Plasma and Electromagnetic Simulations of Meteor ... - Springer Link

Earth Moon Planet (2008) 102:383–394 DOI 10.1007/s11038-007-9189-8

Plasma and Electromagnetic Simulations of Meteor Head Echo Radar Reflections Lars Dyrud Æ Derek Wilson Æ Steiner Boerve Æ Jan Trulsen Æ Hans Pecseli Æ Sigrid Close Æ Chen Chen Æ Yoonjae Lee

Received: 6 July 2007 / Accepted: 5 November 2007 / Published online: 29 November 2007 Ó Springer Science+Business Media B.V. 2007

Abstract Recently, meteor head echo detections from high powered large aperture radars (HPLA) have brought new measurements to bear on the study of sporadic interplanetary meteors. These same observations have demonstrated an ability to observe smaller meteoroids without some of the geometrical restrictions of specular radar techniques. Yet incorporating data from various radar reflection types and from different radars into a single consistent model has proven challenging. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influences meteor trail properties at every stage of evolution. In order to overcome some of the unknown relationships between meteoroid characteristics (such as mass and velocity) and the resulting head echo radar cross-sections (RCS), we present our results on meteor plasma simulations of head echo plasmas using particle in cell (PIC) ions, which show that electric fields strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body at speeds as large as several kilometers per second. We also present the results of finite difference time domain electromagnetic simulations (FDTD), which can calculate the radar cross-section of the simulated meteor plasma electron distributions. These simulations have shown that the radar cross-section depends in a complex manner on a number of parameters. In this paper we demonstrate that for a given head echo plasma the RCS as a function of radar frequency peaks at sqrt (2*peak plasma frequency) and then decays linearly on a dB scale with increasing radar frequency. We also demonstrate that for a fixed radar frequency, the RCS increases linearly on a dB scale with increasing head echo L. Dyrud (&) D. Wilson C. Chen Y. Lee Center for Remote Sensing Inc, Fairfax, VA, USA e-mail: [email protected] S. Boerve Norwegian Defense Research Establishment, Kjeller, Norway J. Trulsen H. Pecseli University of Oslo, Oslo, Norway S. Close Las Alamos National Laboratory, Las Alamos, New Mexico

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plasma frequency. These simulations and resulting characterization of the head echo radar cross-section will both help relate HPLA radar observations to meteoroid properties and aid in determining a particular radar facility’s ability to observe various meteoroid populations. Keywords

Meteors Radar Meteor head echoes

1 Introduction Current estimates for the annual global meteor flux vary from 2,000 to 200,000 tons per year and estimates for the average velocity range between 10 and 60 km/s (Cziczo et al. 2001; Janches et al. 2000; Taylor 1995; Ceplecha et al. 1998; Mathews et al. 2001). Understanding the interplanetary meteoroid environment is important for several fields of study from solar system evolution, atmospheric physics, and most critically to manned and unmanned space flight. Yet, the basic properties of this global meteor flux, such as the average mass, velocity, and chemical composition remain poorly constrained (Mathews et al. 2001; Dyrud et al. 2004). Here we present an investigation aimed at improving our ability to characterize meteoroids via high powered large aperture radars (HPLA) radar observations of head echoes, and to more precisely characterize any bias or filter that a particular radar facility may have to a certain population of meteoroids, i.e., mass or velocity. We believe much of the mystery surrounding the basic parameters of a dominant source of the interplanetary meteor flux (mass ranges of *0.1–10-7 mg) exists for the following reasons; the unknown sampling characteristics of different radar meteor observation techniques, which are used to derive or constrain most models, and a need to relate meteor radar observables to the true meteoroid properties of interest. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influence meteor trail properties at every stage of evolution. In this paper we demonstrate that plasma simulations and electromagnetic finite difference time domain electromagnetic simulations (FDTD) simulations can be utilized to provide detailed estimates of the radar scatter from meteors, specifically head echoes. Further, the work presented in this paper is motivated by the need for the most detailed understanding of head echo scattering processes in order to provide parameterizations for the modeling efforts of the global meteoroid flux from head echo observations by Janches et al. (2006); Fentzke and Janches (2007); and Plane (2004) and investigations into HPLA radar biases towards meteors of certain velocities and sizes as discussed within Close et al. (2007), and Janches et al. (2007). The introduction continues with a background scientific description to place this work in context. For decades ground based meteor observations were typically made with photographic and TV cameras and specular meteor radars. Specular radars detect reflections from the trail of ionization formed perpendicular to the radar beam by a meteoroid during atmospheric entry. This specular condition requires that only trails formed perpendicular to the radar beam reflect strongly without destructive interference (Tayler 1995; Ceplecha et al. 1998). The resulting meteor parameters deduced from these radar observations are sensitive to the geometrical radio scattering requirements of this condition. Over the past decade, two new types of radar meteor reflections have become known or widely used. These reflections are known as meteor head echoes and non-specular trails and are largely observed and studied with HPLA designed for incoherent scatter remote

