Observation and modeling of magnetospheric cold electron heating by electromagnetic ion cyclotron waves

Authors


  • This article was corrected on 28 OCT 2014. See the end of the full text for details.

Abstract

[1] A cold electron heating event associated with electromagnetic ion cyclotron (EMIC) waves is observed and modeled. The observational data of particles and waves are collected by the Time History of Events and Macroscale Interactions during Substorms spacecraft at magnetic local time 17.0–17.2. During this event, intense He+ band EMIC waves with the peak frequency 0.25 Hz are excited, corresponding to the observed phase space density (PSD) of distinct anisotropic ions. Meanwhile, substantial enhancements in energy flux of cold (1–10 eV) electrons are observed in the same period. The energy flux of electrons below 10 eV is increased by several to tens of times. We use a sum of kappa distribution components to fit the observed ion PSD and then calculate the wave growth rate driven by the anisotropic hot protons. The calculated result is in good agreement with the in situ observation. Then, we investigate whether the excited EMIC waves can transfer energy to cold electrons by Landau resonant absorption and yield electron heating. Using the typical Maxwellian distribution for cold electrons, we evaluate the wave damping rates resulted from the cold electrons in gyroresonance with EMIC waves. The simulating results show that the strong wave growth region in the He+ band induced by anisotropic ions corresponds to the strong wave damping region driven by cold electrons. Moreover, cold electrons can be heated efficiently at large wave normal angles. The current results provide a direct observational evidence for EMIC-driven cold electron heating—a potential mechanism responsible for stable auroral red arc.

1 Introduction

[2] During geomagnetic storms, the enhancement of ionospheric electron temperature produces stable auroral red (SAR) arc [Chandra et al., 1971, 1972]. The subauroral ionospheric heating is thought to be a consequence of energy transfer from the ring current to magnetospheric electrons and the subsequent downward heat conduction into the ionosphere [Brace et al., 1967; Kozyra et al., 1986; Khazanov et al., 1992]. Simulations [Slater et al., 1987] show that low energy (<10 eV) magnetospheric electrons can heat the ionospheric electron to temperatures which produce the 6300 Å SAR arc emissions. Two potential mechanisms have been proposed to explain the process of energy transfer from the energetic ring current ions to magnetospheric cold electrons. One is Coulomb collisions of the magnetospheric electrons with the ring current H+ ions and the other is absorption of H+-generated electromagnetic ion cyclotron (EMIC) waves through Landau resonance with magnetospheric electrons.

[3] Cole [1965] suggested that electron heating and the associated SAR arcs can be attributed to Coulomb collisions with the ring current H+ions. Kozyra et al. [1987] and Fok et al. [1991] demonstrated that the O+ions, especially with energies below 20 keV, play a more important role than H+ ions in the Coulomb scattering of electrons. According to the observational analysis by Gurgiolo et al. [2005], while Coulomb collisions may account for the plasmasphcric electron heating near the magnetic equator, how the heat flux into the ionosphere remains a question.

[4] Cornwall et al. [1971] suggested electron heating by resonant Landau damping of EMIC wave. EMIC wave is an important agent for energy and momentum exchange between the particles in collisionless plasmas. They can interact with protons, electrons, and heavy ions, leading to resonant scattering of ring current protons [Summers et al., 1998; Erlandson and Ukhorskiy, 2001; Sakaguchi et al., 2008; Xiao et al., 2011, 2012] and relativistic electrons [Thorne and Kennel, 1971; Bortnik et al., 2006; Su et al., 2010, 2011; Meredith et al., 2003; Li et al., 2007; Summers et al., 2007a, 2007b; Chen et al., 2011a, 2013] and the heating of thermal heavy ions [Thorne and Horne, 1993, 1994]. A recent study [Xiao et al., 2013a] has shown that EMIC wave can scatter solar wind protons into the atmosphere, producing the cusp aurora. By using the method of ray tracing, Thorne and Horne [1992] theoretically demonstrated that the electron temperature parallel to the ambient magnetic field is increased due to the absorption of oblique EMIC wave. This provides a natural mechanism to account for transporting the energy downward into the upper ionosphere and drive stable SAR arc. Erlandson et al. [1993] reported the evidence of the energy transportation from EMIC waves to ionospheric electron. Based on a self-consistent model of magnetospheric ring current and propagating EMIC waves [Khazanov et al., 2006], Khazanov et al. [2007] examined two energy sources for the heating of the plasmaspheric thermal electrons: the EMIC wave energy absorption due to Landau resonance with thermal electrons and the Coulomb energy degradation of the ring current H+ and O+ ions. Their simulation results have demonstrated that the electron heating produced by EMIC waves has a structure of the spot-like patches, accounting for the observed small-scale structures in the SAR arcs [Kozyra et al., 1997]. However, based on our knowledge, the correlated observation and corresponding modeling of cold electron heating by EMIC waves have seldom been reported so far. In this paper, using the data from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft, we present simultaneous observations and the corresponding modeling of magnetospheric cold electron heating in association with EMIC waves.

