerical simulation work,it has been observed that if the irregularity is in about meter scale or less,then due to ambipolar diffusion there is an ion density enhancement in the region of the reduced electron density[16].

In order to add the winter parameters in the PMSE heating model of Scales and Chen[16],we analyze the ambipolar diffusion effect during the heating of PMWE and the charging of dust particles by electrons.Before the HF heating switch-on,the mesospheric electrons are in equilibrium with the densityne0.However,when the heating switches on,the electromagnetic radio waves change the electron density,which is given as

where,on the left side,tdenotes the time andxdenotes the one dimensionx-axis,neis the electron density,andDais the ambipolar diffusion coefficient.The term on the right side of (2) indicates the electron density reduction due to charging,wherekis the rate coefficient of electrons absorbed onto dust andndis the dust density.AndDais given as

whereKis the Boltzman constant;TeandTiare the electron and ion temperatures,respectively.Heremiis the ion mass,Zd0is the number of charges on the dust particle in equilibrium,υinis the ion-neutral collision frequency,andne0andnd0are the electron and dust densities in equilibrium,respectively.The rate coefficient of electrons absorbed onto dust is given as

whereIeis the electron current,eis the charge on electron,rdis the dust radius,υte0is the electron thermal speed before heating,andrhis the ratio of the electron temperature during heating to that before heating.The change in the electron density irregularity in a relatively fixed space near dust particles is given as

whereδne(t) is the change in the electron density due to heating,tis time,δne0is the change in the electron density at equilibrium,δnd0is the change in the dust density at equilibrium,andτdis the diffusion time.The remaining parameters are already defined in the text.In this study,the PMWE parameters for simulation were selected asTe=Ti=150 K,mi=50 amu,rh=4,nd0=1×109m?3,ne0=1×1010m?3,δne0=4.9×107m?3,δnd0=2×108m?3,andrd=10 nm.

4.Dusty Plasma Parameters

The detail of physical processes of dusty plasma creation and evolution in the near earth-space environment was given in [19].Numerical results show that in weakly ionized dusty plasma,the electrical conductivity changes significantly due to the dust charge,radius,and density.Consequently,it causes changes in ionospheric properties[20].In this section,we present the temporal evolution of dusty plasma parameters and only consider the heating-on period.Here in all cases,the heater is switched on for 975 s.

4.1.Dust Particle Radius

When the dust density is relatively low,the dust radius has a great effect on the charging time.Fig.3 presents the temporal evolution of PMWE during the radio wave heating for different dust sizes.From Fig.3,it is clear that just after the heating switch-on the electron density irregularity amplitude shows an increase for the increasing dust radius.The amplitude of the irregularity increases linearly with the increase of the dust radius.It is worthy to mention that the speed of electron irregularity decay is approximately positively related to the dust radius,i.e.the largest radius (5 nm)shows the fastest decay.

Fig.3.Effect of dust radius on electron density irregularity.Time starts from 0 s whereas the heating starts at 25 s.

4.2.Charge on Dust Particle

Dust particles are charged by electrons and ions.As the thermal velocity of the electron is much faster than the ions,consequently dust particles are usually negatively charged.Because of large mass and the small thermal velocity,the charging time of the ion onto dust is much larger than the electron charging time.It is shown that the ion charging time onto the uncharged dust grain is about 100 s[21].This indicates that ion charging is of much less importance during the switch-on of the radio wave heating.So in practice,positively charged dust particles are negligible.The dust charge directly affects the ambipolar diffusion coefficient.Most dust particles absorb only 1 electron,and the number of negative charges on dust can be increased by electron absorption or turbulence.Fig.4 presents the effect of dust charging on the electron density irregularity.For simulation,the assumed dust charges areZd0=1,2,3,and 4,which is the number of charges residing on the dust grain surface.It is clear that a greater number of electrons absorbed on the dust result in a greater electron irregularities amplitude.The difference in peak values of different dust charges is not large and the dust charging effect shows a good linear relationship with the electron density irregularity amplitude.

