Cluster observations of outflowing electron distributions and broadband electrostatic emissions above the polar cap



[1] We investigate the excellent correlation between ionospheric upgoing electron beams and broadband electrostatic emissions (0–6 kHz) observed by Cluster, at ∼5 to 9 Earth's radii above the polar cap. In the absence of detailed, high time resolution waveform data in that region, we precisely analyzed several electron beams to obtain information concerning wave-particle interactions. Our results indicate that these beams are extremely variable and occasionally show multiple components. The processes involved might then occur on very short time scales, of the order of or shorter than sampling rates, typically 100 ms. We suggest that non linearities are at the origin of the spread of the frequency range of the waves simultaneously observed, as well as of the beam variability. We conclude that these electron beams are likely to destabilize Langmuir waves and, by the non-linear evolution of the electron bump-on-tail instability, could be responsible for the appearance of electrostatic solitary waves above the polar cap.

1. Introduction

[2] Electron beams outflowing from the polar ionosphere were detected for the first time by Cluster at about 5–9 Earth's radii (RE) altitude above the polar cap, during periods of northward or weak interplanetary magnetic field (IMF) [Teste et al., 2007]. Teste et al. [2007] (hereafter referred to as T07) considered the polar cap as the region of high magnetic latitude (>80°) in which the magnetic field lines are semi-open; anchored in the ionosphere on one end and spreading far in the magnetotail across the very tenuous lobe plasma on the other end. T07 showed that these outflowing electron beams are very narrow and collimated along the magnetic field B direction. They generally have low energies, typically <70 eV, and their fluxes are both very strong, comparable to typical fluxes in the auroral zone when projected at ionospheric altitudes [Carlson et al., 1998], and very variable on the time scale at which they are detected (<1 s). No magnetic fluctuations are simultaneously detected, but a good temporal correlation of the beams with broadband electrostatic (ES) emissions suggests the existence of beam-plasma interactions, with the electron beams as the most probable local source of free energy.

[3] Broadband electrostatic noise (BEN) has been observed in numerous regions of the magnetosphere [Scarf et al., 1974; Gurnett et al., 1976] as well as in the magnetosheath [Kojima et al., 1997; Pickett et al., 2008]. Waveform observations revealed that its high-frequency part consists of a series of electrostatic solitary waves (ESW), polarized along the magnetic field and crossed by the spacecraft in only a few milliseconds. Such short time scales suggest these waves are related to the dynamics of the electrons rather than to that of the ions. ESW are often observed in the plasma sheet boundary layer (PSBL) [Matsumoto et al., 1994; Kojima et al., 1994, 1999; Omura et al., 1999], in the auroral zone [Temerin et al., 1982; Boström et al., 1988; Ergun et al., 1998], at high latitudes (L-shell between 6 and 12) in the polar magnetosphere [Franz et al., 1998] and in the polar cap boundary layer [Tsurutani et al., 1998]. From a statistical study of the Cluster Wide Band Data (WBD), Pickett et al. [2004] showed that isolated ES structures in the form of bipolar or tripolar pulses are observed in all regions crossed by Cluster with amplitudes from a few hundredth up to 100 mV/m with duration from a few μs to a few ms. At a few RE above the polar cap and for B∼400 nT, the ES structures, much less numerous than for statistics in other regions, have amplitudes of 0.1 to 10 mV/m and durations of a few ms.

[4] In the present paper, we focus on electron beams outflowing from the polar cap ionosphere (magnetic latitude >80°) during periods of northward or weak IMF and on the ES wave bursts that accompany them. The purpose is to precisely analyze these beams and to examine the relationship with theories of wave-particle interactions.

2. Observations

[5] During periods of northward IMF, T07 revealed the presence of intense outflowing electron beams above the polar cap. The study however involved only the most energetic ones; those with energies well above the photoelectron energy level, as the one displayed in Figure 1a.

Figure 1.

(a) Cluster 3 spectrograms for 8 April 2003, 0108-0112 UT: (top) Field-aligned energy-time electron energy flux (PEACE) anti-parallel to B. (middle and bottom) Frequency-time E fluctuations at high (WHISPER) and low (STAFF-SA) frequencies. (b) Pitch angle representation of the electron energy flux from B (red arrow) at 0109:12 UT (white arrow on Figure 1a).

