Anomalous electron heating and its effect on the electron density in the auroral electrojet



[1] Measurements made with the Sondrestrom incoherent scatter radar during the April 17, 2002 magnetic storm are presented. The magnetic storm produced strong convection electric fields with no particle precipitation at Sondrestrom. The observed increase in the E-region electron temperature was caused by the anomalous electron heating in the altitude range of 100–120 km, where Farley-Buneman turbulence is localized. An model of anomalous electron heating was validated by comparison with the ISR data. Estimates of electron density perturbations during the strong electric fields show a good agreement with the model that accounts for suppression of the electron/ion recombination rate due to anomalous electron heating. The observed increase in the electron density leads to modification of the ionospheric conductivity. This effect is of importance for ionosphere–magnetosphere coupling, and should be included in global models that are developed for space weather forecast.

1. Introduction

[2] Numerous radar observations have demonstrated strong enhancements of electron temperature in the E-region auroral electrojet during magnetic storms [Schlegel and St.-Maurice, 1981; Williams et al., 1992; Foster and Erickson, 2000]. This effect, which is often called anomalous electron heating, correlates with increases in amplitude of the convection electric field Ec. The conventional frictional heating caused by the convection electric field cannot account for the observed increase in E-region electron temperatures, and it has been widely accepted that the primary cause of the anomalous electron heating is the turbulent electric field generated by the Farley-Buneman (FB) instability. In the auroral regions, some electron heating can also be caused by precipitating particles with energies spanning from hundreds eV to hundreds keV, which enter the atmosphere along the magnetic field lines [Rees, 1989; Doe et al., 1997; Mishin and Telegin, 1989; Schlesier et al., 1997].

[3] Earlier theoretical models of anomalous electron heating [Robinson, 1986; St.-Maurice, 1987] have some physical inconsistencies (see discussion by Farley [1996] and Dimant and Milikh [2003]). A new quantitative model of FB wave heating of electrons [Dimant and Milikh, 2003; Milikh and Dimant, 2003] associates strong electron heating with small turbulent electric fields parallel to the geomagnetic field [St.-Maurice and Laher, 1985; Providakes et al., 1988; St.-Maurice, 1990] and provides good agreement with existing observations.

[4] Strong anomalous electron heating can also lead to an increase in the local electron density, since the electron heating reduces the electron-ion recombination rate [Gurevich, 1978; St.-Maurice, 1990; Dimant and Milikh, 2003]. While the effect of strong electron heating on ionization/recombination balance in the mid-latitude E-region has been firmly established in some experiments on artificial ionospheric modification, [e.g., Golyan et al., 1982], there have been no unambiguous observations of the electron density changes during natural events of anomalous electron heating at high latitudes.

[5] The objective of this paper is to present and analyze the results of anomalous heating and electron density variations, both correlated with a strong convection electric field. The measurements were made with the Sondrestrom incoherent scatter radar [Kelly et al., 1995] during the April 17, 2002 magnetic storm during a period of enhanced Ne with no detectable particle precipitation. We compare the observations with the model of anomalous electron heating with special emphasis on the increase in the electron density.

2. Observations

[6] In this paper we analyze the data set collected by the Sondrestrom ISR during the April 15–17, 2002 World Day experiment. A magnetic storm of kp = 7+ occurred on 17 April 2002. The ISR observations show a large decrease in the F-region electron density on 17 April 2002 [Goncharenko et al., 2005]. However, in the E-region the electron density increases in the narrow range of altitudes, between 100 and 120 km. A strong convection electric field along with an increase in electron and ion temperatures are observed during the same time period. Figure 1 shows the time series of the measured electric field, (Figure 1a), electron temperature Te (Figure 1b), and normalized electron density Ne/Ne0 (Figure 1c) observed at 111 km altitude during the time between 11 and 15 UT on 17 April 2002, when the convection electric field reached its peak of about 150 mV/m. Here Ne0 is the unperturbed electron density which was observed under quiet conditions on April 15 and 16, 2002.

Figure 1.

