Plasma instabilities in meteor trails: 2-D simulation studies

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A2, 1064, doi: /2002ja009549, 2003 Plasma instabilities in meteor trails: 2-D simulation studies Meers M. Oppenheim, Lars P. Dyrud, and Axel F. vom Endt Center for Space Physics, Boston University, Boston, Massachusetts, USA Received 19 June 2002; revised 29 August 2002; accepted 12 September 2002; published 6 February [1] Field-aligned plasma density irregularities detected as nonspecular echoes by radars with large aperture-power products indicate the presence of plasma turbulence within meteor trails. This paper presents two-dimensional simulations of meteor trail instabilities and compares these results with theory and observations. In particular, this paper describes techniques for simulating trail turbulence and then discusses two sample cases using realistic plasma density gradients, masses, and atmospheric conditions appropriate for a 102-km altitude. In the first case, the trail lies along the geomagnetic field, B. In the second, it lies perpendicular to B and is subject to a small external electric field pointing parallel to it. These cases show the spontaneous development of instabilities leading to turbulence and field-aligned irregularities. These irregularities can create nonspecular echoes with broad spectral lines and small Doppler shifts similar to those observed by radars with large aperture-power products. The simulations also show turbulenceenhanced cross-field diffusion rates. Finally, the paper describes simulations of trails containing multiple ion species and shows how turbulent mixing greatly reduces species fractionation. INDEX TERMS: 6245 Planetology: Solar System Objects: Meteors; 2439 Ionosphere: Ionospheric irregularities; 2435 Ionosphere: Ionospheric disturbances; 2471 Ionosphere: Plasma waves and instabilities; KEYWORDS: meteor, trail, radar, plasma, instability, turbulence Citation: Oppenheim, M. M., L. P. Dyrud, and A. F. vom Endt, Plasma instabilities in meteor trails: 2-D simulation studies, J. Geophys. Res., 108(A2), 1064, doi: /2002ja009549, Introduction and Background Copyright 2003 by the American Geophysical Union /03/2002JA [2] Radars probing the atmosphere between 70 km and 130 km frequently receive echoes from plasma trails left by ablating micrometeoroids. These echoes have proven useful in determining the speeds, directions of origin, and, to a lesser extent, the masses of small meteoroids. Meteor trail echoes are also used extensively to estimate mesospheric and thermospheric temperatures and wind velocities. However, meteor plasmas contain large amounts of free energy which can drive rapid plasma drifts and instabilities. This paper develops the plasma physics of meteor trails and applies this theory to explain the origin and characteristics of radar measurements. Oppenheim et al. [2003] describes the linear theory of meteor trails with characteristics analogous to those discussed in this paper. [3] This paper begins with background on simulations of meteor trails and E region turbulence. Background material discussing the theory and observations of meteor trails is described in the companion paper. Then we present the simulation methods applied and their advantages and limitations. Next, we present two simulated meteor trails at 102 km altitude: The first is aligned perfectly along B and shows the development of waves, moderate turbulence, and anomalous diffusion. The second is aligned perpendicular to B and develops stronger turbulence because of a small (1 mv/m) external field. The Doppler spectra of the second trail s fieldaligned irregularities look similar to those from nonspecular radar echoes. Last, we present the first simulations of multispecies meteor trails showing that turbulent mixing weakens the effect of diffusive separation. Finally, we summarize and discuss needed research enhancements Simulation Background [4] The first simulations of meteor trails were conducted only recently by our research group and preliminary results were published in two recent articles [Oppenheim et al., 2000; Dyrud et al., 2001]. However, simulations of other E region waves and turbulence have been conducted by a number of research groups and presented in various papers. These fall into two categories: simulations of the Farley Buneman instability and of gradient drift waves. Both are important to the current simulation techniques and the following paragraphs briefly review the relevant literature. [5] The earliest simulations of the Farley Buneman instability were conducted in the late 1970s by A. L. Newman and E. Ott [Newman and Ott, 1981]. These were pure fluid simulations with an enhanced, wavelengthdependent viscosity to model the important kinetic Landau damping effect. The next set of simulations was conducted in the mid-1980s by Machida and Goertz [1988]. They used a pure particle-in-cell (PIC) [Birdsall and Langdon, 1985] code to model the auroral Farley Buneman instability. These simulations modeled wave activity in a plane parallel to the Earth s magnetic field, a geometry which neglects the largest nonlinear term of the fluid equations. More recently, Janhunen [1994] conducted pure PIC simulations in the SIA 8-1