2 Observations

[5] The THEMIS spacecraft, which consist of five identical probes in near-equatorial orbits, provide the high-quality observational data for the studies on interactions of electromagnetic waves and particles in the equatorial magnetosphere [Angelopoulos, 2008]. Energy flux data, pitch angle distribution, and phase space density for particles are collected by the electrostatic analyzer (ESA, ∼6 eV–25 keV for ions and ∼7 eV–30 keV for electrons) [McFadden et al., 2008] and the solid state telescope (SST, 25 keV–6 MeV for ions and 25 keV–1 MeV for electrons) [Angelopoulos, 2008]. The fluxgate magnetometer (FGM) [Auster et al., 2008] measures background magnetic fields and their low-frequency fluctuations (up to 64 Hz).

[6] EMIC waves are excited by the anisotropic energetic ring current protons near the magnetic equator, with the typical frequency between 0.1 and 5.0 Hz [Kennel and Petschek, 1966; Mauk and McPherron, 1980; Roux et al., 1982; Loto'aniu et al., 2005; Chen et al., 2009, 2010]. In the multi-ion (H+,He+, and O+) space plasma, EMIC waves occur in three separate frequency bands: H+ band with frequencies between math formulaand math formula, He+ band between math formulaand math formula, and O+ band below math formula. The frequencies math formula, math formula, and math formula are the gyrofrequencies of hydrogen, helium, and oxygen, respectively.

[7] Figure 1 shows the simultaneous data of ions and EMIC waves collected by the THEMIS A spacecraft between 17:40:00 UT and 17:55:00 UT on 24 June 2010. The time evolution of the omnidirectional ion energy flux as a function of ion kinetic energy observed from the ESA and SST instruments is shown in Figure 1a. The peak of energy fluxes is ∼5×106eV·cm−2·s−1·sr−1·eV−1, appearing in the range of 10–30 keV. Figures 1b–1d show the ion pitch angle spectrograms for various energy channels: 10–25 keV (ESA), 30–50 keV (SST), and 50–100 keV (SST). Pitch angle distributions are most pronounced between 70° and 110° for 10–25 keV and 60° and 130° for 30–50 keV and 50–100 keV, indicating that the highest pitch angle anisotropy occurs in the range of 10 to 25 keV. Figure 1e plots the dynamic power spectrum of EMIC wave produced by the fast Fourier transform (FFT) method. The intense He+band EMIC waves are observed from 17:40:15 UT to 17:55:00 UT, in the frequency range of 0.12–0.25math formula. The local gyrofrequencies of He+ion (solid line) are evaluated by the local magnetic field data collected from FGM.

Figure 1.

Observations by THEMIS A on 24 June 2010. (a) The omnidirectional energy-time spectrograms of ion energy fluxes from ∼6 eV to 500 keV obtained from the ESA and SST instruments. (b–d) Pitch angle distributions for 10–25 keV, 30–50 keV, and 50–100 keV ions, respectively. (e) The dynamic power spectrum of the magnetic field. The solid line represents the local gyrofrequency of ion helium.