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sensing of the ionosphere (Chapin and Kudeki 1994; Dyrud et al. 2002, Zhou et al. 2001). Examples of these two scattering mechanisms are shown in Fig. 1. This figure shows a meteor head echo followed by trail reflections, termed non-specular, which occur despite the fact that many trails are roughly aligned with the radar beam. While the head echo plasma is believed to be a cloud of electrons moving at the speed of the meteoroid, the nonspecular trail echoes are attributed to coherent radio scatter from plasma turbulence– generated field aligned irregularities (FAI). Additionally, because these observations produce such detailed signatures, and seem to convey meteors entering anywhere within the radar beam, they show great promise as tools for deriving more complex parameters about meteoroids and the atmosphere they interact with. We continue the introduction with some background explanation of the plasma processes expected to occur during meteoroid entry. Our current understanding of the physical processes occurring during the early stages of meteoroid atmospheric entry remains somewhat anecdotal and can be summarized as follows. As a meteor enters the Earth’s atmosphere near 100 km altitude, the particle heats up and atoms begin boiling off the surface in a process known as ablation. Depending on energy, the ablated meteor atoms are ionized (freeing an electron from the atom, producing a positively charged ion and negatively charged electron) upon collision with an air molecule. These newly produced meteor ions cool after approximately 10 collisions, which takes between a fraction of a millisecond at 80 km and as long as one millisecond at 110 km (Jones 1995). This stage is depicted in cartoon form in panel (a) of Fig. 2. During this thermalization process, the plasma density near the meteoroid is very high, and it is assumed that head echo scattering occurs at this stage. As we continue our description of the evolution of a meteor trail, the effects of plasma turbulence become all the more evident and important. Once the meteor plasma has cooled, the result is a large trail or column of enhanced ionization near 100 km altitude, which may extend between 10 and 20 km in length. It is during this stage of development that specular radar echoes from the trail commence. Our understanding of the next stages of evolution depicted in Fig. 2 result directly from super computer simulations of plasma instability and

Fig. 1 Altitude-time-intensity image of a head and subsequent non-specular echoes over extended range from ALTAIR VHF Radar. The diagonal line to the left is called a head echo, while the echoes spread in range and time to the right are the non-specular trail. Figure reproduced from Close et al. (2002)

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(a)

Ablation and ionization stage

(b) Cooled trail plasma 115 km

~15 m radius ion-electrion pairs

meteoroid Head echo reflections

(c) Short wavelength waves 115 km

~1 m radius 90 km

(d) Meter scale turbulence 115 km

Non-specular trail reflections

90 km

90 km

Fig. 2 Paneled cartoon depicting the four main stages of meteor trail evolution. The four stages ordered in increasing time are: (a) the ablation and ionization stage, head echo reflections are assumed to result from meteor plasma at this stage, (b) a cooled trail plasma column that has increasing radius at higher altitudes, (c) Farley-Buneman-gradient-drift (FBGD) waves at short wavelengths grow after only a few milliseconds after the stage (b), (d) The final stage depicts that the unstable portion of the meteor trail has become turbulent with structure at a broad range of wavelengths. Specular trail reflections are expected to occur throughout stages b–d, while non-specular trail reflections should only appear near stage d after sufficient field aligned irregularities (FAI) have formed