Data collected by the ISR at Sondrestrom. (a) Measured convection electric field, (b) electron temperature, and (c) fitted electron density normalized by its unperturbed value found during the two previous quiet days 04/15–16. The electron temperature and density correspond to the range gate centered at 111 km altitude.

[7] In this paper we focus on the near doubling of the electron density observed in the E-region between 100 and 120 km during the strong electric fields on 17 April 2002. Such localized increases in the electron density cannot occur due to particle precipitation, unless the energy spectrum of the incoming particles is monoenergetic, which is not a likely scenario. DMSP passes do show significant particle precipitation at latitudes south of Sondrestrom. UV images collected by the POLAR satellite during 11:00–14:12 UT of 17 April 2002 show noticeable E-region emissions caused by the particle precipitation to the south of Sondrestrom. However, the radar observations were taken near zenith and we conclude that the increase in the electron density is not related to particle precipitation, with posible exception of the periods around 1130 and 1330–1345 UT.

[8] The anomalous electron heating is localized between 100 and 120 km, where the magnetized electrons exceed the acoustic speed of the unmagnetized ions, thus, leading to the Farley-Buneman instability. Because of the strong convection electric field driving the electron speeds in the E-region, this instability results in strong anomalous electron heating, suggesting that the observed increase in the electron density is caused by the anomalous heating.

[9] Thus, on 17 April 2002 we had the interesting situation where a strong convection electric field existed in the absence of particle precipitation. This allows us to isolate the effects caused by electron anomalous heating on the E-region plasma. In our analysis, we focus on the altitude of 111 km, where we expect the strongest anomalous electron heating.

[10] In the present analysis, the incoherent scatter radar experiment used the alternating-code pulse scheme on one frequency to provide 3-km range resolution in the E-region while also transmitting an uncoded long pulse (320 μsec or 48-km range resolution) on another frequency for F-region analysis. The antenna is cycled through three fixed positions every 3 minutes with one position directed along the magnetic field line and the other two positions separated in azimuth by 120 degrees with a common elevation angle of 70 degrees. All the data for both pulse schemes are integrated for 3-minutes before performing any spectral analysis. The long-pulse, F-region plasma velocity data from the three positions are used to determine the convection electric field. The electric field is well estimated statistically with errors that lie typically in the range of 1–2 mV/m. However, systematic errors related to temporal and spatial variability on scales smaller than defined by the combined line-of-sight measurements can lead to larger uncertainties. One approach to test the validity of the assumed conditions is to compare the estimated ion temperature in each line-of-sight measurement used to compute the electric field. In doing so, we find the ion temperatures to be relatively consistent and correlated well with the electric field magnitudes. Electric field measurements from the F-region data are assumed to map to the E-region without attenuation. This assumption is valid for electric field structures with spatial scales greater than 10 km [Heelis and Vickrey, 1991] and is generally met, as electric field measurements were made on the scales of ∼250 km. Contributions from electric field with <10 km spatial scale could cause additional errors. An overall uncertainty due to cumulative effects of these error sources is difficult to access.

[11] The alternating-code data are used to determine the E-region plasma properties. These data were integrated for three minutes and a 3-km range resolution was maintained for altitudes below 120 km. Under these unique conditions, a number of spectral fitting schemes to estimate the plasma parameters of electron density, electron temperature and ion temperature in the lower E-region were excersized. The final gate-by-gate fitting scheme to the E-region spectra employed a model ion-neutral collision frequency using MSIS-00 neutral densities and allowed for the ion temperatures and electron temperatures to be independent fitting variables. During the period of large electric fields, the electron temperature exceeded the ion temperature by a ratio of about 4-to-1. This results in a reduction in the incoherent scatter radar cross section and consequently reduced backscatter power. Thus, the statistical errors in estimating the plasma parameters increase during this time but their relative error remained reasonable. As no systematic differences were found in different pointing directions, a 3-point running mean was used to represent the electron density.

[12] Furthermore, estimates of ionospheric parameters and their errors are based on the assumption of a Maxwellian plasma distribution, which is not valid for strong electric fields. However, we account for this effect in temperature and density by introducing a kinetic correction to the electron temperature based on our theoretical model [Milikh and Dimant, 2003].