2 SIA 8-2 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS plane perpendicular to the Earth s magnetic field and thus included the dominant nonlinear term. Janhunen observed two-stream waves develop and propagate, though he was unable to let them reach saturation because of the simulations computational expense. His main observation was the turning of the waves so that k E 0 < 0, where k is the wave vector and E 0 is the driving or polarization electric field. Shortly thereafter, we published a number of papers on the nonlinear Farley Buneman instability using a hybrid kinetic simulator similar, but not identical, to that used for the meteor trails discussed in this paper [Oppenheim et al., 1996; Oppenheim and Otani, 1996]. These papers described the saturation mechanism of the instability and the resulting Doppler spectra. In a pair of subsequent papers, we looked at wave driven anomalous diffusion and a number of its consequences [Oppenheim, 1996, 1997]. [6] Gradient drift wave simulations have been used to study the turbulence driven by relatively long and weak gradients found in the natural equatorial electrojet and to explain the radar and rocket measurements of these waves. They have typically limited themselves to the large scales (>100 m) and the fluid regime, damping out shorter waves numerically. The earliest two-dimensional simulations showed how wave-wave coupling leads to isotropization of wave spectra and the generation of waves which the linear theory predicts are stable [McDonald et al., 1975; Ferch and Sudan, 1977; Keskinen et al., 1979]. More recently, detailed comparisons between 2-D fluid simulations, local and nonlocal linear theory and the observational data have been made [Ronchi et al., 1991; Hu and Bhattacharjee, 1998]. At high latitudes, fully 3-D fluid simulations of unstable plasma patches have shown the importance of 3- D in understanding high-latitude irregularities [Guzdar et al., 1998]. 2. Simulation Methods and Results [7] To study the evolution of meteor trails during the linear stage and beyond, we developed a numerical simulator for the 2-D plane perpendicular to the magnetic field, with x pointing east and z pointing up. By working in this plane, our simulator resolves the strongest nonlinear behavior, wave coupling between perpendicular modes [Oppenheim et al., 1996]. Using this simulator we have explored the cross-field dynamics of meteor trails at a number angles with respect to B. This section begins by describing the methods applied to simulating meteor trails and the results of a number of simulations Simulation Methods [8] Our simulator uses a hybrid approach to model full ion kinetic effects, but only fluid electron behavior. This method captures the dominant physical processes at work in an unstable meteor trail. [9] The particle-in-cell (PIC) method used for the ions accurately models all ion dynamics including thermal effects. This method, described in detail in the book by Birdsall and Langdon [1985], models the ions as a collection of macroparticles, each representing the behavior of many actual ions. These macroparticles each have an inertia and a position within a rectilinear mesh. [10] At the beginning of each iteration, electric fields have been defined at the vertices of mesh. For each particle, this electric field is linearly interpolated to the actual macroparticle position (a process called a scatter). Then, the Lorentz force equation is used to calculate ion accelerations. Since B is fixed and pointing out of the simulation plane, we use a Boris mover to efficiently and accurately update the velocities and positions of the macroparticles [Boris and Roberts, 1969]. Collisions between ions and neutrals are modeled as hard sphere elastic collisions where the likelihood of collision is linearly proportional to the macroparticles velocity with respect to a neutral particle. [11] Electrons are modeled as a fluid on the same mesh used for the electric field. Since we do not assume quasineutrality, we first approximate a solution to the electron fluid velocity using the fluid momentum equation, dv e dt ¼ e ð m E þ v e BÞ kt e rn e n e v e ; ð1þ m e n e and the continuity t n e ¼ rðn e v e Þ: ð2þ To accurately solve these equations, we use a second-order Adams-Bashfourth-Moulton predictor-corrector scheme [Butcher, 2000]. Since electron velocities and positions evolve