Characteristics of electrostatic solitary waves in the Earth's foreshock region: Geotail observations

Authors


Abstract

[1] We observed electrostatic solitary waves (ESW) in the Earth's foreshock region by the Geotail spacecraft. The foreshock region is classified into electron foreshock and ion foreshock regions, which are dominated by energetic electrons and superthermal ions, respectively. The Geotail waveform observations show the existence of ESW in both electron and ion foreshock regions. To understand the wave features of ESW, we examine the waveform and perform statistical analyses on the spatial distribution of the ESW. The results show that the occurrence and amplitude of ESW decrease as the distance from the bow shock transition increases. In the electron foreshock region, we find that ESW and electron beams are observed simultaneously. The plasma conditions are similar to those in the plasma sheet boundary layer (PSBL), in which ESW were first discovered by the Geotail spacecraft. In the ion foreshock region, ESW are simultaneously observed with superthermal ions reflected by the bow shock. We find two types of ESW in the ion foreshock region based on the orientation of their bipolar waveforms. We examine the angle between the magnetic field and the shock normal dependence of the occurrences of ESW in the ion foreshock region. The results show that ESW observed in the quasi-parallel shock have characteristics that differ from those observed in the quasi-perpendicular shock. From waveform and statistical analyses, the most plausible generation mechanism of the first type of ESW is the Buneman instability based on the superthermal ions and background electrons. A possible mechanism of the second type of ESW is the positive potential ESW propagating from the upstream region to the bow shock due to the reflection by the negative potentials or the negative potential ESW generated by the reflected superthermal ions.

1. Introduction

[2] Electrostatic solitary waves (ESW) have been observed in several regions, including the Earth's magnetotail, bow shock/solar wind, and polar magnetosphere [e.g., Matsumoto et al., 1994b, 1997; Ergun et al., 1998; Franz et al., 1998; Kojima et al., 1999a; Pickett et al., 2003]. ESW are series of impulsive and isolated bipolar pulses and are considered to be the propagating electrostatic potentials. Their electric field polarizations are parallel to the ambient magnetic field and their typical pulse widths are a few milliseconds. The ESW in the magnetotail was discovered by Matsumoto et al. [1994b] as a high-frequency part of the broadband electrostatic noise (BEN) in the plasma sheet boundary layer (PSBL). The generation of ESW in the PSBL is understood to be the result of nonlinear evolution of the electron bump-on-tail instability based on the collaboration of observations and computer simulations [Matsumoto et al., 1994b; Omura et al., 1994]. Computer simulation show the instability at the nonlinear stage reaches the very stable state called Bernstein-Greene-Kruskal (BGK) mode. In this state the isolated potentials with positive polarity flow along the ambient magnetic field in the almost same order of flow velocities with electron beam velocities of energy source. On the other hand, solitary waves in the auroral region, which are equivalent to the negative isolated potential, are also reported [Temerin et al., 1982; Boström et al., 1988; McFadden et al., 2003]. The negative potentials correlate with upward flowing energetic ions [e.g., Koskinen et al., 1987], and those spatial scales are larger than characteristics scales of electron dynamics. Mälkki et al. [1989] demonstrated that the nonlinear ion hole instability is the best candidate for the generation mechanism of the negative isolated potentials. The ion holes can be formed as the long time nonlinear evolution of ion-ion beam instabilities. This model is the counterpart of the ESW which has positive potential generated by the electron beam instability. Further, the similar solitary waves have been also observed in the bow shock transition [Matsumoto et al., 1997; Bale et al., 2002] and in the solar wind at 1 AU from the Sun [Mangeney et al., 1999]. Bale et al. [2002] argued that the bipolar pules are formed by BGK trapped particle equilibriums of electrons. Several computer simulations, which focus on electrodynamics in the bow shock, have demonstrated that the isolated positive potentials are generated by the Buneman instability [Matsumoto et al., 2005; Shimada and Hoshino, 2000] due to the interaction of the backstreaming ions and background electrons.

