Mapping HF waves in the reconnection diffusion region


Corresponding author: H. Viberg, Swedish Institute of Space Physics, Uppsala, Sweden. (


[1] We study in detail high-frequency (HF) plasma waves between the electron cyclotron and plasma frequencies within a reconnection diffusion region (DR) encountered by Cluster in the magnetotail using continuous electric field waveforms. We identify three wave types, all observed within the separatrix regions: Langmuir waves (LW), electrostatic solitary waves (ESWs), and electron cyclotron waves (ECWs). This is the first time the ECWs have been observed inside this region. Direct comparison between waveforms and electron distributions are made at the timescale of one energy sweep of the electron detector (125 ms). Based on the wave and electron distribution characteristics, we find that the separatrix region has a stratified spatial structure. The outer part of the region is dominated by LW emissions related to suprathermal electron beams propagating away from the X-line. Furthest in, nearest to the current sheet, we observe ESWs associated with counterstreaming electron populations. Studying HF waveforms allows for a precise mapping of kinetic boundaries in the reconnection region and helps to improve our understanding of the electron dynamics in the DR.

1 Introduction

[2] Waves play an important role in the reconnection process [Vaivads et al., 2006; Fujimoto et al., 2011]. Scattering of particles by plasma waves can support anomalous resistivity, which is needed for merging of field lines in collisionless plasmas. Wave generation leads to relaxation of steep gradients in plasma parameters and strong currents, and thus observation of a particular wave mode provides insight into details of the particle distribution functions generating the wave, which can be otherwise difficult to resolve using particle instruments.

[3] Various types of HF waves have been observed in situ in relation to reconnection. Electrostatic solitary waves (ESWs) were observed in the reconnection regions in the magnetotail [Deng et al., 2004; Cattell et al., 2005; Khotyaintsev et al., 2010] and at the magnetopause [Retinò et al., 2006]. Langmuir waves (LWs) have been observed in the reconnection regions in the magnetotail [Farrell et al., 2002], at the magnetopause [Vaivads et al., 2004], and in the exterior cusp [Khotyaintsev et al., 2004]. Vaivads et al. [ 2006] speculated that electron cyclotron waves (ECWs) can also be generated in the reconnection regions by transverse electron temperature anisotropies or loss cone distributions; however, no observations of such waves have been reported. HF waves are generated by unstable electron distributions and thus provide detailed information about the electron-scale dynamics. As fields can be sampled at much higher cadences than the particle distributions, the wave observations can potentially provide the highest possible resolution diagnostics of the electron-scale processes in the reconnection regions. However, this requires detailed understanding of the relation between the different types of waves and electron distributions produced throughout the reconnection region, and, despite numerous reports of HF waves, such a relation is still only partially established.

[4] In this letter, we present detailed in situ observations of electrostatic HF waves and related electron distributions inside the reconnection diffusion region (DR). We map observations of different wave types to different parts within this region and discuss possible generation mechanisms.

2 Observations

[5] We present an observation of a reconnection DR encountered by four Cluster spacecraft (S/C) at [ − 19,2.1,0.7]RE (GSM) on 10 September 2001, during southward interplanetary magnetic field (IMF). We use data from C1, C3, and C4. Magnetic field data are acquired using the fluxgate magnetometer (FGM) instrument [Balogh et al., 1997]. For ion and electron data, we use the Cluster Ion Spectrometry (CIS) [Reme et al., 1997] and plasma electron and current experiment (PEACE) [Johnstone et al., 1997] instruments, respectively. The HF waveforms are measured by the cluster wide band data (WBD) [Gurnett et al., 1997] instrument. For the entire event, the WBD instrument continuously samples the electric field waveform at 27.4 kHz, covering the electron plasma frequency, fpe 10 kHz.

[6] Figure 1 shows an overview of a DR crossing observed by C4. This interval has been identified as a reconnection DR by Eastwood et al. [2010]. The reconnecting component of B, Bx, is positive throughout the event (Figure 1a), except for a short interval between 08:01:30 UT and 08:03:00 UT, consistent with the S/C being located north of the current sheet (CS) most of the time. A reversal of ion flow from tailward to earthward (vx in Figure 1b) is observed between 07:56:10 UT and 07:57:45 UT, which can be interpreted as a reconnection X-line passing the S/C in the tailward direction. Consistent with this, during the flow reversal the component of B normal to the CS (Bz in Figure 1a) changes sign from southward to northward. Simultaneously, the component along the current direction, By, changes from − 10 nT to +10 nT, consistent with a crossing of the Hall quadrupole field structure north of the CS [see, e.g., Vaivads et al., 2004].

