lab-inf-4_tasks / 2777

Abstract. Radars frequently detect meteor trails created by the ablation of micro-meteoroids between 70 and 120 km altitude in the atmosphere. Plasma simulations show that density gradients at the edges of meteor trails drive gradientdrift instabilities which develop into waves with perturbed electric elds often exceeding hundreds of mV/m. These waves create an anomalous crosseld di usion that can exceed the crosseld (? B) ambipolar di usion by an order of magnitude. The characteristics of the instabilities and anomalous di usion depend on the trail altitude, latitude, and density gradient. A simple relation de nes the minimum altitude at which meteor trail density gradients drive plasma instabilities and anomalous di usion. These results impact a number of meteor radar studies, including those that use di usion rates to determine trail altitude, and atmospheric temperature.

Introduction

This study investigates the small scale electrodynamics of weakly ionized meteor trails in the ionosphere [Ceplecha et al.,1998, @]. The Earth is continually bombarded by dust to sand grain size ( 10−5 kg) meteors. These small meteors ablate their atoms during atmospheric entry, generating cylinders of ionization often orders of magnitude more dense than the surrounding ionospheric plasma. Radars observe meteor generated plasma columns between 70 and 120 km, with most observed between 80 and 105 km. Our plasma simulations reveal that meteor trails, above a certain altitude, are subject to instabilities which create eld-aligned irregularities and anomalous crosseld di usion. These processes a ect the interpretation of radar echoes from meteor trails.

Researchers have attributed the observation of some nonspecular radar echoes of meteor trails to the development of a gradient-drift type instability within the trail plasma [Chapin and Kudeki,1994, @; Chang et al.,1999, @]. To test this hypothesis, Oppenheim et al. [2000] simulated meteor trails in the equatorial electrojet. This paper showed that the gradient-drift Farley-Buneman (GDFB) instability develops where the trail density gradient and electric eld are largest [Fejer et al.,1975, @]. Further, these simulated meteor trails develop eld-aligned irregularities and, initially, do not move with the neutral wind.

Combining knowledge of meteor trail di usion rates with radar measurements has allowed researchers to determine a number of characteristics of both the trails and the surrounding atmosphere: (1) Di usion rates have been used to determine the altitude of meteor trails which would other-

Copyright 2001 by the American Geophysical Union.

Paper number 2000GL012749. 0094-8276/01/2000GL012749$05.00

wise remain ambiguous due to the wide beam pattern of many meteor radars [Baggaley,1981, @]. (2) A meteor trail's initial radius is de ned as the average distance meteor particles travel during thermalization. Determination of this value from radar echoes requires accurate knowledge of trail di usion rates [Baggaley and Fisher,1980, @]. (3) Knowledge of meteor trail di usion rates enables the use of radar observations to obtain atmospheric temperatures [Tsutsumi et al.,1994, @; Hocking,1999, @].

A number of theoretical papers show that the geomagnetic eld inhibits crosseld di usion of meteor trails, particularly at high altitudes [Kaiser et al.,1969, @; Jones,1991, @]. However, radar observations used to compare the relative importance of crosseld and parallel di usion rates have returned ambiguous results [Watkins et al.,1971, @; Baggaley and Webb,1980, @]. Our research shows that instability-driven anomalous di usion enhances crosseld trail expansion and may explain the observational ambiguities.

Simulation methods and results

We employ a hybrid plasma simulator that represents ions as a fully kinetic plasma and electrons as a warm inertial fluid in the 2-D plane perpendicular to the geomagneticeld, B. We assume a trail and background plasma composed of an ion species close in mass to Si+, NO+, and O+2 which are common species found in meteor debris and the local atmosphere. The simulator advances these ions in 2-D space and 3-D velocity using a massively parallel Particle-in- Cell (PIC) method using 128 million particles. Ion-neutral interactions are modeled as hard sphere collisions with an energy dependent cross section [Birdsall,1991, @]. The electron momentum and continuity equations are integrated using a second order predictor-corrector method. Finally, the simulator solves Poisson's equation to generate the electricelds assuming periodic boundary conditions. We have compared the results to a quasi-neutral version of the simulator and found that the development and e ects of the instability remain essentially the same [see, Oppenheim et al. 2000].

The meteor trails evaluated in this study run parallel to B and the 2-D simulations follow the dynamics in the plane perpendicular to B. Although perfect alignment is an uncommon occurrence in nature, this con guration eliminates the gradients along B and allows us to isolate the dynamics in the perpendicular direction. This con guration also captures the dominant physics of meteor trail instabilities, despite neglecting oblique modes of the GDFB instability. We have conducted a number of simulations with the trail at di erent orientations to the geomagnetic eld and nd that the main results presented in this paper, i.e. increased di usion in the perpendicular plane, remain the same.

We initialize the trail as a 2-D Gaussian distribution with a peak density of 20 times the background density. The ve-

locities and electric eld are initialized according to a steady state solution of the fluid equations. The trail has an initial FWHM of 1 m and the 256 by 256 mesh spans 5 by 5 m. Choosing this shape allows us to maintain reasonable gradients across the simulation grid cells as required for numerical accuracy. The majority of meteor trails observed by radars probably have substantially larger peak densities and gradients, which will lead to higher growth rates and stronger anomalous di usion than seen in the examples below.