far faster than ion quantities, we cycle the electrons faster than the ions while linearly interpolating ion evolution. We used an adaptive timestep for the electrons which depends on the electron plasma frequency, the highest frequency that the simulation resolves. [12] To assure numerical stability, we add hyper-diffusion terms, c x 4 n and c x 4 v to equation (1). Varying the hyperdiffusion coefficients by two orders of magnitude does not change the physical results of our simulations. We also compared the results to a code which assumes quasineutrality and found essentially identical behavior early in the simulation; though, at later times, the quasineutral code developed convergence problems. [13] Every time the electron or ion positions change, we must update the electric field to self-consistently reflect the new charge densities. The electron density automatically arises from the solution to equation (2). To calculate the ion density, we assume that each ion macroparticle describes a charge density which decreases linearly as one moves away from the specified particle location (called a tent particle-shape function), going from a peak in the center to zero at one grid spacing, dx or dy, away from the center. To get the total ion charge density, we sum the fraction of ions contained within each grid cell. In order to minimize the noise from the somewhat random particle positions, we use thousands of particles per grid cell, making this step the most computationally costly component of the simulations. To reduce the time necessary to perform this step and the scatter step, we distribute the particles evenly over a number of processors and then, after calculating the density over the entire mesh for each processor, we sum the density meshes over all processors to obtain a total ion charge density. [14] We model the initial meteor trail as a column of enhanced plasma density with Gaussian cross-section of radius r t and peak ion density, n p, usually about 30 times

3 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS SIA 8-3 the background density. This relatively small peak density allows us to keep modest density gradients over each grid cell, a compromise necessary to maintain simulation accuracy. The initial ambipolar potential is calculated by solving r (nrf) = D T /m T r 2 n where n is the ion density and the electron density is then defined so that Poisson s equation yields this potential. The initial velocities are set to the Pedersen and Hall drift velocities. Equations describing these initial conditions are derived and discussed in section 3.1 of the preceding companion paper. [15] Our 2-D simulations do not model meteor trail dynamics parallel to B. To justify neglecting the parallel dimension we argue that the GDFB instabilities are strongly field aligned, developing little wave energy in modes propagating more than a few degrees away from perpendicular [Kudeki and Farley, 1989]. Parallel to B we expect a simple ambipolar diffusion while perpendicular to B, we expect cross-field diffusion and instability-driven turbulence. At 102 km, the ambipolar diffusion rate is 50 m 2 /s while the cross-field ambipolar diffusion rate is 7.8 m 2 /s [Jones, 1991]. Hence, the diffusive time-scales are much longer than the instability growth time-scales for the wavelengths which dominant the simulation. While 2-D simulations do not capture all the physics, they do include the details of the fast instability processes, the dominant nonlinearity and the slow cross-field diffusion. Table 1. Physical and Simulation Parameters for the 102 km Equatorial Simulation Parameter Value External magnetic field B T Neutral gas density n n m 3 Temperature T i,n 250 K e -neutral coll. freq. v en s 1 Ion mass m i kg Peak/background ratio n e /n 0 30 Trail line density N line m 1 Background e density n m 3 Trail radius r t 1.5 m Ion-neutral coll. freq. v in s 1 Grid size n x,z 256 Grid spacing x,z m Time step t s 2.2. Simulation Results [16] Two-dimensional simulations can model cross-sections of meteor trails oriented in a number of directions with respect to the geomagnetic field, B. We will begin by simulating the cross-field dynamics of a trail lying exactly parallel to B, where the trail cross-section is circular. Two dimensional simulations with this orientation represent the physics of a 3-D trail accurately because parallel to B one expects the plasma to remain largely homogeneous, as implicitly assumed in 2-D. This simulation geometry allows us to isolate the dynamics perpendicular to B and study 2-D growth rates, turbulence, and anomalous diffusion rates. Trails that actually align perfectly along B will be rare and a tilt of a few degrees will substantially change the dynamics by enabling the electrons to neutralize the electric fiels by traveling along