[3] We observed the ESW in the foreshock region. Their detailed features and generation mechanisms have not been reported. The foreshock region is the region between the tangential interplanetary magnetic field (IMF) line and the bow shock and is filled with backstreaming electrons and ions. Near the tangential interplanetary field line, superthermal electrons travel to the upstream region from the bow shock [Feldman et al., 1983]. Intense Langmuir waves are excited by these electrons. This region, which is filled with superthermal electrons, is usually regarded as the electron foreshock region. Reflected ions and diffuse ions are observed further downstream from the tangential filed line [Greenstadt et al., 1980; Paschmann et al., 1981]. These backstreaming ions excite large-amplitude electromagnetic waves by the ion-ion two stream instability. Ion acoustic-like waves can be observed, simultaneously, with the electromagnetic waves [Anderson et al., 1981; Matsumoto et al., 1997]. This region is known and is described as the ion foreshock region. Furthermore, Matsumoto et al. [1997] classified the foreshock region in more detail into the electron beam region, the electron heat flux region, and the superthermal ion region based on the behavior of superthermal electrons and ions from the Geotail observations. As mentioned above, the electron and ion foreshock regions are filled with backstreaming superthermal electrons and ions, respectively. These superthermal electrons and ions play an important role in exciting plasma waves, such as Langmuir waves and ion acoustic waves, in the upstream region of the bow shock. The present waveform and plasma observations indicate that the ESW are simultaneously observed with superthermal electrons and/or ions. We can expect that the superthermal electrons and/or ions are related to the generation of the ESW in the foreshock region.

[4] In the present paper, we present the simultaneous observation of the ESW and electron velocity distribution functions in the foreshock region. The Geotail waveform observations indicate the existence of ESW in both the electron and ion foreshock regions. In order to understand the wave features of the ESW in the foreshock region, we conducted statistical analyses based on the Geotail waveform data. In the present paper, we discuss the generation of ESW in the foreshock region based on observation results. In section 2, we describe a typical example of the ESW observed in the electron foreshock, and in section 3, we show a typical example of the ESW observed in the ion foreshock. The results of the statistical analyses are shown in section 4, and the generation models of the ESW in the foreshock region are discussed in section 5. In section 6, we summarize the present paper.

2. ESW in the Electron Foreshock

[5] In the electron foreshock region, we frequently observe ESW and superthermal electrons, simultaneously. In this section, we introduce the typical case of the ESW and electron velocity distribution with a superthermal component observed in the electron foreshock region.

[6] Figure 1a shows the dynamic spectrum of the electric component observed in the vicinity of the Earth's bow shock during the period from 0400 UT to 0600 UT on 12 July 1996. The dynamic spectrum is generated by the Sweep Frequency Analyzer (SFA) of the Plasma Wave Instruments (PWI) [Matsumoto et al., 1994a] on board the Geotail spacecraft. The white line shown in Figure 1a represent the electron cyclotron frequency. The Geotail spacecraft stays in the electron foreshock region before it crosses the bow shock at 0530 UT. Matsumoto et al. [1997] classified the electron foreshock into two different regions based on the features of superthermal electrons. The regions defined by Matsumoto et al. [1997] are shown in the top of Figure 1a as the green and yellow bars. While intense Langmuir waves near 30 kHz are the typical wave signature in the electron beam region, as shown by the green bar, the electron heat flux regions identified by plasma data are indicated by the yellow bar. The Geotail observations show that ESW is most often observed in the electron heat flux regions in the electron foreshock.

Figure 1.

(a) Dynamic spectrum and (b) waveform of the electric field component observed in the electron foreshock region on 12 July 1996, as well as (c) orbit of the Geotail spacecraft.

[7] Figure 1b shows snapshots of the (top) parallel and (bottom) perpendicular electric field waveforms with respect to the ambient magnetic field observed during the period from 0447:44.121 UT to 0447:00.202 UT on 12 July 1996. This time period is indicated by the red arrow in Figure 1a. The bipolar waveforms shown in Figure 1b are the ESW. Since they appear in the parallel electric field component, the orientation of the electric field vector is parallel to the ambient magnetic field. The pulse widths of the ESW waveforms shown in Figure 1b are approximately equal to 1 ms, and the maximum amplitude of ESW is approximately 70 μV/m. From the ESW observations in the electron foreshock region, the electric field amplitudes of the ESW are less than approximately 100 μV/m. Figure 1c shows the Geotail orbit for the period of 11 July 1996 to 13 July 1996 in the Geocentric Solar Ecliptic (GSE) Coordinate System. The Geotail location for the time period of 0447 UT on 12 July 1996 is shown as the dot in Figure 1c. Solid and dotted arrows show the directions of the ambient magnetic field (B) and solar wind ion bulk flow (VSW), respectively. The magnetic field data were acquired from the Magnetic Field Instrument (MGF) [Kokubun et al., 1994] on board Geotail.