3. Model of Anomalous Electron Heating and Perturbations of the Electron Density

[13] In this Section, we will first review the major elements of the Dimant and Milikh [2003] model and then apply it to compute electron and ion temperatures as a function of convection field. Then we will discuss the effect of anomalous electron heating on the electron density, and compute the electron density enhancement as a function of the electric field, E.

[14] Dimant and Milikh model of anomalous electron heating is based on heuristic assumptions regarding the nonlinearly saturated FB turbulent electric field. The key element is a hypothesis that mainly the parallel electric field spectrum of FB waves is responsible for the increased electron temperatures. The heuristic model of nonlinearly saturated turbulent electric field is based on two assumptions. First, for an electric field well above the FB threshold field, the transverse root mean square (RMS) turbulent electric field is of the order of the convection electric field. Second, the parallel fluctuation electric field is such that the saturated FB turbulence is marginally stable according to the linear stability dispersion relation. Having determined the RMS turbulent electric field from the above model, we employ a special kinetic code which allows us to compute the electron distribution function. The kinetic code includes inelastic energy losses by electrons and allows one to compute the effective electron temperature for a given convective electric field at different altitudes. The code implementations clearly demonstrate that under strongly driven conditions the electron population readily becomes non-Maxwellian. In those cases, using a theoretically derived correction factor, we find the deviations of the effective electron temperature from that determined from radar observations.

[15] An important effect of the anomalous electron heating in the E region is the increase of the local electron density due to a partial suppression of the electron-ion recombination rate by the electron temperature elevation [Schlegel, 1982]. Sheehan and St.-Maurice [2004] reviewed a laboratory measurement of the dissociation recombination rates for O2+ and NO+ ions, which are the major ions in the ionospheric E-region. Their analysis shows that the dissociation rate coefficients have different electron temperature dependencies at moderate temperatures (Te < 1,200 K) and at high temperatures (Te > 1,200 K). We use the rate coefficients recommended by Sheehan and St.-Maurice, applying a matching condition at Te = 1,200 K in order to avoid singularity. Thus we obtain for the O2+ recombination rate, α(cm3/s) = 1.95 × 10−7 (300/Te)0.7, if Te < 1,200 K, and 1.72 × 10−7 (300/Te)0.61, if Te > 1,200 K. For the NO+ recombination rate, we have α(cm3/s) = 3.5 × 10−7 (300/Te)0.69 if Te < 1,200 K, and 2.92 × 10−7 (300/Te)0.56 if Te > 1,200 K.

[16] Furthermore, the error analysis provided by Sheehan and St.-Maurice shows that the inaccuracy in α is about ±15%. Note, however, that the above rate coefficients neglect the vibrational excitation of O2+ and NO+ ions. As shown by Sheehan and St.-Maurice, if the vibration excitation does exist, it suppresses the dissociative recombination rate of O2+ and NO+ by a factor of 1.5–2.0.

[17] To estimate time evolution of the density disturbances, we consider a simple situation when at some moment t = 0 the electron temperature suddenly changes from T0 to T1 and remains constant. This evolution is determined by the solution of the ionization/recombination equation

equation image

where q is the ambient ionization rate, with the initial condition Ne(t = 0) = N0. For t > 0, the solution of equation (1) yields

equation image

where α0 = α(T0), α1 = α(T1). Thus the characteristic timescale of the electron density changes is τch = 1/(2 equation image n0), while the total heating time needed for the electron density to reach 0.9 of its stationary value N = N0equation image is of about 2τch.

[18] Thus a time shift of 2τch exists between changes in the electron temperature and resulting changes in the electron density.

4. Discussion and Conclusions

[19] In this section we present the results of the Sondrestrom ISR measurements made during a magnetic storm17 April 2002 and compare these results with our theoretical model. Figure 2 shows scatter plots of Ne/Neo ratio (Figure 2, left) and electron temperature (Figure 2, right) as a function of convection electric field for the gated altitude of 111 km along with the theoretical results made with the model described in Section 3. The model calculations are based on unperturbed electron temperature, neutral density and ion composition from the MSIS_00 Atmosphere model and the International Reference Ionosphere. The solid lines show the modeling results without the kinetic correction, while the dashed lines show the results that include the kinetic correction.