[8] Figure 2 shows simultaneous observations of EMIC waves and the energy flux of electrons. The wave dynamic power spectrums obtained by FFT and Morlet wavelet transform methods are shown in Figures 2a and 2b. Obviously, the obtained wave spectrums from both methods are very similar. As shown in Figure 2c, the energy flux of electrons below ∼10 eV experiences a drastic increase. The flux of electrons with energies above ∼10 eV, by comparison, almost remains constant during this period. In order to get a closer look at the variation of the energy flux of cold electron, we present the measurement results of the lowest three energy channels (7.27 eV, 9.21 eV, and 12.60 eV) from ESA instrument in Figure 2d. In the period of 17:47–17:55 UT, the energy fluxes at 7.27 eV and 9.21 eV are strongly modulated by EMIC waves and are increased by several times to tens of times. However, the energy flux at 12.60 eV is essentially unchanged.

Figure 2.

Observations by THEMIS A on 24 June 2010. (a) The dynamic power spectrum of the wave magnetic field. (b) Wavelet power spectrum of the magnetic field. The solid lines represent the local gyrofrequency of ion helium. (c) Electron energy flux collected by the ESA instrument. (d) Energy fluxes of the 7.27 eV, 9.21 eV, and 12.60 eV electrons.

[9] Ion distributions measured by the ESA instrument are used to generate 2-D slices of the three-dimensional velocity distribution. Figure 3 shows the 2-D slice of the ion velocity distribution (0–2000 km/s) collected by the ESA instrument. In Figure 3, the standard B-V coordinate system is adopted, where VB is the velocity parallel along the magnetic field and VV contains the average velocity vector, perpendicular to the magnetic field. The velocity distribution is averaged over the time interval from 17:47:59 to 17:48:30 UT, just before the appearance of the intense He+ band EMIC emission between 17:49:00 and 17:49:30 UT. An obvious temperature anisotropy occurs with a higher effective thermal speed perpendicular to the ambient magnetic field. Such anisotropy distribution can provide a source of free energy for the excitation of EMIC waves [Horne and Thorne, 1994; Summers and Thorne, 2003].

Figure 3.

Observation by the ESA instrument from 17:47:59 to 17:48:30 UT. Two-dimensional phase space density (PSD) cut of the full ion distribution in the B-V plane.

3 Numerical Simulation

[10] It has been generally accepted that non-Maxwellian particles in the collisionless plasmas can be well modeled by a generalized Lorentzian (kappa) distribution [Vasyliunas, 1968; Christon et al., 1988; Xiao et al., 2008]. Previous study [Zhou et al., 2013] has investigated the excitation of EMIC waves by bi-Maxwellian and kappa distributions, respectively. The results show that the path-integrated wave gain simulated from the kappa distribution is more consistent with observations. Therefore, we fit the observed PSD of ions with a sum of kappa components. The kappa distribution function fκ(v,v) for ion species s is

display math(1)

where Ns is the number density of ion species s; v, v, θ, and θ are the velocity components and effective thermal speeds parallel and perpendicular to the ambient magnetic field, respectively; and Γ is the gamma function. The temperature anisotropy of ion species s is defined as

display math(2)

[11] By using the nonlinear least squares estimation [Marquardt, 1963; Moré, 1978], the parameters of kappa distribution function (equation (1)) are obtained from 1-D cuts of PSD along the horizontal line VV = 0 and the vertical line VB= 0 in Figure 3. Although the ESA instrument does not measure the ion composition, the presence of cold He+ and O+ cannot be neglected because they can significantly influence the instability of EMIC waves [Zhou et al., 2012]. We use four proton components to fit the observed PSD of ions and then determine the parameters of cold He+ and O+according to the parameters of cold proton. The density of cold He+ and O+ is calculated by the typical value of cold ion composition: math formula, and math formula[Jordanova et al., 2008]. The effective thermal velocities of cold math formula and math formula are assumed to be math formulaand math formula, respectively. The fitted parameters of ions are given in Table 1.

Table 1. Fitting Parameters of Ions for Observation on 24 June a
SpeciesN (cm−3)θ (m/s)θ (m/s)
  1. a

    In the kappa distribution, κ=2 functions for all species.