Figure 1.

Overview of the DR encounter by Cluster 4, on 10 September 2001. (a) Magnetic field from FGM, (b) ion velocities (CIS), (c) ion spectrogram (CIS), (d) electron spectrogram (PEACE), (e and f) electron anisotropy (PEACE), and (g) wave spectrum with sampling frequency 27.4 kHz (WBD). The electron plasma frequency (fpe, computed from the electron density measured by PEACE) and electron cyclotron frequency (fce, computed from FGM data) are plotted in Figure 1g as solid black lines. The colored dots at the bottom of Figure 1g indicate the times when ECW (blue), ESW (red), and LWs (black) are detected.

[7] Cluster encounters several regions with different plasma characteristics within the DR. The exhaust (ion outflow, labeled “O”) regions are characterized by | vx | > 100 km/s (Figure 1b) and Bx < 10 nT. There we observe the plasma sheet (Te ∼ 1 keV) plasma with flat-top electron distributions [Asano et al., 2008]. At the flow reversal, an inflow region is observed (labeled “I”). It is characterized by vz of several tens of kilometers per second in the negative z-direction (inflow of plasma into the CS), near-zero vx, and large Bx. The inflow is populated with the cold lobe plasma (Te ∼ 100 eV); the electron distributions are mostly anisotropic, with parallel pressure exceeding the perpendicular one, similar to observations at the magnetopause [Egedal et al., 2011]. Between the outflow and inflow regions are the separatrix regions (SR) [Khotyaintsev et al., 2006; Lindstedt et al., 2009], labeled “S.” The SR are populated with a mix of plasma sheet and lobe plasmas; the electron distributions are anisotropic. To characterize the anisotropy, we introduce anisotropy factor α: α = 1 − (PSDa / PSDp) for PSDp < PSDa, and α = (PSDp / PSDa) − 1 for PSDp > PSDa, where PSDp and PSDa denote the electron phase space densities in the parallel and antiparallel to B directions, respectively. So that for α > 0(α < 0), the parallel to B electron flux is higher (lower) than the antiparallel. We plot α for two energy bands: 70–400 eV (lobe, Figure 1e) and 400–1000 eV (plasma sheet, Figure 1f). The largest anisotropy is localized in the SR close to the flow reversal and that α has opposite signs for the high- and low-energy bands consistent with low (high)-energy electrons flowing towards (away from) the X-line.

[8] Figure 1g shows an electric field spectrogram in a frequency range 0.02–13.5 kHz which contains the electron cyclotron frequency, fce, and the electron plasma frequency, fpe. Most of the wave power is concentrated in the SR with the highest amplitude waves localized within ± 3 min around the flow reversal. Figure 2a shows a detailed spectrogram for a part of the SR between 07:56:00 and 07:56:16 UT illustrating the three main types of the wave emissions observed: narrowband emissions at fce and fpe and broadband emissions. Using the fact that the angle between B and the electric field boom (EFW p12) is changing with the S/C spin, we investigate the polarization of the electric field for the different types of emissions. We find that E is primarily perpendicular to B for the narrowband emissions at fce, and parallel to B for the other two types. Therefore, we identify the three types of emissions as ECWs, LWs, and ESWs. Figures 2b– 2d show typical examples of waveforms and spectra for the three emission types, as well as the electron distributions associated with them; the presented waveforms are sampled during 125 ms-long intervals of the PEACE energy sweep. The ECWs, E ⟂  ≫ E | | , have a sharp peak at fce, 2 orders of magnitude larger than the signal below fce (Figure 2b). For the LWs, E | |  ≫ E ⟂ , the waveform has a distinct beat-like shape, and the spectrum has a sharp peak at fpe (Figure 2c). The beating could originate from nonlinear wave-wave interactions [Khotyaintsev et al., 2001], or a linear process whereby electron beams in the presence of density inhomogeneities generate several Langmuir modes at different frequencies, which mix to form the modulation [LaBelle et al., 2010]. ESWs (Figure 2d) are bipolar pulses of E | |  with a corresponding broadband spectrum [Matsumoto et al., 1994].

Figure 2.

(a) An example of a SR crossing, (b) an EC wave, (c) a LW, and (d) ESWs. The panels show (1) waveform observed simultaneously with the electron distribution (time in milliseconds after start of PEACE sweep), (2) the spectrum of the waveform, with fce and fpe marked, and (3) the electron phase space density, corrected for the S/C potential and measured at 0°, 90°, and 180°. The dashed line shows the one-count level of the instrument.