[8] Figure 2 shows the electron velocity distribution observed by the Low Energy Particle (LEP) detectors [Mukai et al., 1994] on board Geotail. They were observed at 0447 UT and at 0426 UT on 12 July 1996, respectively. The left-hand panels show the contours of the phase space density of the electron velocity distribution function in the BE × B velocity space plane, where E and B represent the ambient electric and magnetic fields, respectively. The right-hand panels show the electron velocity distribution cut through f(v) along the ambient magnetic field. The positive velocity is referred to as the ambient magnetic field direction. The green lines show one count level of the instrument. While we observed ESW in the time period of Figure 2a (the same time period as in Figure 1b), plasma wave activities are very weak in the time period shown in Figure 2b. In Figures 2a and 2b, the strahl electrons, as superthermal components, appear in the energy range of from 10,000 km/s to 15,000 km/s in the antiparallel direction of the ambient magnetic field. Figure 2a shows the superthermal electron enhancement from 10,000 km/s to 15,000 km/s in the ambient magnetic field direction. Since the observed superthermal electron components are directed upstream, away from the bow shock, they could be the result of the acceleration in the bow shock transition.

Figure 2.

Electron velocity distribution observed (a) at 0447:12 UT and (b) at 0426:28 UT on 12 July 1996. The left-hand panel shows contours of the phase space density of the electron velocity distribution function in the BE × B velocity space plane. The right-hand panel show the electron velocity distribution cut through f(v) along the ambient magnetic field.

[9] The propagation direction of the ESW is identified from the phase of the ESW waveforms [Kojima et al., 1999b] under the assumption of the polarity of ESW potentials. When we assume the positive potential for the ESW, the propagation direction of the ESW is parallel to the ambient magnetic field from the bipolar structure of the ESW in Figure 1b. This direction is shown in Figure 1c. Therefore the propagation direction of ESW is the same as the direction of the electron heat flux shown in Figure 2. If we assume the electron hole model for the generation of the ESW, the ESW potentials quickly thermalize electron beams. Therefore the observed superthermal electrons are believed to be the result of this thermalization by the generation of the ESW.

3. ESW in the Ion Foreshock

[10] In this section, we present examples of the bipolar type waveforms observed in the ion foreshock region. Figure 3a shows the dynamic spectrum of the electric field observed during the period from 2000 UT to 2200 UT on 13 October 1997. During this time period, plasma waves which are know as the ion acoustic wave are observed in the frequency range between the electron cyclotron frequency (∼100 Hz) and the electron plasma frequency (∼20 kHz). The appearance of these waves suggests that the Geotail spacecraft remains in the ion foreshock region. Figure 3b shows the waveform of the electric field observed during the period from 2153:14.774 UT to 2153:14.892 UT on 13 October 1997. First, a monochromatic wave is excited, and its electric field intensities gradually increase in the time period of (I) in Figure 3b. Then, the monochromatic wave is modulated from 2153:14.827 UT as shown in the time period of (II). Finally, the monochromatic waves change to bipolar waveforms (by the red arrows) in the time period of (III). From the waveform observations in the ion foreshock region, bipolar waveforms are frequently observed with monochromatic waves, as shown in Figure 3. This change of the waveforms is thought to show the nonlinear evolution of excited waves. Furthermore, the peak-to-peak amplitudes of the observed ESW are approximately equal to 6 mV/m, and bipolar pulse widths are a few milliseconds. Importantly, the amplitudes of the ESW observed in the ion foreshock region are much larger than those of the ESW observed in the electron foreshock region.

Figure 3.

(a) Electric field and (b) waveforms of electrostatic solitary waves (ESW) in the ion foreshock observed on 13 October 1997.