Fig.4.Effect of dust charging on electron density irregularity.Time starts from 0 s whereas heating starts at 25 s.

4.3.Electronic Temperature

The electron temperature is an important dusty plasma parameter.Lübkenet al.[22]showed at the VHF radar the observations of “mesopause jump” which means the decrease in the temperature is associated with the increase of the mesopause altitude.After the heating is turned on,the electron temperature in the target area significantly increased.This increase in the electron temperature is expected to increase the dust charging and as a result,the electron and dust densities irregularities are changed.

Before heating,the electron temperature is taken to be equal to the ion temperatureTe=Ti=150 K.For the simulation shown in Fig.5,rhis the ratio of the electron temperature during heating to that before heating,which is set asrh=2,4,6,and 8.Atrh=2,the amplitude of the electron irregularity is not very large.But asrhincreases,the amplitude of the electron density irregularity also increases significantly.However fromrh=6 to 8,the increase of the amplitude is comparatively small.

Fig.5.Effect of electron temperature on electron density irregularity.Time starts from 0 s whereas heating starts at 25 s.

4.4.Initial Electron Density

In ionosphere,the background electron density varies,when PMWE occurs.It also increases due to the ionization produced by the particle precipitation.This increase in the electron density changes the PMWE response to HF heating.Fig.6 shows the variation in the electron density irregularity with varying the initial electron density during heating.The simulation result shows that the electron irregularity is positively correlated with the initial electron density,i.e.,for increasingne0,the irregularity amplitude also increases.

4.5.Collision Frequency

PMWE occurs at the bottom of the ionospheric D-region,where the gravity is dominated by neutral gas with the considerable background electron density.The collision frequency of the ion and neutral gas exists within a certain range.Fig.7 shows the simulation result for different collision frequencies.After the heating is turned on,the electron irregularity amplitude increases non-linearly with the increasing ion-neutral collision frequency.

Fig.6.Effect of initial electron density on electron density irregularity.Time starts from 0 s whereas heating starts at 25 s

Fig.7.Effect of ion-neutral collision frequency (vin) on electron density irregularity.Ion-neutral collision frequency is in Hz.Time starts from 0 s whereas heating starts at 25 s.

4.6.Dust Particle Density

The dust density also significantly affects the temporal evolution of electron density irregularities of PMWE during heating.Both the diffusion and charging time scales are not significantly affected by increasing the dust density as long as the ratioZdnd/neis smaller than one.Similarly,for the dust density variation(0.1<δnd0/nd0<0.5),the electron density irregularity is not affected significantly[21].

However,for the high dust density (50% of the background plasma density),the amplitude of the electron density irregularity is greatly suppressed.Fig.8 shows the effect of the dust density on the electron density irregularity and hence on radar echoes.It is obvious that with increasing the dust density,the electron density irregularity decreases non-linearly.The irregularity amplitude decreases largely when the dust density increases from 1×109m?3to 2×109m?3.

Fig.8.Effect of dust particle density on electron density irregularity.Dust density is in m?3.Time starts from 0 s whereas heating starts at 25 s.

5.Conclusions

Using the analytical model,the effect of different dusty plasma parameters on PMWE during the heating switch-on period has been analyzed.In the creation of PMWE,the important role of the charged dust particle is confirmed again.It is found that the heating of PMWE by increasing most of the dusty plasma parameters,including the dust radius and dust charges,initial electron density,ion-neutral collision frequency,and the electron temperature,can increase the electron density irregularity amplitude and hence the PMWE strength.On the other hand,increasing the dust density can cause the decrease in the electron density irregularity amplitude and hence the PMWE strength.

Acknowledgment

The authors thank the EISCAT Scientific Association,which is supported by the research councils of China,Finland,France,Germany,Japan,Norway,Sweden,and the UK.