[9] We have analyzed waveforms for all 125 ms-long intervals of PEACE measurements (2 times per ∼ 4 s S/C spin) for the time intervals presented in Figure 1. To compare the waveforms and the electron distributions, we select only the cases where the waveforms show similar characteristics during the whole PEACE energy sweep. Typically one type of waveform can be observed for up to 10 s (see for example Figure 2a); however, the ECWs usually have a shorter characteristic timescale, with some of the shortest waveforms being only 50 ms long. Also, we have selected only the high-amplitude waves for which the wave power exceeds a certain amplitude threshold (different for the different wave types). This resulted in a data set of 50+ intervals of each of the three emission types for all three Cluster S/C with WBD data available. The examples presented in Figure 2 are some typical examples selected from this data set. The intervals with different emission types for C4 are marked in the bottom of Figure 1g. One can see that the LWs and ESWs are related to strongly anisotropic electron distributions detected around the flow reversal, with the LWs being related to a beam-like distribution (Figure 2c, panel 3) and ESWs to counterstreaming distributions (Figure 2d, panel 3). The electron distributions observed with ECWs do not show strong anisotropies (see for example Figure 2b, panel 3). However, the electron measurements at lower energies are strongly affected by photoelectrons emitted by the EFW probes, and we cannot exclude the possible presence of cold electron beams or shell-type distributions.

3 Discussion

[10] To put the wave observations into the reconnection context, we draw the approximate paths of C1, C3, and C4 (no WBD data on C2) together with a sketch of the reconnection DR (Figure 3b). The positions of the Cluster S/C in the GSM XZ plane are shown in Figure 3a. The S/C are first located in the tailward flow and then enter the earthward flow. C1 and C4 are north of the CS, at approximately the same distance from the center, and C3 is south of the CS and somewhat closer to the center than C1 and C4, as C3 observes the exhaust most of the time. The waves are almost exclusively localized in the SRs (initially determined from the particle data), which are encountered multiple times. Similar to magnetopause observations of Retinò et al. [ 2006], statistically the order in which the different wave types are observed suggests a spatially stratified SR:

Figure 3.

Sketch of the event, with (a) the positions of the Cluster S/C and (b) the reconnection DR, with the approximate paths of C1, C3, and C4. Wave observations are indicated by the colored dots, and the different regions within the DR (blue box) are labeled.

[11] Inflow. The electron fluxes parallel and antiparallel to B are equal, the distribution is stable, and no waves are observed. Electron pressure anisotropy is developing with approach towards the electron DR [Egedal et al., 2011].

[12] Outer SR. With the crossing of the separatrix (electron edge), the first electrons coming from the X-line arrive. These electrons will be seen as a suprathermal low density beam due to the acceleration at the X-line and the time-of-flight effect (most energetic electrons are expected closer to the inflow boundary). Such an electron distribution can be unstable to the bump-on-tail instability generating LWs [Omura et al., 1996]. This expectation is consistent with the observed LWs, which are primarily detected in the outer part of the SR (closest to the inflow). Also the electron distributions observed with the LWs show presence of a suprathermal beam. Moreover, at all the crossings of the boundary between the inflow and the SR, the LWs are the first waves detected; therefore, such waves are a signature of the separatrix (electron edge).

[13] Inner SR. Deeper inside the SR, the density of the beam electrons moving away from the X-line increases, and also the background population carrying the Hall current experiences a significant net drift towards the X-line. Such a distribution can set up two-stream and Buneman instabilities generating ESWs [Omura et al., 1994, 1996; Markidis et al., 2012; Divin et al., 2012]. We observe the ESWs deeper in the SR and in relation to counterstreaming low- and high-energy electron populations.

[14] Ion outflow. In the ion outflow regions, rather isotropic electron distributions which are stable to wave generation are expected. This is consistent with observed flat-top shaped distributions and little or no wave activity.

[15] Figure 2a shows an example of a SR crossing illustrating the proposed stratified structure of the region. In the beginning of the interval, C4 is in the inner part of the region and detects ESWs. Then it moves to the outer part with LWs, and then finally wave activity ceases, marking the crossing of the separatrix (electron edge) and transition to the inflow region. The boundary to the outflow can be nicely seen in Figure 1g at 8:01:10 and 8:01:30 UT when C4 crosses the center of the exhaust (Bx = 0) and the wave activity ceases.