[6] Its top panel shows the electron energy flux measured, in the normal mode, by the PEACE experiment onboard Cluster 3 on 8 April 2003 in the direction anti-parallel to B. This corresponds to upflowing fluxes above the northern polar cap. This magnitude is measured within 125 ms, i.e., a full energy sweep, once a spin (4 s) [Johnstone et al., 1997]. The electron outflowing beam can be identified near 0109 UT by large fluxes between 50 and 100 eV. Both flux intensity and peak energy vary from one spin to the other. The beam is crossed in about 35 seconds, corresponding to a size of ∼140 km at 5.1 RE (for Vs/c ∼4 km/s). Figure 1b shows the distribution of the energy flux as a function of energy (radial) and pitch angle (clockwise) from B (red arrow) at 0109:12 UT. Each angular sector is 15° wide. Fluxes are weak in all directions (blue), as expected in the lobes, except in the anti-parallel one (red). Thus, the beam is well collimated along B at the measurement resolution (15°). Beams were detected by the other 3 spacecraft at different times. They were however either embedded in the photoelectrons or unidentifiable with those observed by Cluster 3.

[7] The bottom and middle panels of Figure 1a represent the simultaneous time variations of the electric field E spectral density obtained from the STAFF-SA [Cornilleau-Werhlin et al., 2003] (10 Hz; 2 kHz) and WHISPER [Décréau et al., 2001] ((2; 80) kHz) experiments. Broadband ES emissions are detected in excellent correlation with the electron beam and at variable frequencies, generally below 5 kHz, occasionally reaching 10–15 kHz. The plasma frequency fpe is ∼3.3 kHz, smaller than the gyrofrequency (∼10 kHz) in these regions. Two other ES wave bursts also appear later; before 0110 UT and near 0111 UT with weaker spectral densities and lower frequencies. They are also correlated with two minor electron beams with much weaker fluxes. The vertical bars are data gaps. No associated magnetic fluctuations were simultaneously detected.

[8] More detailed measurements on particles and waves are usually taken during the so-called “burst” mode periods during a few hours per orbit (57 h). Other high resolution information are obtained from the Wide Band Data instrument [Gurnett et al., 2001] which gives the waveform 1 h/orbit. These modes and experiment often target regions of interest such as plasma sheet, cusps, shock, boundaries, … but rarely the lobes which are not expected to be very active regions. Unfortunately, it was impossible to find any conjunctions between detailed wave observations and our data base of the most energetic outflowing beams.

[9] In the following, we focus on the first and strongest beam around 0109 UT. A careful analysis of the electron spectra, corrected relative to the spacecraft potential (∼−4.5 V), enables to separate the distribution functions (DF) of the ambient plasma at rest Fplasma and of the upflowing beam Fbeam (cf. T07). The solid line in Figure 2a represents Fplasma at 0109:12 UT, averaged over all directions except the one containing the beam (dotted curve). Fplasma total density N∼0.14/cm3 was estimated after calibration with fpe deduced from WHISPER. Fbeam, estimated by subtracting the plasma component, is displayed by the solid line in Figure 2b. It corresponds to a large bump-on-tail configuration between 10 and 200 eV. In this case, it is best fitted (dotted line) by two Maxwellians (dash-dotted lines): a large core with a mean energy E1∼52 eV and a temperature T1∼4.6 eV, and an additional weaker suprathermal tail with E2∼108 eV and T2∼1.2 eV. The beam is characterized by higher energies than the plasma but its density, computed by integration of Fbeam only present in the anti-parallel direction, is small (∼0.003/cm3) and its density ratio (beam/plasma) hardly reaches 2.0%. From statistics given by T07, these values and configuration are quite typical for electron beams outflowing from the polar cap.

Figure 2.

On 8 April 2003 at 0109:12 UT: (a) Fplasma (solid) averaged over all directions except the anti-parallel one (dashed) containing the field-aligned beam, (b) Fbeam (solid curve) fitted by Maxwellian functions (dash-dotted curves), and (c) WHAMP predictions of growth rates versus frequencies, normalized to fpe. On 20 March 2003: (d) Successive distribution functions of a measured anti-aligned electron beam versus energy.