[11] Furthermore, we simultaneously observed bipolar waveforms and superthermal ions in the ion foreshock region. Figure 4a shows the electric field dynamic spectrum observed in the ion foreshock region during the period from 2300 UT to 2400 UT on 29 July 1996. The spectra were generated from data with high temporal resolution obtained by the multichannel analyzer (MCA) receiver of the Geotail PWI [Matsumoto et al., 1994a]. The solid, dashed, and dot-dashed lines shown in Figure 4a represent electron cyclotron, ion plasma, and electron plasma frequencies. The Geotail spacecraft crosses the bow shock at 2320 UT. After 2320 UT, the Geotail spacecraft remains in the ion foreshock region. Figure 4b shows the snapshots of the electric field waveforms with respect to the ambient magnetic field observed during the period from 2336:34.714 UT to 2336:34.755 UT on 29 July 1996. The configuration of Figure 4b is the same as that of Figure 1b. Bipolar waveforms are observed in Figure 4b (by the red arrows). The observed waveforms look like unclear bipolar shapes, as compared with waveforms of the ESW observed in the electron foreshock region shown in Figure 1b. However, it is likely that observed waveforms are modulated by the nonlinear effect. Figure 5a and Figure 5b show the electron and ion velocity distributions for the same time period as those of Figure 4. The definitions of Figure 5 are the same as those of Figure 2. Figure 5a shows that the electron velocity distribution is almost isothermal. Their isothermal characteristics are different from those of the electron velocity distribution observed in the electron foreshock region. In Figure 5b, we can find reflected ion beams, which is a sign of the ion foreshock region observed at around −500 km/s in the ambient magnetic field direction. The cold ion component observed near 200 km/s in the ambient magnetic field direction corresponds to the solar wind flow. It is clear that the Geotail spacecraft remains in the ion foreshock region.

Figure 4.

(a) Electric field and (b) waveforms of ESW in the ion foreshock observed on 29 July 1996.

Figure 5.

(a) Electron and (b) ion velocity distributions in the ion foreshock at 2336:25 UT to 2336:37 UT. The definitions are the same as those of Figure 2.

[12] Since only superthermal ions are observed, it appears reasonable to assume that superthermal ions are related to the generation of ESW. Since bipolar waveforms are only observed in the parallel component in Figure 4, the ESW observed in the ion foreshock region propagate parallel to the ambient magnetic field. We can identify the propagation direction of the ESW in the ion foreshock region by applying the same method to the ESW in the electron foreshock region. We also examine the analyses of the propagation direction of the ESW based on the polarization of the bipolar waveforms. Here, in order to determine the propagation vector of the ESW, we assume that the polarity of the potential, either positive or negative. If we assume the positive potential, the ESW shown in Figure 5 are propagated upstream, away from the bow shock. This is the same propagation direction as that of the reflected ion beams shown in Figure 5b under the assumption of the positive potential. We conceive that these waveform and plasma features are a clue to understanding the generation of the ESW. The generation of the ESW is discussed later.

[13] From the waveform observations of the ESW in the ion foreshock region, ESW with opposite propagation directions were observed simultaneously in one WFC observation period (8.7 s). Figure 6a shows the electric field dynamic spectrum observed in the ion foreshock region during the period from 2000 UT to 2200 UT on 5 September 1996. Since we can observe ion acoustic waves in a wide frequency range under the frequency of the electron plasma waves, the Geotail spacecraft is located in the ion foreshock region. Figures 6b and 6c show snapshots of the electric field waveforms with respect to the ambient magnetic field. The configuration of Figures 6b and 6c are the same as those of Figure 1b. The observation periods in Figures 6b and 6c are from 2145:21.779 UT to 2145:21.809 UT on 5 September 1996 and from 2145:25.521 UT to 2145:25.562 UT, respectively. This time period is shown by the red arrow in Figure 6a. The ESW are observed in the latter part of Figure 6b (by the red arrows) and in Figure 6c. By comparing both waveforms, clearer bipolar waveforms are shown in Figure 6c. The interval between Figures 6b and 6c is only ∼4 s. Figure 6d shows the Geotail orbit for the period of 4 September 1996 to 6 September 1996. The configuration of Figure 6d is the same as that of Figure 1c. Figures 7a and 7b show the electron and ion velocity distributions in the same time period in Figure 6. The electron velocity distribution is almost isothermal in Figure 7a. Unfortunately, during this time period, the observation mode of the LEP does not cover the low energy range (<5.1 keV/Q) of ions. Superthermal ions can be observed at approximately 1000 km/s, which is a signature of the ion foreshock region.

Figure 6.

(a) Electric field and (b and c) waveforms of ESW in the ion foreshock observed on 5 September 1996, as well as (d) orbit of the Geotail spacecraft.

Figure 7.

(a) Electron and (b) ion velocity distributions observed same period as Figure 6. The definitions are the same as those of Figure 2.