turbulence within meteor trails published in a number of papers (Dyrud et al. 2005; Dyrud et al. 2001, 2002; Oppenheim et al. 2000). Regarding meteor trails: a tremendous amount of work has been done to characterize specular reflections of meteor trails (see Cervera and Elford (2004) and references therein), but none of these take into account the now known turbulence present in all meteor trails. An examination of the effect of plasma turbulence on specular trail observations represents a future direction of study that we expect to pursue, with some initial work presented by Dyrud et al. (2004). Regarding head echoes: very recent attempts have been made to model the electron distribution responsible for head echo reflection with certain degrees of success (Close et al. 2004; Pellinen-Wannberg 2004). Yet these analyses assumed that the

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meteor head echo plasma distribution is Gaussian in shape. In the following sections we use a particle in cell (PIC) plasma simulation to determine the plasma shape of a head echo, and FDTD EM simulations to simulate radar scatter from these plasmas.

2 Head Echo Plasma Simulation Some results from our head echo plasma simulations are shown in Figs. 3 and 4. Figure 3 shows the simulation ion density as a function of two spatial dimensions, the x-axis is along the meteoroid path, and the y-axis is perpendicular to it. This plasma simulation uses a kinetic PIC treatment for ion physics by solving the complete Lorenz force equation for each ion (Birdsall and Langdon 1985). The electric field is then solved for iteratively assuming the electrons satisfy the standard non-linear Boltzman relation (Chen 1984). While the effects of the Earth’s magnetic field electron motion should normally be considered for meteor and plasma physics near 100 km altitude, it has been ignored here, since the electrons have a significantly larger Larmour radius then the plasma density gradient length scale. This comparison indicates that the ambipolar electric field will dominate the short scale electron dynamics, and that magnetic field gyration can be ignored in the earliest timescales. Therefore the overall distribution of the plasma, once thermalized, near the tail end of Fig. 3, may not accurately represent the true physics of actual meteor plasma thermalization and expansion. However, the early stage plasma distribution near the meteoroid body should be accurately represented, and that is the focus of the research presented in this paper. The ions simulated had a mass of 50 AMU in order to represent an iron dominated meteor plasma, we also used an elastic collision cross-section of 2.61 9 10-20 m2, which was based upon numerical calculations conducted by H. R. Skullerud (Private Communication, see Skullerud et al. (1999) for more information regarding the numerical techniques). The background ion temperature, and electron temperature were taken as thermalized 257 K. It is possible that they electrons are hotter if

Fig. 3 Results from a meteor plasma simulation after the ablation stage. This figure shows the color representation of the plasma density surrounding a meteor. The meteor simulated here was producing 1012 ions per meter traveled, and was moving against the surrounding atmosphere at a rate of 40 km/s. The axes are in units of local Debye length; in the ionosphere near 100 km altitude Debye lengths are of the order of 1 cm

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Fig. 4 Plot of ion phase space for the same simulation and time shown in Fig. 3: This figure shows the color representation of the plasma density surrounding a meteor. The meteor simulated here was producing 1012 ions per meter traveled, i.e., line density. The y-axis of this figure is in simulation units of velocity 1 unit = 8 km/s. The x-axis is in the same Debye length units as Fig. 3. The meteor ions are being produced at the x-coordinate of 600 and generated isotropically with a 2,000 K temperature. The air molecules then blow past the meteoroid at 40 km/s or in the dimensionless simulation units used in the figure, v = –5. The highest density portions are in black and was moving against the surrounding atmosphere at a rate of 40 km/s. The axes are in units of local Debye length; in the ionosphere near 100 km altitude Debye lengths are of the order of 1 cm

produced by impact ionization, however Murad et al. (2003) predicts a two-stage ionization, which would produce cooler electrons, and given the paucity of other theoretical work on meteoric ionization, we have adopted a thermalized temperature. The electron density distribution from this plasma simulation is then input into an EM simulation to analyze the radio scattering properties of such an electron distribution. These EM simulations are discussed in the next section.