B. [17] We will follow the circular simulation with a line simulation which models a trail aligned exactly perpendicular to B. Since the size of our simulation box is much smaller than the typical length of a meteor trail, we will use periodic boundary conditions, making the trail infinitely long. This geometry allows us to incorporate the effects of an external E region electric field or, equivalently, a neutral wind, without having that effect immediately canceled by a polarization electric field, as discussed below. [18] Simulations allow us to probe the behavior of turbulent plasma trails in great detail. We can examine the spatial and temporal variation of densities, fields, temperatures, and fluxes. This allows us to develop a better understanding of the dominant physics. It also enables us to emulate observational techniques used by radars and, therefore better interpret these observations. In particular, the Fourier transform of the plasma density gives jn(k, t)j 2 which is proportional to the expected Bragg scatter strength returned by a radar when observing trail plasmas Trails Parallel to B [19] Our first simulation represents a trail aligned exactly parallel to B at 102 km near the magnetic equator. This is the highest altitude, at this latitude, where our current simulator can accurately model meteor trail dynamics. At higher altitudes, the initial radius of the trail becomes larger while the expected dominant instability wavelength remains small (10 20 cm). The makes the range between the total simulation size and smallest wave size too large and the simulation too costly. At lower altitudes the lower instability growth rates means the simulation takes longer to reach saturation, also adding to the simulation cost. Dyrud et al. [2001] and Oppenheim et al. [2000] described simulations of trails at 105 km with an artificially short gradient scale length. Nevertheless, the meteor trail physics described in those papers remains correct. [20] For this simulation, we initialize a 2-D Gaussian plasma distribution with a peak density of 25 times the background density. We set the ion and electron velocities and electric field according to a steady state solution of the fluid equations as described in section 3.1 of the companion paper. The trail has an initial full-width at half-max of 1 m and the 256 by 256 mesh spans 4 by 4 m. Choosing this peak density and shape allows us to maintain the reasonably modest gradients across the simulation grid cells required for numerical accuracy. Table 1 lists other relevant parameters. [21] Figure 1 shows trail densities, perpendicular electric field, E?, and density spectra from the 102 km circular simulation. In the leftmost set of panels, 0.2 ms into the simulation, the density profile remains Gaussian, and E? results from the ambipolar diffusion electric field which points everywhere into the trail. Using the equations from section 3.1 of the companion paper, we calculate an expected ambipolar electric field of 55 mv/m, close to the value generated by the simulator. The density spectrum of this stage shows only the Fourier transform of a Gaussian. Only a radar pointing perpendicular to the trail, in a specular configuration, would measure the trail at this stage. [22] The middle column of panels shows the instability at the end of the linear stage of wave development, at 0.4 ms, with striations forming in the density and large wave-

4 SIA 8-4 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS Figure 1. The trail density, electric field and density spectra at three different times. The top panels show the ratio of the local plasma density to the background density, n e /n 0 with the magnitude indicated by the color bar on the upper right. The center panels show the vector electric field, E, in mv/m where the direction of E is given by the position of the color in the color wheel and the magnitude by the saturation scaled to the maximum value given above each panel. The bottom panels show the power spectra of the density, n(k x, k z ) n*(k x, k z ) in a log scale indicated by the color-bar on the right. Note that the simulation resolves waves out to k = 210 m 1. All panels show cross-sections perpendicular to both the trail axis and B, which points into the page. See color version of this figure at back of this issue. generated electric fields exceeding 160 mv/m. The density spectrum shows 12 cm waves in all directions perpendicular to B. It is unlikely that a 1.2 GHz radar could observe these waves because the amplitude at 12 cm lies roughly 4 orders of magnitude below the peak (specular reflection) and, at this early stage, the total trail size remains only a few meters in diameter. [23] Using linear kinetic theory as shown in the companion paper (see Figure 4), we predict a dominant wave number of