The development and evolution of meteor trail instabilities changes with altitude and latitude because the collision frequencies vary by several orders of magnitude between 95 km to 115 km and B varies by a factor of two with latitude. Therefore, we conducted six simulations using parameters consistent with ionospheric conditions found at altitudes from 95-115 km. Five of the six simulations were conducted assuming an equatorial B of 2:5 10−5 T and the sixth simulation was conducted with B = 5:9 10−5 T, comparable to 70 MLAT.

Figure 1 shows trail densities and perpendicular electriceld, E?, from the 105 km simulation using parameters listed in Table 1. In the leftmost pair of panels, 0.2 ms into the simulation, the density pro le remains Gaussian, and the predominant electric eld results from ambipolar di usion, pointing into the trail. These panels also show the instability during the linear stage with striations forming in the density and electric eld. The central pair of panels, at 1.5 ms, shows a saturated instability with peak electric elds exceeding 200 mV. The last pair of panels, at 3.5 ms, shows a turbulent wave pattern, a peak density reduced to 1/3 of the original value, and a trail that has di used outwards due to anomalous di usion.

Comparing the simulated trail density to the density predicted by crosseld ambipolar di usion demonstrates the

instability's e ect on the outward expansion of the trail. We use the solution for the density of a meteor trail undergoing ambipolar di usion from Jones [1991], n(r) =

exp[r2=(4D? )]=(4 D? ) ; where D? is the di usion co- e cient, is the line density of the trail, r is the radius, and

is time plus a constant calculated from the initial radius of the trail. Fig. 2 shows that the two densities match at early times before the instability develops, then after 1 ms quickly diverge. The slope of the simulation density changes rapidly and inconsistently, showing that di usion within a turbulent trail results in a non-exponential decay of the trail density. For cases where no instability develops, the simulated and calculated densities match, con rming that the simulator accurately models di usion.

Di usion Analysis

To make accurate comparisons between the di usion co- e cients obtained from meteor radar observations and the simulations, we use a mathematical method similar to those used to interpret underdense radar returns. The amplitude of the radar return from an underdense trail is proportional to the Fourier transform of the electron density, ne, at onehalf the radar wavelength [Jones,1995b, @]. Therefore, we calculate perpendicular di usion coe cients from the average exponential decay rate of the simulation density at a given wavelength. Since meteor radars commonly operate at 50 Mhz, we use 3.0 m as our wavelength, but found that the di usion coe cient varies by less than 5% as the wavelength varied from 2-5 m.

Fig. 3 compares the di usion rates obtained from our simulations to the perpendicular and parallel ambipolar diffusion rates. Below 100 km, the simulation di usion rate matches the perpendicular ambipolar di usion rate because

Table 1. Physical and simulation parameters for 105km equatorial simulation.

no instability exists to drive anomalous di usion. Between 100 and 105 km, the simulation di usion rate matches the parallel di usion rate. This represents a dramatic increase in the crosseld di usion. At 105 km, the anomalous diffusion rate exceeds the crosseld ambipolar di usion rate by an order of magnitude. Above 105 km, the anomalous di usion rate remains essentially flat at 50 m2=s, but well above the instability-free di usion rate.

Discussion and Summary

The simulations of meteor trails presented above show instabilities and anomalous crosseld di usion. These ndings have a number of implications for understanding the physics of meteor trails and interpreting meteor radar observations. The remainder of this paper discusses the physical mechanism underlying the anomalous di usion, the minimum altitude at which instabilities appear, implications for meteor radar studies, and a summary.

Instability threshold A simple calculation predicts the minimum altitude of meteor trail instabilities and anomalous di usion. Fejer et al. [1975] shows that the

gradient-drift instability becomes unstable when E? rn > 0. If no large-scale electric eld or neutral winds exist, then the perpendicular electric eld, E?, results solely from the crosseld ambipolar di usion. Above 100 km, collisions dominate ion motion causing them to di use out of the trail. The magnetized electrons do not have su cient mobility to follow the ions, resulting in an ambipolar electric eld. Below 100 km, electron-neutral collision rates increase until the ion and electron crosseld di usion rates are equal. At this point, E? = 0 and no instabilities will develop to drive anomalous di usion. Below this altitude, electrons di use across eld lines more rapidly than ions and E? will have the reverse sign, damping the instability. We de ne a parameter, Q, as the ratio of electron and ion crosseld diffusion rates, Q = Ti=Te(ΩeΩi= en in), where Ti=Te usually varies between 1 and 1/2 and Ωe;i are the electron and ion cyclotron frequencies. When Q > 1, E? points in the direction of rn and the instability grows. For Q < 1 the eld reverses direction, preventing instability. Fig. 4 shows lines of Q = 1, the minimum altitude for instability growth, as a function of CGM latitude. For Ti=Te = 1, instability is suppressed below 100 km at equatorial latitudes. For warmer electron temperatures the Q = 1 line indicates that instability develops at higher altitudes. This criterion for trail instability neglects the e ects of external electric elds and neutral winds, both common in the E-region. It also assumes that meteor trails contain a single and moderately heavy ion species and no dust. Observed meteor trails may violate one or more of these assumptions and become unstable at lower altitudes.

Altitude determination Radars frequently observe trails within a broad beam pattern, preventing an accurate determination of trail altitude. Since the decay rate of radar return power is assumed to be proportional to the trail expansion rate and since di usion rates vary rapidly with altitude, observers use echo decay rates to infer trail altitudes [Jones,1991, @]. However, anomalous di usion affects trail expansion rates above the Q = 1 altitude. In these cases, using ambipolar di usion rates to calculate altitude may lead to errors of several kilometers.