3 Finite Difference Time Domain (FDTD) Plasma Formulation The analysis of electromagnetic fields generated in the scattering of waves by complex objects presents many difficulties, especially if such scatterers include scale sizes having characteristic dimensions comparable to the incident radiation wavelength, and exhibit dispersive characteristics such as in plasma. In many cases the only alternative to experimental measurements is the direct solution of Maxwell’s equations by numerical methods. The FDTD method was first introduced by Yee (1966) and later developed by Taflove (1995) and others. The standard FDTD formulation places a limitation such that the constitutive parameters must be specified as constants, i.e., l, e, and r must be described by a single number. While this is true for free space, good conductors, and ideal dielectrics, it is only approximately true for most real materials. For some materials over a narrow band of frequencies, the approximation is excellent, while for other materials over a wider band of frequencies, it is not. For some materials, such as plasmas and ferrites, the permittivity may be zero or negative, so that the basic FDTD equations we have presented cannot be used at certain frequencies as some of the terms become singular. Thus special treatments are needed to use the FDTD method for simulation of dispersive materials and we briefly explain the FDTD algorithm to be used for simulation of dispersive plasma media. There are many different ways to simulate the electromagnetic interactions in plasma. Two major schemes that are used in FDTD simulations are the direct integration (DI) and the recursive convolution (RC) methods. In the former, Maxwell’s equations are coupled to an auxiliary ordinary differential equation modeling the response of the current (J) to the field (E) and

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the latter is based on the time domain integral relating the flux (D) and the field (E). The DI method (Nickisch et al. 1992) was used in the simulation results shown in this paper. For a complete treatment of the FDTD formulation in anisotropic plasma, the reader is referred to (Nickisch et al. 1992; Boardman 1982). For completeness, the set of field equations for a non-magnetized cold plasma that were used in our FDTD formulation are presented in Eqs. 1–3 (Burden 1985). r~ E ¼ lo

~ ¼ eo rH

~ oH ot

~ oE þ~ J ot

~ oJ ~ ¼ eo x2~ þ mJ pE ot

ð1Þ

ð2Þ

ð3Þ

where E and H are electric field (V/m) and magnetic field (A/m), respectively, eo and lo are electric permittivity (F/m) and magnetic permeability (H/m) of free space, respectively, J is plasma current density (A/m2), xp is the plasma frequency (rad/s) and m is collision frequency (Hz). Figure 4 shows an example result of the spatial distribution of the electric field output from one of our meteor FDTD simulations. We place the meteor plasma that was output from a numerical plasma simulation of a head echo (shown in Fig. 3), near the center of the EM simulation space, and then launch a broad-banded radar pulse towards the meteor and measure the reflected electric field. The comparison between the impinging and reflected electric field yields the radar cross-section, or RCS, for that particular object. Since FDTD simulations are conducted in the time domain and we use a broad-banded pulse, the postprocessing of a single simulation outputs the type of information shown in Figs. 5 and 6, i.e., RCS as a function of impinging radar frequency. We have simulated a 50 9 50 m box where the third dimension into the page is narrow and made effectively 2D by choosing a perfect electric conductor (PEC) boundary at the top and bottom of the box in the z direction. A grid spacing of 10 cm is achieved with a 500 9 500 grid, which limits the applicability of the results to about 300–350 MHz, due to discretization of the simulated fields. However, we have conducted several runs with 5 cm grid spacing and see no changes to the results shown here, and little deviation from the below demonstrated trends as the results are extend to higher radar frequencies. The polarization of the radio wave electric field is also linear in the into page direction. Figure 5 shows the electric field magnitude in color, the RF pulse, which is traversing upward and has passed the meteor head. Much weaker reflections from the meteor can be seen propagating downward. We continue with a description of some of the results of these FDTD simulations. Figure 6 shows RCS as a function of radar frequency for four different meteor plasmas, which were derived using two different techniques. All of the lines shown are for plasma distributions with the same peak plasma frequency of 70 MHz. Plasma frequency is defined as fp = 9.0 * sqrt(n) where f is Hz and n is defined in units of m-3. It is generally considered that plasma is overdense or behaves similar to a metal object for impinging EM waves below the plasma frequency and is evanescent for EM waves above that frequency.