k 70 m 1, 20% higher than that generated by the simulator. This discrepancy probably occurs because the simulator uses a trail with a Gaussian density profile while the linear theory assumes a constant gradient scale length, rn 0 /n 0. To eliminate the possibility that it results from numerical damping we ran a simulation with twice the mesh resolution and found the same dominant wave number. [24] The last set of panels, at 3.5 ms, shows a wave pattern with clear nonlinear effects. The peak density has fallen to 1/3 of the original value and the trail has diffused outwards due to anomalous diffusion. The peak electric field remains strong though the ambipolar field for a trail of this size should have diminished to 1/2 of its original value. While the density spectrum is still dominated by the long wavelength Gaussian structure of the trail, the wave generated components of the spectrum has broadened to include waves ranging from 10cm upward and the total trail size has increased. Nevertheless, it remains unlikely that a radar will measure structures this small from this stage of an unstable meteor trail. [25] A Gaussian trail with a higher initial peak density 2 orders of magnitude higher is plausible superimposed on the same background density will evolve in a similar manner since wave dynamics receive their impetus from rn/n which depends strongly on the size of the trail and only weakly (logarithmically) on the peak density. The trail size is largely determined by altitude because the ionization and collisional mean-free-path paths depend principally on the atmospheric neutral density and slightly on meteoroid composition, size, and velocity. Though our simulator cannot yet follow the evolution of high density trails, we expect that such a trail

5 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS SIA 8-5 Figure 2. Ratio of trail density to initial density versus time from 102 km simulation. The solid line shows the average, full-width half-max, density from the simulation and the dashed line shows the density for a trail expanding due to cross-field ambipolar diffusion. will continue this type of evolution until it becomes large enough that short-wavelength reflections become possible. The next section shows how trails oriented perpendicular to B may develop far stronger short-wavelength and nonspecular components to their spectra. [26] Anomalous diffusion caused this trail to expand at approximately twice the rate predicted by simple ambipolar diffusion. Figure 2 shows this by comparing the simulated trail density to the density predicted by cross-field ambipolar diffusion. To make this comparison for Gaussian shaped trails, we used the solution for the density of a meteor trail undergoing ambipolar diffusion from Jones [1991], nr ðþ¼aexp r 2 = ð4d? tþ = ð 4pD? tþ; ð3þ where D? is the diffusion coefficient, a is the line density of the trail, r is the radius, and t is time plus a constant calculated from the initial radius of the trail. The two densities match at early times before the instability develops, then, after 0.5 ms, quickly diverge. The slope of the simulation density changes rapidly and inconsistently, showing that diffusion within a turbulent trail is chaotic. The magnitude of the anomalous diffusion depends strongly on trail altitude as discussed by Dyrud et al. [2001] Trail Perpendicular to B [27] Next, we will discuss the simulation of a trail aligned perpendicular to B. Since the two dimensional representation of such a trail necessarily requires homogeneity along B, we are actually studying the dynamics of a slab. While a fully 3-D simulation would improve the accuracy of this system, it remains beyond the capacity of our simulators at this time. Nonetheless, we argue that the 2-D representation catches much of the essential physics in part because the parallel and perpendicular physics are somewhat independent and because actual trails will rapidly become extended in the parallel direction because of the high parallel mobility of the electrons. [28] The simulated trail spans our simulation box perpendicular to B. This means it represents an infinite trail in this direction because of the periodicity of the simulations. While meteors are not truly infinite in length, head echo measurements indicate they extend for many kilometers along the meteoroid trajectory while remaining only a few meters in width. Since our simulations span only tens of meters and tens of milliseconds, we only introduce relatively limited errors by representing this as an infinite trail. Over a longer timescale, such a representation would probably introduce unphysical behavior. [29] As with the parallel trail discussed in the previous section, we will study a trail at 102 km altitude for the set of parameters listed in Table 1. In this case, we also