[14] As shown in Figures 4 and 5, the ESW are observed to have a superthermal ion component. In the time period of Figure 7 the superthermal ion component, which is suggestive of diffuse ions, is observed. In contrast, no superthermal electron component is observed during this time period. Therefore we expect that the existence of the ESW in the ion foreshock region is related to the superthermal ion component. We also examine the analyses of the propagation of the ESW based on the polarization of bipolar waveforms. As mentioned above, in order to determine the propagation direction of the ESW, we assume an element of their potential structure. When we assume the positive potential, such as electron holes for the ESW, the propagation vectors of the ESW shown in Figure 6b and Figure 6c are identified to be parallel and antiparallel to the ambient magnetic field, respectively. In other words, the ESW shown in Figure 6b propagate to the upstream region away from the bow shock, and the ESW shown in Figure 6c propagate to the bow shock from the upstream region of the bow shock based on the assumption of positive potential for the ESW. From the results of the observations of different polarization ESW, we expect the possibilities of the different propagation or generation mechanisms of the ESW.

4. Statistical Analyses

[15] In the previous sections, we have shown the ESW observed in the electron and ion foreshock regions by waveform observations. We show that the ESW are simultaneously observed with superthermal electron and ion components in the electron and ion foreshock region, respectively. It is expected that generation mechanisms and/or generation points of each type of ESW differs in the electron and ion foreshock regions. In addition, we have shown the two types of ESW that have different polarizations in the ion foreshock region, as shown in Figure 6. Since the characteristics of the ESW observed in the foreshock region quickly change within a few seconds, as shown in Figure 6, it is not easy to compare the ESW waveforms with the electron and ion velocity distributions. In order to clarify the additional characteristics of the ESW, we investigate the spatial distributions of the ESW in the foreshock region.

[16] To classify the generation and propagation of the ESW, we need to consider the possibility of the formation of the ESW not only by the positive potential but also by the negative potential. Hereinafter, in the analyses of the ESW, we normally assume that the potential of the ESW consist of electron holes because the ESW observed in many regions, except for the polar region, are related to the electron hole generated by the bump-on-tail instability [e.g., Matsumoto et al., 1994a]. On the basis of the above assumption, we classify the ESW observed in the foreshock region into two types with the polarizations of their bipolar waveforms. The first type includes ESW that propagate to the upstream region away from the bow shock (upstream propagating ESW), and the second type includes ESW that propagate to the bow shock from the upstream region (downstream propagating ESW).

[17] In the statistical analyses, we use the WFC data observed by the Geotail spacecraft from 1 January 1995 to 31 December 1998 when the Geotail spacecraft was in near Earth orbit (<30 RE). In the present paper, we use the ESW detection method developed by Kojima et al. [1999b]. The WFC receiver captures the waveform data for 8.7 s at intervals of 5 min. Here, we defined the term “sample” as one 8.7-s observation. In order to eliminate the observation in the bow shock transition and magnetosheath region, we select the WFC data under the condition of ∣B∣ < 10 nT and the Geotail orbit. The statistical results show that 30,307 WFC samples and 127,599 ESW counts were observed.

4.1. Spatial Distribution of ESW

[18] Figure 8 shows the spatial distribution of the ESW in the upstream region of the bow shock. The X-Y plane is normalized by the foreshock coordinate system [cf. Etcheto and Faucheux, 1984; Kasaba et al., 2000]. The number of ESW are normalized by the samples which is the counts of a observational period (8.7 s) of the WFC. The tangential field line represented by the white solid line is set as 120 degrees.

Figure 8.

Spatial distribution of ESW in the upstream region of the bow shock normalized by the foreshock coordinates.

[19] At first, we show the occurrence frequencies of all ESW observed in the upstream region of the bow shock in Figure 8. It is clearly seen that occurrence frequency of the ESW downstream of the tangential field line is much higher than that in the upstream region of the tangential field line. This result shows that the ESW are observed with superthermal electrons and/or ions that are only observed in the downstream of the tangential field line. Furthermore, occurrence frequency of the ESW decreases as the distance from the bow shock increase.