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Fig. 5 Example results from one of the FDTD simulations conducted for analyzing the radar meteor scatter known as the meteor head echo. This plot shows the electric field in the simulation as a function of space, which is directed into the page. A broad-banded radar pulse was launched from the bottom of the page boundary and is seen propagating upward and passing the meteor head echo plasma. Faint reflections from the meteor are also seen propagating downwards. These reflections are then measured and compared with the input energy to determine the radar cross-section of this particular meteor as a function of input radar frequency

Fig. 6 Comparisons between analytical cross-section calculations, and simulations of Gaussian profiles and realistic plasma simulation produced profiles at two angles. All of the lines shown are results from a meteor plasma with similar peak plasma frequencies of 70 MHz

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This plot makes clear that peak plasma density is not an ideal proxy for estimating head echo RCS or vice versa. Our explanation of this figure starts from the top line and ends with the bottom. The top line is one of our FDTD simulations for spherical-Gaussian head echo plasma. This simulation had the same peak density as all the other lines and a Gaussian sigma of 2 m, which gives it the same total number of electrons as the meteor shaped simulation. The next two lines are simulations of meteor shaped plasma at two different angles to the radar. The bottom line is an analytical calculation for the RCS of a Gaussian shaped meteor as a function of radar frequency from Close et al. (2004). So that the analytical solution would match the simulated RCS from the meteor distribution, we had to use a very small size of about 20 cm. This is similar in size to the very high density region near the tip shown in Fig. 3, but much smaller than the overall size of the meteor plasma that had a 3r width (i.e., the distance transverse to the meteoroid direction where the head echo plasma effectively blends into the background ionospheric plasma) of 6 m across. In order to provide a result one can be confident in, any good simulation should be compared with the existing analytical theory. Figure 6 presents comparisons with the analytical calculations of Close et al. (2004), and simulations of RCS as a function of a Gaussian shaped peak meteor density, and compared the results with the theoretical calculations of Close. What this plot shows is that the Close analytical model and the simulated head echo RCS possess the same slope as a function of radar frequency, but that the location of the knee in the Close model is predicted to be near the peak plasma frequency of the meteor head. Our simulations show that this knee occurs at approximately f = sqrt(2) * (peak plasma frequency).

4 Head Echo RCS as a Function of Peak Plasma Frequency Here we use our simulation results to examine head echo RCS as a function of the peak plasma density in the head echo, which has been considered as a proxy for head echo RCS in a modeling effort of the interplanetary meteor flux by Janches et al. (2006). In this case we compare FDTD simulations with a fixed head echo size, and incident radar angle but scaled density. The angle chosen is for a meteoroid path that is straight down the beam, and the size of the head echo plasma had a 3r width of 10 m, and is therefore similar in size to the meteoroid simulation shown in Fig. 3. Both Figs. 7 and 8 show that for the same meteor size, RCS is proportional to peak plasma frequency. One notable feature shown in Fig. 7 is that for radar frequencies near the plasma frequency large fluctuations in RCS occur as a function of frequency, particularly in the 72 MHz line, Mie scattering resonances appear to influence the RCS with fluctuations near 8 dB deviation from the general smooth trend. Such rapid fluctuations may account for the occasional unusual head echo returns seen by some observers. It may be that deviations from smooth SNR as a function of altitude for head echoes may simple be a head echo that possesses a plasma density that has a plasma frequency near the radar frequency. The head Echo RCS dependency on radar frequency and peak electron density is characterized by the following equation which was derived via a polynomial fit to the results of over 30 FDTD simulations of head echo plasmas with 3sgme sizes from 2 to 15 m.

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Fig. 7 Radar Cross-Section (RCS) versus Radar Frequency comparison at different meteor peak plasma frequencies with same meteor size. 3r size = 10 m

Fig. 8 Same as Fig. 7 but for a single radar frequency of 150 MHz, the results are a near linear trend in RCS as a function of peak plasma frequency

RCSðf Þ ¼ 1:5 107 f 3 þ 2 104 f 2 0:1 f þ a

ð4Þ

where a µ meteor peak plasma frequency, and a could be approximately expressed as: aðkp Þ ¼ 0:38kp C

ð5Þ

where kp is the peak plasma frequency defined in units of MHz, and C is a calibration constant in dB, for the plots shown here C = 74, but this number would be adjusted for comparisons with a particular observatory, or for calculations in dBsm.