add a downward pointing (1 mv/m) external electric field aligned with the trail to incorporate the effects of an E region polarization electric field. These fields can reach hundreds of mv/m in the auroral E region, tens of mv/m near the geomagnetic equator, and a few mv/m at midlatitudes. For a parallel trail, this external field has little effect since the trail rapidly polarizes to cancel the field. For a perpendicular trail, the periodic boundary conditions make it impossible for the trail to cancel the field and this modifies the trail dynamics substantially. [30] Our simulations progress through three distinct stages of meteor trail evolution as shown in Figure 3: (a) the rise of a trail field immediately after the formation of the trail, (b) the formation of a GDFB instability at the edges of the trail and (c) the development of turbulence. In order to better visualize the trail evolution, we urge the reader to view the MPEG animations. 1 [31] The middle panels of Figure 3 show evolution of the trail electric field. Initially, the simulation maintains the trail field predicted by E x ¼ D T m x n n 1 E 0 1 n b ; ð4þ m T B 0 n which can be derived from equation (4) of the companion paper where E E x^x + E 0^y. After only 0.4 ms, strong 15 cm wavelength GDFB waves appear prominently on the westward edge of the trail, as seen in the center column of panels. On the right edge of the trail, the weaker electric fields drive slower wave growth as expected from the smaller E rn. The linear theory of the GDFB instability describes the early stage of meteor trail evolution. [32] Plasma turbulence follows the linear stage and leads to the development of larger scale density perturbations which, to some degree, shred the trail. These density irregularities affect the spectra and, hence, the expected radar signatures of the trail. As seen in the bottom right panel, a range of wavelengths develop which will allow radars to make nonspecular measurements. By taking the Fourier transform in time of the density perturbations at a given wavelength, we can emulate a coherent (Bragg) scatter radar return. Figure 4 shows two such returns. These examples show broad Doppler spectra with a small Doppler shift (0 400 m/s) reminiscent of type II echoes [Rogister and D Angelo, 1970] and are typical of cm returns 1 Available via Web browser or FTP from ftp://kosmos.agu.org (username = anonymous, password = guest ); directory append subdirectories arranged by paper number or from ~meerso/meteor. Information available at about.html.

6 SIA 8-6 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS Figure 3. The trail density, electric field and density spectra at three different times. The top panels show the ratio of the local plasma density to the background density, n e /n 0 with the magnitude indicated by the color bar on the upper right. The center panels show the vector electric field, E, in mv/m where the direction of E is given by the position of the color in the color wheel and the magnitude by the saturation scaled to the maximum value given above each panel. The bottom panels show the power spectra of the density, n(k x, k z ) n*(k x, k z ) in a log scale indicated by the color-bar on the right. Note that the simulation resolves waves out to k = 210 m 1. All panels show cross-sections perpendicular to both the trail axis and B which points into the page. See color version of this figure at back of this issue. that one would receive if the slab simulations accurately represent the dominant physics of meteor trail turbulence. [33] The turbulent evolution of trails cannot explain observations of meteor trails persisting for minutes or longer [Chapin and Kudeki, 1994]. Meteor trails with an order of magnitude or two higher initial density will evolve in a manner similar to the ones shown above, since the instability growth rates depend on the logarithm of the density. Even these will last only a few seconds instead of the tens to hundreds of milliseconds that our simulated trails last. These long-lived trails probably require the combination of slowly diffusing meteor dust and an electrojet existing in a state close to instability. [34] At later times, periodic boundary conditions cause the meteor trail to begin interacting with itself. To study the evolution of these meteor trails further in time, one must increase the simulation size significantly. This would also allow for a more detailed study of east-west asymmetry and higher peak plasma density. For the existing version of the simulation code, this exceeds today s computer capabilities. Figure 4. Doppler spectra at two wavelengths from the simulation shown in Figure 3. We generate the spectra by Fourier transforming 64 data points between 15 and 20 ms after using a Hanning function to window the time sequence.