[20] To distinguish the characteristics of the different polarization ESW with respect to the ambient magnetic field, we show the spatial distribution of the occurrence frequency of the ESW both upstream and downstream propagating ESW in Figure 9. The left-hand and right-hand panels of Figure 9 show the spatial distributions for the upstream and downstream propagating ESW, respectively. The downstream propagating ESW are frequently observed to be closer to the bow shock than the upstream propagating ESW. Since the upstream propagating ESW are observed farther from the bow shock than the downstream propagating ESW, it is reasonable to assume that the upstream propagating ESW propagate to the upstream region away from the bow shock. Figure 10 shows histograms of the occurrences of the ESW with respect to the distance from the bow shock along with the ambient magnetic field. Figures 10a and 10b correspond to the Figures 9a and 9b, respectively. Figure 10 shows that the upstream propagating ESW are observed farther from the bow shock than the downstream propagation ESW.

Figure 9.

The spatial distributions of (a) the ESW propagating to the upstream region and (b) the ESW propagating from the upstream region. The definitions are the same as those of Figure 8.

Figure 10.

Histograms of the occurrences of the (a) ESW propagating to the upstream region and (b) the ESW propagating from the bow shock with respect to the distance from the bow shock along to the ambient magnetic field.

4.2. Shock Normal Dependence

[21] In the previous section, we showed that ESW are observed with superthermal electrons in the electron foreshock region. On the other hand, when ESW are observed in the ion foreshock region, the electron velocity distributions are almost isothermal, as shown in Figures 5 and 7. We also show the spatial distribution of the ESW in the foreshock region. The obtained results show that the ESW are frequently observed in the ion foreshock region. Since reflected ions or diffuse ions are commonly observed in the ion foreshock region, the ESW observed in the ion foreshock region will be simultaneously observed with superthermal ions. The characteristics of the superthermal ions in the ion foreshock region depend on the shock angle. In order to clarify the relationship between the ESW and the shock angle, we examine the shock angle dependence with the occurrence frequency of the ESW.

[22] Figure 11 shows the shock angle dependence of the ESW occurrence. The occurrence frequency of the ESW gradually decrease with the increase in the shock angle. This tendency of the occurrence of the ESW is consistent with the results of the spatial distribution of the ESW shown in Figure 8. In the upstream region of the quasi-perpendicular shock, the dominant ion motion is gyration around the ambient magnetic field. On the other hand, superthermal ions in the quasi-parallel shock region propagate along the magnetic field line more easily than those in the quasi-perpendicular shock region. Therefore since the ESW are observed more frequently in the upstream region of the quasi-parallel shock, it makes sense that observations of ESW are greatly affected by the field aligned superthermal ions.

Figure 11.

Angle between the magnetic field and the shock normal dependence of the occurrences of ESW.

4.3. Electron Foreshock Region

[23] We examine the dependence of the occurrences of the ESW on the distance from the bow shock in the electron foreshock region (Figure 12). As the electron foreshock region, we selected the data sets of the ESW that propagate to the upstream region from the bow shock, and in the region of an angle of 15 degrees from the tangential field line toward the bow shock centered at the contact point. In Figure 12, solid and dashed lines show the occurrence frequencies of the upstream propagating ESW and downstream propagating ESW, respectively. The ESW are more frequently observed in the vicinity of the bow shock. The occurrences of the downstream propagating ESW decrease as the distance from the bow shock increases. Furthermore, the upstream propagating ESW are continuously observed far from the bow shock. Since the upstream propagating ESW are well observed in the distant region from the bow shock, we conceive that the ESW in the electron foreshock region are generated not only near the bow shock but also far from the bow shock. [Matsumoto et al., 1997] reported the reflected electron beam formation along the tangential field line. In this previous study, the electron beam hump in the velocity distribution was assumed to be well defined at some distance from the contact point. We believe that the results shown in Figure 12 are dependant on the formation of electron beams, and the generation of the upstream propagating ESW in the electron foreshock region depends on the state of the electron beams.

Figure 12.

Occurrence frequency of the ESW with respect to the distance from the bow shock in the electron foreshock region.

[24] We also observe the downstream propagating ESW in the electron foreshock region as shown in Figure 12. In our waveform observations, the downstream propagating ESW are mainly observed in the ion foreshock region. Further, we can not clearly separate the electron and ion foreshock region, especially in the vicinity of the bow shock, in the statistical analysis of Figure 12. Therefore we conceive that the downstream propagating ESW associate with superthermal ion components in the ion foreshock region.

5. Discussion

[25] In the electron foreshock region, the ESW are simultaneously observed with superthermal electrons, the velocity range of which range approximately from 10,000 km/s to 15,000 km/s. The observed superthermal electron components do not sufficiently form as electron beams in order to generate ESW. However, since electrons are easily thermalized by generation of the waves, it is conceivable that the electron beams existed and were thermalized by the growth of the ESW. Therefore we expect that the ESW are excited by the electron beams in the electron foreshock region.