[16] We present the first observations of the ECWs in the reconnection DR. The ECWs are observed at different locations in the SR, with some tendency to be farther away from the flow reversal than LWs and ESWs. Rather isotropic distributions similar to flat-top are observed together with the ECWs; however, we are unable to fully resolve the low-energy part of the electron distribution and thus cannot rule out the presence of low-energy electron beams and shell-like distributions. The observed ECWs are very bursty, with the shortest wave packets lasting only for several tens of electron gyroperiods (fce ∼ 0.5 kHz), which indicates that the instability driving the wave is rather strong. Vaivads et al. [ 2006] speculated that ECWs can be generated in the DR by, for example, unstable shell/loss cone [Sundkvist et al., 2006] or beam distributions [Menietti et al., 2002]. The ECWs can be responsible for isotropization of shell distributions (forming flat-tops) which are formed as electron beams enter regions with increasing B. Rapid increase of B is expected, for example, in the flux pileup region leading to, among others, generation of whistlers [Fujimoto and Sydora, 2008; Khotyaintsev et al., 2011], as well as at the separatrices in the vicinity of the X-line. At the moment, there is no clear picture of ECW generation in the DR, and this problem requires further investigation by simulations.

[17] We present a detailed comparison of waves and electron distribution obtained at very short periods of time compared to previous studies of HF waves in magnetotail reconnection [Farrell et al., 2002; Deng et al., 2004], and most importantly, we compare simultaneous wave and electron measurements at timescales of one energy sweep of the electron detector. A similar study of HF waveforms and sub-spin electron data has been performed by Retinò et al. [ 2006] at the magnetopause SR. For the magnetotail case presented here, the typical plasma scales are a factor of 10 larger than for the magnetopause, and also, the S/C observe the DR for a significantly longer period. These factors combined with multi-S/C observations allow us to collect a sufficiently larger data set of wave observations and draw a “statistical” picture of the distribution of the waves in the ion DR.

4 Conclusions

[18] We presented detailed multi-spacecraft observations of high-frequency (HF) electrostatic waves in a frequency range containing fce and fpe and related electron distributions in the reconnection diffusion region (DR) which is encountered by the Cluster S/C separated by several ion scales in the terrestrial magnetotail. We used the high-resolution electric field waveforms continuously sampled by WBD throughout the DR by three of the Cluster S/C.

[19] We have identified the three main types of the HF emissions in the DR as Langmuir waves (LWs), electrostatic solitary waves (ESWs), and electron cyclotron (EC) waves, which are reported for the first time. In order to study the relation of the different waveforms to electron distributions, we compare the waveforms with electron distributions measured at timescales of one energy sweep of the electron detector (125 ms), as the observed waveforms are rapidly changing on timescales of the order of seconds. As we have measurements on three Cluster S/C and the S/C spend several minutes in the DR, we are able to collect a large data set of waveforms and corresponding electron distributions.

[20] We find little or no activity in the inflow and outflow regions, and most of the wave activity is localized to the separatrix regions (SR), which are crossed multiple times by Cluster. From the multiple crossings of the separatrix region, we find that it has a spatially stratified structure. In the outer part of the region (closest to the inflow), the LWs are observed, generated by suprathermal low density electron beams propagating away from the X-line, and thus, the appearance of the first LWs when the S/C is entering the DR from the inflow is a signature of the separatrix (electron edge). In the inner part of the SR, mostly ESWs are observed together with electron distributions showing counterstreaming electron populations (low-energy towards the X-line, high-energy away from the X-line). EC waves are observed in different parts of the SR; they have the shortest timescales of the three observed wave types (down to several tens of milliseconds or several tens of electron gyroperiods), which possibly reflects fast relaxation of perpendicular electron anisotropies created in the DR. There is also a rather distinct boundary seen in waves between the SR and the central part of the exhaust, where no waves are observed.

[21] We provide new and important information concerning the properties and locations of HF waves and electron dynamics in the reconnection DR and provide a precise mapping of the kinetic boundaries. Improved particle instrumentation, such as provided by the upcoming MMS mission, would allow us to study the electron dynamics at the X-line in even greater detail.


[22] We thank the ESA Cluster Active Archive for providing the data for this study. This research is supported by the Swedish National Space Board and the Swedish Research Council under grants 2007-4377, 2009-3902, and 2009-4165. J.S.P. acknowledges support from NASA GSFC under Grant NNX11AB38G.