3. Wave-Particle Interactions

[10] Such bump-on-tail distributions are known to trigger beam-plasma instabilities. To properly take into account the whole beam DF in a realistic way, we solved numerically the dispersion equation: ε(k, ω) = 0, where ε is the dielectric tensor, k the wave vector and ω the complex oscillation ω = ωr + i ωi. To do so, we used the Waves in Homogeneous Anisotropic Magnetized Plasma (WHAMP) code, developed by Rönnmark [1982], which solves the kinetic linear dispersion equation for a homogeneous and magnetized plasma, assuming that the growth rate ωi is sufficiently smaller than the real oscillation ωr. The observations of electron beams, very collimated along B, suggest that the wave vectors are also mainly aligned along this direction. We then assumed kk//, with k = 10−4λDe (the electron Debye length∼20 m) and k//∼0.08 to 0.1 λDe, where k and k// represent the perpendicular and parallel components of k. These k// values are the only ones found to give undamped solutions.

[11] We used the modelling of the observed DF described above. The determination of the perpendicular temperature T of the beam was not possible due to the narrowness of this feature. However, Figure 1b indicates T was similar to T// and not greater than ∼2 eV (by simple geometric calculation). So, we considered T ∼1 eV, i.e., comparable to those observed in the auroral zone [Carlson et al., 1998]. A test on the beam temperature anisotropy, all other parameters conserved, revealed that T has no influence on the frequency range obtained with WHAMP. The plasma and beam electron populations were neutralized by an ambient ion population at rest. We also checked that the ion characteristics did not play any role on the results (consistent with Omura et al. [1996]).

[12] Figure 2c shows the resulting growth rate versus real frequency, both normalized to fpe. The predicted wave emissions have frequencies around fpe, as expected. The instability domain Δf is small (0.88 to 1.02 fpe), with a maximum ωi at fmax∼0.96 fpe. Contrary to what could be believed from Figure 2a, the isotropic nature of the background plasma makes it more important than the field-aligned (FA) and very collimated electron beam. This explains the low values of ωi. Its magnitude in fact depends on the fitting of Fplasma. The consideration of oblique k vectors provides a slightly wider unstable mode frequency range (0.82 to 1.02 fpe), and the more oblique k, the smaller the frequency and the weaker ωi. This then justifies our assumption of parallel propagating waves.

4. Comparison With Observations

[13] PEACE, WHISPER and STAFF experiments, respectively dedicated to the detection of electrons and E fluctuations, have different time resolutions and non-coincident datasets. PEACE sweeps the whole energy range in 125 ms every 4 s while WHISPER records all emissions in a period of 200 ms every 2s and STAFF integrates its measurements on the same time period as its temporal resolution, here 1 s. However, electron beams and ES emissions are extremely well temporally correlated. They also respectively have variable fluxes and energies and a bursty nature.

[14] As seen in the previous section, the linear theory predicts for such a plasma and beam configuration the triggering of Langmuir waves close to fpe (∼3.3 kHz here). WHISPER and STAFF data, however, do not show such a peak of intensity around that frequency but rather the existence of broadband ES emissions (0 to 6 kHz) with a strong intensity at low frequency. Thus, even by taking into account the complexity of the measured DF, the linear beam-plasma instability appears to be insufficient to explain by itself the observed extension of the wave emissions to such low frequencies with such high values.

[15] Unfortunately, no waveform data nor “burst” modes with an enhanced temporal resolution in E were available for these electron beams, as usual for the most energetic beams detected above the polar cap.

5. Existence of Multi-component Beams

[16] We performed a precise analysis of our data base of outflowing electron beams detected over the polar cap. It showed the existence of more complicated distributions. Although most of the beams are composed of a Maxwellian core and a suprathermal tail, large distortions are observed. Figure 2d displays the example of beams observed on 20 March 2003 for 16 seconds after 0046 UT. It first presented a narrow core at low energy and a large tail spread over a wide energy range (red). Then, it almost disappeared (dashed red). The DF then showed two beams and an even more energetic tail (black). The following Fbeam was again extremely small (dashed green). Finally, the beam showed a wide core at intermediate energies without a tail (green). Note that nothing was observed in any other detection sector when the flux measured in the anti-aligned direction decreased (dashed lines).