[26] In order to clarify the generation mechanism of the ESW in the electron foreshock region, we roughly estimated the potential scale of the ESW [Omura et al., 1999; Kojima et al., 1999b]. We assume the potential structure has a Gaussian distribution ϕ(z) = ϕ0 exp(−z2/λ2), where ϕ0 is potential depth of the ESW, and z is a direction of the ambient magnetic field. Thus spatial waveform of the ESW is defined as

equation image

When z = ±λ/equation image, the electric field become maximum value ∣Emax∣. Here, we assume the spatial width LESW of the ESW as three times of peak-to-peak width Lpp of ESW waveform. Thus LESW = 3Lpp = 3equation imageλ. Therefore the potential depth ϕ0 of the ESW are derived from ∣Emax∣ and LESW of the ESW:

equation image

Further,

equation image

where Vb is the drift velocity of the electron beams and TESW is the ESW pulse width in the time domain. Several particle-in-cell simulation results show that the ESW potentials are carried by the electron beams, and the traveling velocity of the potentials of the ESW is approximately the same as the drift velocity of the electron beams [i.e., Omura et al., 1999]. Therefore in this section, we assume electron beam velocities Vb as the drift velocity of the electron beams. We roughly estimate the velocity of the ESW that are generated and carried by the electron beam as 15,000 km/s. From Figure 1, the maximum electric field intensity is ∼0.07 mV/m, and the pulse width of the ESW is ∼0.5 ms.

[27] The estimated potential depth ϕ0 is ∼0.144 eV. From this result, the estimated potential depth of the ESW is roughly a few percent of the ambient electron temperature of a few electron volts in the foreshock region. The waveform characteristics of the ESW, such as the electric field vector and the pulse width are similar to those observed in the magnetotail region. The generation mechanism of the ESW observed in the electron foreshock region is then similar to the magnetotail ESW that are generated by the bump-on-tail instability.

[28] In the ion foreshock region, the results of waveform observations and statistical analyses indicate that the ESW are simultaneously observed with superthermal ions. In the previous section, we classify ESW into two types. One type of ESW propagates upstream, away from the bow shock, when we assume that the ESW were formed by positive potentials, such as electron holes. One possible generation mechanism of the ESW is the Buneman instability, which generates positive potentials in the nonlinear stage based on superthermal ions and background electrons. In order to estimate the potential scale of the ESW, we use equation (2) in the same manner as in the estimation of the potential scale of the ESW in the electron foreshock region. Here, we assume the ESW are carried by the superthermal ions. During the time period of Figure 4, the relative velocity Vd is roughly estimated to be 1000 km/s, the electric field intensity is approximately 5 mV/m, and the pulse width of the ESW TESW is approximately 1 ms.

[29] The estimated potential depth ϕ0 is 1.37 eV. This potential depth of the ESW is larger than that observed in the electron foreshock region and is comparable in intensity to the ambient electron temperature in the foreshock region. If these large amplitude ESW are generated and carried by higher velocity beams, such as the electron beam observed in the electron foreshock region, in which the velocity is approximately 15,000 km/s, the potential depth will be approximately 10 times larger than the estimated potential depth and this assumption is not realistic. Conversely, Buneman instability can generate the large electron potential observed in the ion foreshock. Full particle computer simulation results in the upstream region of the bow shock also agree with the generation of ESW by the Buneman instability for the parallel shock [Matsumoto et al., 2005] and perpendicular shock [Shimada and Hoshino, 2000]. Thus, the most plausible generation mechanism of one type of ESW is the Buneman instability based on the superthermal ions and background electrons.

[30] Another type of ESW propagates to the bow shock from the upstream region when we assume that the ESW are formed by the positive potentials. Based on this assumption, we expect that the generation region of the ESW is in the ion foreshock region, away from the bow shock, or that the upstream propagating ESW are reflected in the upstream region of the bow shock. However, we have not yet found the source region of the ESW in the upstream region. On the other hand, the ESW formed by the electron holes are expected to be reflected by the negative potential. Parks et al. [2006] reported the Larmor size ion holes in the foreshock region observed by the Cluster spacecraft. Furthermore, since the waveforms of the downstream propagating ESW have clear bipolar shape compared to the waveforms of the upstream propagating ESW, we conceive that the downstream propagating ESW are in the latter stages of the nonlinear evolution of the ESW. Therefore we assume that for the observations of the downstream propagating ESW, time has elapsed from the excitation of the ESW, and the ESW are well propagated from the source regions. Even though we do not examine the relationship between the ESW and the ion holes, one possibility is that the ESW are propagated upstream and are reflected by the negative potential formed by the ion holes after being well propagated from the source regions.