Figure 2.

Scatter plots of (left) electron density normalized by its unperturbed value and (right) electron temperature collected by the Sondrestrom ISR on 17 April 2002. All the data are for the gated altitude of 111 km. Solid lines correspond to the theoretical model without kinetic corrections, dashed lines include kinetic corrections.

[20] It was shown by Milikh and Dimant [2003] that strong low-frequency electric fields result in a significant non-Maxwellian distortion of the electron distribution function. Therefore the apparent electron temperature retrieved from ISR data may exceed the actual electron temperature. A kinetic correction to an electron temperature measured by the ISR could be introduced [Milikh and Dimant, 2003]. Such kinetic correction which is shown in Figure 2 by dashed lines produces a better agreement between the model and observations.

[21] Note that according to the MSIS_00 model the neutral temperature at Sondrestrom at 111 km varies between 380 and 317 K at 11–15UT on 17 April 2002, with the neutral density changing respectively. Figure 2 reveals results of calculations made for the two ambient temperatures. It shows that such variation in the ambient temperature can lead to about 15% changes in the electron temperature, and thus should be taken into account when analyzing ISR data collected during magnetic storms.

[22] The electron temperature changes in phase with the convection field, while the changes in the electron density reveal a delay with respect to the convection electric field variations, as shown in Figure 1. Assuming an instantaneous change in value of E, the electron temperature will reach its saturation value in a few ms, while the electron density will react much slower. According to equation (2), it saturates in (2–3) τch period, i.e., in 2–3 minutes.

[23] Figure 3 shows by the crosses the time series of the electron density estimated by the Sondrestrom ISR on 17 April, while the X's reveal the values Ne(t) modeled by using the observed electron temperature, as shown in Figure 1, and applying equation (2). Besides, we use unperturbed values of electron density shown by the asterisks which form a continuous trace on the bottom in Figure 3. Since the averaging time of 3 minutes is higher than the electron heating time (2–3)τch we neglect the transient process in equation (2). However, we add the time shift of 2τch between the observed and computed values of electron density. In addition, we calculated Ne(t) from the time series of the observed electron temperature using the same procedure but consider the kinetic corrections. These results are shown in Figure 3 by triangles. Note that the theoretical results include an error of about ±8% related to inaccuracy of values of electron-ion recombination rates as mentioned above in Section 3. Thus our model is in a good agreement with observations.

Figure 3.

The crosses show the electron density measured by the ISR at Sondrestrom 04/17/02. Δ correspond to the electron density model without kinetic corrections, X present kinetic corrections. The unperturbed electron density measured in two previous days is shown by the asterisks.

[24] To conclude, the ISR observations at Sondrestrom made during the storm event on 17 April 2002 were analyzed and the E-region electron density were modeled under these unique conditions. The magnetic storm produced strong convection electric fields, while there was no particle precipitation at Sondrestrom. Therefore, the observed increase in the E-region electron temperature was caused by the anomalous electron heating only. In turn, the electron heating produced an increase in the electron density in the altitude range 100–120 km, where Farley-Buneman turbulence is localized. A recently developed model of anomalous electron heating [Dimant and Milikh, 2003] was validated by comparison with the 17 April 2002 Sondrestrom ISR data. Estimates made of the perturbations in electron density during the strong electric fields show agreement with a model that accounts for the suppression of the electron/ion recombination rate due to anomalous electron heating. The observed increase in the electron density leads to modification of the ionospheric conductivity. This effect is of importance for ionosphere – magnetosphere coupling, and thus should be considered in global models used for space weather forecast.


[25] The authors appreciate discussions with M. Oppenheim and D. Papadopoulos. The research is supported by NSF grants ATM-0334256 and ATM-0332354. The Sondrestrom Facility is operated by SRI International under cooperative agreement with the US National Science Foundation, ATM-0334122. We have used the Polar UVI data provided by instrument PI G.K. Parks and DMSP data provided by F.J. Rich.