[17] Thus, in addition to the variety of beam configurations, this example points out their internal strong variability over 4 s.

[18] Both variety and variability could be explained by processes faster than the measurement resolution to complete an energy sweep (125 ms). Let us assume this is the case. The detector could then miss all beams entirely or, conversely, could catch several peaks. Some of these situations could have occurred in the previous example. Consequently, the involved processes, if occurring on time scales shorter than the instrument resolution - typically 100 ms - could affect the estimate of relevant parameters (E, T, Nbeam and configuration).

6. Discussion and Conclusion

[19] At 5-9 RE above the polar cap (>80° magnetic latitude), PEACE experiment onboard Cluster detected intense electron beams outflowing from the ionosphere and very well correlated with broadband ES emissions simultaneously observed by WHISPER and STAFF instruments.

[20] T07 showed that these beams are strongly collimated along B and reach large fluxes at weak energies, typically <70 eV. They often show bump-on-tail distributions reproduced by a large Maxwellian core at a temperature of a few eV and a weaker suprathermal tail at larger energy. The numerical resolution of the linear dispersion relation with such realistic DF predicts that instabilities should develop around fpe, ∼3.3 kHz for the studied event, with the strongest growth rates. The linear growth of the beam-plasma instability, however, cannot account by itself for the whole observed broadband ES emissions (0–6 kHz) spreading up to more than fpe nor for their large intensities at low frequencies.

[21] From our detailed analysis, these outflowing beams are very variable both in flux and energy, within the same structure, from one spin to the other. They present different kinds of configurations with variable energy ranges, number, intensities and energies of their peaks, importance of the tail, etc. This could be well explained by assuming filamentary beams propagating at a time scale close to or shorter than the energy sweep of the particle instrument; 125 ms.

[22] These time scales are consistent with the statistical results on ES waves by Pickett et al. [2004]: at a few RE above the polar cap, for B∼400 nT, they reported the presence of 1–10 mV/m ES structures with durations of a few ms.

[23] A likely explanation for the presence of broadband ES emissions observed by WHISPER and STAFF simultaneously with these variable electron beams then involves non-linear effects. This is out of the scope of predictions by the linear dispersion relation but signatures of non-linear effects can be recognized, e.g., breaking of the beams into short structures or observed heating of these beams to a few eV, much larger than the ionospheric temperatures.

[24] In the literature, wave observations are interpreted as being due to the electron beams which are not shown. Here, we presented both measurements, especially particles, and showed that the FA electron beams observed above the polar caps can destabilize Langmuir waves via the bump-on-tail instability. In their simulations, Omura et al. [1996] indicated that this instability can be triggered even by a beam with a density ratio as low as 2%, as in our case. Pickett et al. [2001] showed that Langmuir waves in the cusp turbulent boundary layer can present a broad frequency range. The emissions observed here could then be broadband Langmuir waves. Alternatively, Omura et al. [1996] showed that the non-linear evolution of the bump-on-tail instability leads to the coalescence of Langmuir waves which gives rise to ESW. This coalescence is then responsible for the spread of the broadband emissions toward low frequencies. This result does not explain the presence of waves above fpe. However, these solitary waves could have been generated in a region of stronger density, and consequently stronger fpe, closer to the top of the ionosphere for instance, and carried along B by the FA electron beams (as proposed by Kojima et al. [1999] and Omura et al. [1999] in the PSBL) above the polar cap at least up to 5–9 RE where they were detected by Cluster.

[25] Unfortunately in our case, no Wide Band Data nor high time resolution E data were available for comparison and/or identification of such waves and their relationship with the correlated electron beams. In a future work, we plan to investigate the non-linear response of such filamentary structures interacting with the tenuous plasma observed above the polar cap.


[26] We thank A. N. Fazakerley and N. Cornilleau-Werhlin for providing the PEACE and STAFF data and P. Décréau for her help regarding the WHISPER data. PEACE and WHISPER data processing was supported by CNES under contract 60015.