[31] The possibility of the existence of the ESW formed by negative potentials, such as ion holes, remains. One possibility for the generation mechanism of the negative potential is the ion-ion two-stream instability based on the solar wind flow ions and reflected/diffuse ions, which are commonly observed in the ion foreshock region. In a case of negative potential ESW, the ESW propagate to the upstream region, away from the bow shock. We also estimate the potential scale of the negative potential using equation (2) in the same manner as previous one in the time period of Figure 4. Here, we assume the negative potential is created by protons and is carried by the superthermal ions. Since conditions are same as those of Buneman instability, the estimated potential depth ϕ0 is 1.37 eV. The ion-ion two-stream instability may also generate large-amplitude ESW such as those observed in the ion foreshock region formed by the ion holes. This generation model is similar to the ion hole model observed in the auroral region. However, the ion-ion two-stream instability normally forms large-scale ion holes and may collapse the ambient plasmas due to their large-scale negative potentials. Therefore generation and propagation of negative potential ESW are still of concern.

6. Summary

[32] In the present paper, we observed electrostatic solitary waves (ESW) in the Earth's foreshock region by the Geotail spacecraft. The foreshock region is separated into electron foreshock and ion foreshock regions, which are dominated by energetic electrons and superthermal ions, respectively. The Geotail waveform observations show the existence of ESW in both the electron and ion foreshock regions. In order to understand the characteristics of the ESW, we perform waveform analyses and analyses of the spatial distribution of the ESW. Observations of the ESW are related to electron beams away from the bow shock in the electron foreshock region. In the ion foreshock region, ESW are simultaneously observed with superthermal ions reflected by the bow shock. Furthermore, we found two types of ESW in the ion foreshock region based on the orientation of their bipolar waveforms. Statistical results show that the occurrences and amplitudes of ESW decrease as the distance from the bow shock transition increases. In addition, we found the angle between the magnetic field and the shock normal dependence of the occurrences of ESW in the ion foreshock region.

[33] We summarize the generation mechanisms of the ESW in the foreshock region in Figure 13. Dots of (I), (II), (III) and (IV) in Figure 13 show the observation points of the ESW shown in Figure 1, Figure 3, Figure 4, and Figure 6 in superposition to the nominal bow shock position. In the electron foreshock region, observation of the ESW is related to the electron beams propagating away from the bow shock. The potential depth is roughly a few percent of the ambient electron temperature, which is similar to the situation for the magnetotail ESW. In the ion foreshock region, different polarization ESW are observed in the vicinity of the bow shock. A plausible generation mechanism of one type of ESW (the upstream propagating ESW) is the Buneman instability based on the electrons and ions, and these ESW propagate to the upstream region away from the bow shock. A plausible generation mechanism of another type of ESW, which propagate downstream to the bow shock from the upstream region of the bow shock when we assume the positive potential for the ESW (the downstream propagating ESW), is that upstream propagating ESW are reflected in the upstream region by the negative potential. In this type of ESW, if we assume the generation of the ESW is by the ion two-stream instability, the ESW are formed by the negative potential and propagate to the upstream region. The polarizations of the waveforms of the ESW based on these two assumptions are the same features. In the present paper, the generation mechanism for the downstream propagating ESW remains ambiguous. Since it is not easy to decide either the negative or positive potential for the ESW by the Geotail waveform observations, the details of this issue will be discussed using computer experiments in the future.

Figure 13.

Schematic diagram of the generation mechanisms of the ESW in the foreshock region. Dots of (I), (II), (III) and (IV) show the observation points of the ESW shown in Figure 1, Figure 3, Figure 4, and Figure 6 in superposition to the nominal bow shock position.

Acknowledgments

[34] We would like to thank the ISAS/NASA Geotail mission project team for their support. This work was supported by JSPS KAKENHI (15204044).

[35] Amitava Bhattacharjee thanks Pierluigi Veltri and another reviewer for their assistance in evaluating this paper.

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