5 Conclusions This paper presents simulations that aim to improve our understanding of the radio scattering characteristics of the meteor plasma, especially in light of recent work showing that

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plasma turbulence and instability greatly influences meteor trail properties at every stage of evolution. We presented results on a meteor plasma simulation of head echo plasmas using PIC ions, which show that electric fields strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body. This result should indicate the need for renewed modeling on the initial stages of meteor plasma expansion, since electric fields have never been considered in theoretical studies of what is known as the meteor trail initial radius (Jones 1995). We note here that these head echo plasma simulations are still in the preliminary stage, with significant work to be done on evaluating different parameter regimes. However we use it here because it represents the only estimate we have of the shape of the head echo scattering region and is likely to be significantly closer to reality then a spherical Gaussian distribution. Furthering the research on these early stage plasma simulations represents a future direction we plan to pursue. This paper continued with the results of FDTD, which can calculate the radar crosssection of the simulated meteor plasmas by launching a simulated broad-banded EM pulse towards a simulated meteor plasma. These simulations have shown that the radar crosssection depends in a complex manner on a number of parameters. These include the angle between radar and meteor entry (as discussed in Dyrud et al. (2007), a large dependence on radar frequency, which shows that for a given meteor plasma size and density, the peak reflectivity for the meteor varies but is usually less then 100 MHz. Finally, we demonstrated that peak plasma frequency is not an ideal proxy for head echo RCS all by itself, but if the size of the head echo can be estimated, we have presented an empirical formulation for the variation of RCS as a function of changing peak electron density. Further, by conducting the FDTD simulations on plasma distributions form the plasma simulations we are able to study the effects of a number of processes that are not approachable through other means, such as non-Gaussian plasma distributions. In conclusion, we expect these results to be of use for those attempting to model the relationship between meteoroid parameters and radar observations of meteor head echoes. References C.K. Birdsall, A.B. Langdon, Plasma Physics via Computer Simulation. (McGraw Hill, New York, 1985) A.D. Boardman, Electromagnetic Surface Modes. (John Wiley & Sons Ltd., 1982) K.G. Burden, The Propagation of Radio Waves. (Cambridge University Press, 1985) Z. Ceplecha, J. Borovicka, W.G. Elford, D.O. Revelle, R.L. Hawkes, V. Porubcan, M. Simek, Meteor phenomena and bodies. Space Sci. Rev. 84, 327–471 (1998) M.A. Cervera, W.G. Elford, The meteor radar response function: theory and application to narrow beam MST radar. Planet. Space Sci. 52, 591–602 (2004) E. Chapin, E. Kudeki, Radar interferometric imaging studies of long duration meteor echo observed at Jicamarca. J. Geophys. Res. 99, 8937–8949 (1994) F. Chen, Introduction to Plasma Physics and Controlled Fusion. vol. I, (Plenum Press, New York, 1984) S. Close, M. Oppenheim, S. Hunt, L. Dyrud, Scattering characteristics of high-resolution meteor head echoes detected at multiple frequencies. J. Geophys. Res. (Space Physics) 107(A10), 1295 (2002) S. Close, M. Oppenheim, S. Hunt, A. Coster, A technique for calculating meteor plasma density and meteoroid mass from radar head echo scattering. Icarus 168, 43–52 (2004) S. Close, P. Brown, M. Campbell-Brown, M. Oppenheim, P. Colestock, Meteor head-echo radar data: massvelocity selection effects. Icarus (2007). doi:10.1016/j.icarus.2006.09.07 D.J. Cziczo, D.S. Thomson, D.M. Murphy, Ablation, flux, and atmospheric implications of meteors inferred from stratospheric aerosol. Science 291, 1772–1775 (2001) L.P. Dyrud, M.M. Oppenheim, A.F. vom Endt, The anomalous diffusion of meteor trails. Geophys. Res. Lett. 28, 2775–2778 (2001) L.P. Dyrud, M.M. Oppenheim, A.F. vom Endt, Interpretation of non-specular radar meteor trails. Geophys. Res. Lett. 29 (2002)

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