7 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS SIA 8-7 Figure 5. Trail simulation with equal parts Fe + and Mg +. The left panel shows species fractionation as function of space, and the right panel is integrated in the azimuthal direction. [35] In addition to the baseline simulation results for the parameters listed in Table 1, we have performed simulations for a range of parameters reflecting different trail conditions and altitudes. For all realistic parameter variations, the simulation shows meteor trails generating a large trail field followed by wave growth and, ultimately, turbulence. The details of the evolution and turbulence depend on the chosen parameters Multiple Species Simulations [36] Simulations allow us to explore the dynamics of meteor trails composed of a mixture of ion species. These simulations show that instabilities and turbulence generally have a homogenizing effect on number of trail properties. For meteor trails made up of multiple ions one expects lighter species to diffuse faster then heavier ones. Jones and Jones [1990] has shown that this effect results in considerable fractionation differences with important effects on trail chemistry and recombination. Figure 5 shows the species fraction of a simulated unstable meteor trail composed of equal parts Fe + and Mg +, at 2 ms into the simulation. The peak fractionation is less than 10%. This result was compared with a simulation using similar parameters except for a reduced density gradient which was unable to drive instability. At comparable stages during diffusion the stable trail showed a fraction as large as 6 times that of the unstable trail, meaning that instability generated turbulence keeps the species well mixed. This result indicates that turbulent trails should actually have more predictable recombination rates and chemistry than was predicted by Jones and Jones [1990] for laminar trails. 3. Conclusions [37] Two-dimensional hybrid simulations have shown the effects of instability and turbulence on meteor trails. In the case of trails aligned with B, these simulations accurately represent their evolution, showing the trail develop waves followed by relatively strong irregularities. This turbulence causes structuring of the trail and a rapid anomalous diffusion. Trails aligned perpendicular to B will also respond to an externally applied electric field as can occur in the E region, particularly in the equatorial and auroral E regions. Simulations of these cases show waves developing into strong field-aligned irregularities. Doppler spectra of the simulated density irregularities indicate that radars with large aperture-power products should see these as nonspecular meteor echoes with small Doppler shifts and broad spectral widths. Additionally, simulations of trails containing multiple species of ions show that turbulent mixing slows the rate of species fractionation. [38] While these simulations model the evolution quite well, a number of steps could improve their accuracy and representation of the physics. First, fully 3-D simulations would improve the representation of trails aligned perpendicular to B. As computers gain in speed and parallelization improves, such simulations will become possible. Also, simulations could better represent the thermal evolution of meteor trails. In particular, electrons could be modeled with a fully kinetic technique or using a thermal equation more complex than simple adiabatic ones. [39] These findings have significant consequences for interpreting meteor radar echoes. First, the structuring of the trail by plasma turbulence allows for nonspecular reflections of radar signals. Second, trails lying perpendicular to the geomagnetic field may not accurately follow atmospheric wind speeds and directions during the early stages of trail evolution. Third, laminar and anomalous diffusion rates depend strongly on altitude and trail stability. Finally, turbulent mixing can modify fractionation and the ultimate evolution of meteor chemistry. [40] Acknowledgments. The authors would like to thank Yakov Dimant for useful discussions, Kelly McMillon and Licia Ray for editing and producing many of the figures. This material is based upon work partially supported by the National Science Foundation under Grant ATM and NASA Grant NGT References Birdsall, C. K., Particle-in-cell charged particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC, IEEE Trans. Plasma Sci., 19, 65 85, Birdsall, C. K., and A. B. Langdon, Plasma Physics Via Computer Simulation, McGraw-Hill, New York, Boris, J. P., and K. V. Roberts, Optimization of particle calculations in 2 and 3 dimensions, J. Comput. Phys., 4, 552, Butcher, J., Numerical methods for ordinary differential equations in the 20th century, J. Comput. Appl. 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9 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS Figure 1. The trail density, electric field and density spectra at three different times. The top panels show the ratio of the local plasma density to the background density, n e /n 0 with the magnitude indicated by the color bar on the upper right. The center panels show the vector electric field, E, in mv/m where the direction of E is given by the position of the color in the color wheel and the magnitude by the saturation scaled to the maximum value given above each panel. The bottom panels show the power spectra of the density, n(k x, k z ) n*(k x, k z ) in a log scale indicated by the color-bar on the right. Note that the simulation resolves waves out to k = 210 m 1. All panels show cross-sections perpendicular to both the trail axis and B, which points into the page. SIA 8-4

10 OPPENHEIM ET AL.: METEOR TRAIL INSTABILITIES: SIMULATIONS Figure 3. The trail density, electric field and density spectra at three different times. The top panels show the ratio of the local plasma density to the background density, n e /n 0 with the magnitude indicated by the color bar on the upper right. The center panels show the vector electric field, E, in mv/m where the direction of E is given by the position of the color in the color wheel and the magnitude by the saturation scaled to the maximum value given above each panel. The bottom panels show the power spectra of the density, n(k x, k z ) n*(k x, k z ) in a log scale indicated by the color-bar on the right. Note that the simulation resolves waves out to k = 210 m 1. All panels show cross-sections perpendicular to both the trail axis and B which points into the page. SIA 8-6