He+0.261.75×1041.75×104
O+0.048.75×1038.75×103
H+0.51.55×1051.55×105
H+0.41.00×1061.50×106
H+1.85.30×1066.60×106

[12] We plot the fitting curves by the kappa distribution for all species (solid lines) in Figure 4. The blue lines and the red lines represent the parallel kappa distribution fκ(v,0) and the perpendicular kappa distribution fκ(0,v), respectively. The discrete cross and plus symbols indicate the PSD data from ESA instrument. It is shown that the fitting curves are well matched with the observed data. It should be pointed out that there is a region where the gradient of distribution of protons df/dv>0. The protons with the positive df/dv, which can be modeled by a ring distribution, provide a source of free energy for magnetosonic (MS) wave excitation [Curtis and Wu, 1979; Perraut et al., 1982; Boardsen et al., 1992; Chen et al., 2011b; Xiao et al., 2013b]. We have made a rough calculation and found that the contribution of MS waves to cold electron heating is substantially small in cases of interest. Therefore, we ignore the ring distribution feature of protons in this study.

Figure 4.

The kappa distribution fitted to the observed PSD of the full ion distribution measured by the ESA instrument from 7:47:59 to 17:48:30 UT on 24 June 2010. The blue lines and the red lines represent the parallel kappa distribution and the perpendicular kappa distribution, respectively. The discrete cross and plus symbols show the observational data.

[13] The parameters of ions listed in Table 1 are used to calculate the growth rate (γ) of EMIC waves following the method of previous works [Kennel, 1966; Chen et al., 2010].

display math(3)

where Ωs and ωps are the gyrofrequency and plasma frequency of each species s; R, L, P, and S are Stix notations of the cold plasma wave; n is the wave refractive index; ω is the frequency of wave; and ψis the wave normal angle between wave vector and filed line. We set ψ= 0 in the calculation of growth rate because the wave vector is almost field aligned in the source region [Horne and Thorne, 1993, 1994]. The harmonic resonance is denoted by m; Jm is Bessel function of order m. We set the range of m from −10 to 10. We have roughly checked the wave growth rate contribution from the higher harmonic order above 10 and find that it can be negligible. Furthermore, we find that the most essential terms are m=±1 and 0. Our choice for the range of m is less correlated with the accuracy of measurements. D(0)is the determinant of the cold plasma wave dispersion relation matrix. G1s and G2s are defined as

display math(4)

and

display math(5)

where Fs is the normalized distribution function of each species s.

[14] The simulation result of wave growth rates is shown in Figure 5a. Substantial instability occurs in the He+ band math formula and peaks at math formula. This indicates that the observed He+ band EMIC waves in the frequency range of 0.12–0.25math formula(see Figures 1 and 2) are driven by the anisotropic proton. On the other hand, the wave growth rates are negative in the H+ band, suggesting that no grow rate in the H+band occurs due to the weak anisotropy of protons. This result is a good explanation for the absence of H+ band emission in the observed EMIC wave spectrum.

Figure 5.

The simulation results for (a) the local growth rates and (b) the local damping rates for different wave normal angles and (c) different electron temperatures.

[15] EMIC waves excited by the anisotropic hot proton can transfer energy to cold electron through Landau resonant absorption [Thorne and Horne, 1992; Erlandson et al., 1993]. The effect of wave normal angle (ψ) and electron temperature (Te) on the wave Landau damping rate (−γ) is explored based on equation (3). During calculation, the density of electrons Ne = 4 cm−3 is chosen to maintain charge neutrality, and the distribution of electrons is assumed to be Maxwellian because only cold (<10 eV) components are taken into account.

[16] Previous ray-tracing studies [Zhou et al., 2012] show that as EMIC waves travel toward higher latitudes, their wave normal angles increase. We present the dependence of the wave damping rate on wave normal angle in Figure 5b. The Landau damping is very weak when the wave normal angle is small (e.g., ψ = 10°). With the increase of ψ, the damping rate increases dramatically, but the peak frequency of absorption remains the same. Therefore, cold electron heating by EMIC waves might be more effective while wave normal angle becomes highly oblique. As shown in Figure 5c, the peak frequency of absorption decreases with the increasing of Te. When Te= 0.5 eV or 1 eV, the absorption peak of EMIC waves locates at math formula or math formula, respectively, near the upper frequency limit of He+band waves, and the growth rate of EMIC waves at those frequencies is weak. Consequently, the cold electron heating is weak. When Te = 5 eV or 10 eV, the absorption peak shifts to math formula or math formula, respectively, corresponding to the strong growth rate in the He+band. As a result, electrons with energy of 5 eV or 10 eV can obtain energy from EMIC waves more efficiently. Therefore, the heating of the electrons below 5 eV is a positive feedback process that becomes more efficient as Te increases [Thorne and Horne, 1992]. This may account for the immediate energy flux enhancements at 7.27 eV and 9.21 eV, although the initial temperature of the cold magnetospheric electrons is about 1 eV or below.

[17] The strong O+band emissions are quite rare in the Earth's magnetosphere [Meredith et al., 2003; Clausen et al., 2011]. Meanwhile, the interaction between cold electrons and O+ band EMIC waves are very weak. Hence, the effect of O+band waves on the cold electrons can be neglected. In the H+band, 1 eV electrons can obtain energy only from the waves with a frequency above math formula when ψ=60° (see Figure 5b). As ψ increases to 85°, the lowest frequency of the H+ band waves for heating 1 eV electrons is math formula(not shown here for brevity). However, a recent statistical study [Min et al., 2012] shows that the frequencies of H+ band waves are substantially lower than math formula, and the wave normal angle is generally less than 60°. Therefore, the cold electrons with initial temperature below 1 eV are hard to obtain energy from the H+band waves in cases of interest. Only under extreme conditions, e.g., math formula and ψ>85°, cold electrons can be possibly heated by the H+band waves. We leave this to a future study.

4 Summary

[18] We studied an event of cold electron heating associated with EMIC waves. The observational data of EMIC waves and simultaneous electron energy flux are recorded by THEMIS A spacecraft on 24 June 2010. In order to reveal the correlation between EMIC emission and cold electron heating, we simulated the instability of EMIC waves produced by anisotropic ring current protons and the wave damping driven by cold electrons. The following results are obtained:

  1. [19] A pronounced temperature anisotropy of the energetic ions (10–25 keV) is observed. Meanwhile, a strong EMIC emission occurs in the frequency range of 0.12–0.25math formulain the He+band. We fit the PSD (∼6 eV–25 keV) of anisotropic protons by the kappa distribution and then calculate the wave growth rate. Numerical results show that a distinct EMIC wave instability occurs within the frequency range between 0.12 and math formula, consistent with the observation. This illustrates that the observed EMIC waves are excited by temperature anisotropy of hot protons.

  2. [20] During the period of EMIC wave activity, the energy flux of the electrons below ∼10 eV is increased by several times to tens of times. Using the typical Maxwellian distribution for cold electrons, we calculate the wave damping rates due to the cold electron in gyroresonance with EMIC waves. The absorption peak in the He+band caused by 1–10 eV electrons lies in the same frequency range of EMIC instability, suggesting that the energy transmission from wave to electron is the reason of cold electron heating.

  3. [21] In the He+band, the peak frequency of damping decreases with the increasing of cold electron temperature (Te), shifting from math formulato math formulawhen Te increases from 0.5 eV to 10 eV. This indicates that cold electron heating is more effective in the energy range 5–10 eV and that the heating of the electrons below 5 eV is a positive feedback process.

  4. [22] The wave damping rates due to the cold electron increase dramatically with the increase of the wave normal angle, implying that the cold electron can be heated more efficiently in gyroresonance with highly oblique EMIC waves.

Acknowledgments

[23] This work is supported by 973 Program 2012CB825603, the National Natural Science Foundation of China grants 41204114, 40925014, and 41274165, the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province, and the Construct Program of the Key Discipline in Hunan Province. We acknowledge NASA contract NAS5-02099 and V. Angelopoulos for use of data from the THEMIS mission. Specifically, C.W. Carlson and J.P. McFadden for use of the ESA data, D. Larson and R.P. Lin for use of SST data, and K.H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302.

[24] Masaki Fujimoto thanks George Khazanov and an anonymous reviewer for their assistance in evaluating this paper.

Erratum

  1. In the originally published version of this article, the definition of THEMIS is incorrect in the abstract and paragraph 4.The abstract should read:The observational data of particles and waves are collected by the Time History of Events and Macroscale Interactions during Substorms spacecraft at magnetic local time 17.0–17.2.The last sentence in paragraph 4 should read:In this paper, using the data from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft, we present simultaneous observations and the corresponding modeling of magnetospheric cold electron heating in association with EMIC waves.