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2fpRadio Source in Geotail Observations and Numerical Simulations ~Microscopic View~
2fp RADIO SOURCE IN GEOTAIL OBSERVATIONS AND NUMERICAL SIMULATIONS - M I C R O S C O P I C V I E W Y.Kasaba t, H. Matsumoto 2, Y. Omura 2, and T. Mukar i TheInstitute ofSpace andAstronautical Science (ISAS), Sagamihara,Kanagawa 2 2 9 - 8 5 1 0 , Japan 2RadioScienceCenterfor Space andAtmosphere (RASC), Kyoto University, Uji,Kyoto 611-001 l,Japan
ABSTRACT We have studied several topics related to the ~ radiation generated in the terrestrial electron foreshock. Our investigation started from the macroscopic geometry d" the radio source, and is expanding to the microscopic processes. In this paper, we present a summary of latter studies, especially about the generation mechanism of electrostatic and electromagnetic 2fp waves and the electron acceleration at the quasi-perpendicular shock.
I N T R O D U C T I O N : M A C R O S C O P I C V I E W O F 2~ RADIOSOURCE "2fp radiation" is frequently observed in the terrestrial upstream region at twice the electron plasma frequency. Its source is thought at the electron foreshock. Energetic electrons are accelerated at quasi-perpendicular shocks and backstreaming along the interplanetary magnetic field (IMF) lines. These electrons generate Langrnuir waves by electron beam instability. Electromagnetic 2fp radiation is finally generated from these Langmuir waves. The geometry of this radio source has been estimated by two indirect methods. One is "direction finding analysis", statistics based on single spacecraft observation (Kasaba et al., 2000) and the triangulation by two spacecraft (Reiner et al., 1997). Another method is "frequency variation" (Kasaba et al., 1997). Associated with the fluctuation of the plasma density at the radio source, new 2fp line at twice the new plasma frequency appears and the old 2fp line vanishes. The extension of the radio source can be estimated by the timing of these variations. These results indirectly suggest that the radio source should be the electron foreshoclc Direct evidence is provided by the first global mapping of 2fp radio flux around the foreshock (Kasaba et al., 2000). Figure 1 shows that the center of 2fp flux density is superposed on the region along the IMF lines connected to the quasi-perpendicular shocks in which strong Langrnuir waves and energetic electrons are confined. The 2fp radio flux distribution also leads to two questions. One is the different diffusion rate at the region distant from the shock. The decrease rate of the Langrnuir wave and electron flux is smaller than that in 2fp radio flux. The other is weak ~ radio flux in the region near the perpendicular shock. Quasi-perpendicular shock region supplies energetic electrons to the foreshock, but the region near the shock seems not to have strongest radio emissivity. These questions are related to microscopic views. The former is concerning to the generation mechanism of the radiation. The radiation near the electron plasma frequency is common in solar and stellar radio burst, but its mechanism has not been established enough. The latter is concerning to the acceleration of electron beam. Electron acceleration at quasi-perpendicular shock is common in interplanetary and interstellar shocks. The electron foreshock provides us a natural laboratory for fundamental processes related to these phenomena. GENERATION MECHANISM Several mechanisms have been proposed for 2fp radiation [Ref: in Kasaba et al., 2001]. Strong instability (ex. Langrnuir soliton) was not supported by observations, so two weak instability models are remained, "modeconversion' and "direct-conversion'. The former is based on the conversion from electrostatic ~ wave, but its
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excitation and the conversion to electromagnetic 2fp in space plasma are not established The latter is based on the conversion from Langmuir wave. It consists of two processes: Backscattering of Langmuir wave by the interaction with ion acoustic waves, and the coupling of the backscattered and primary Langrnuir waves to the electromagnetic 2fp. However, the expected growth rate is too small to account for the production of 2fp waves in the foreshock [cf. Yoon et al., 1994]. There are two observational evidences for the radiation mechanism. First is the relation between 2fp radio flux and Langmuir wave activity. We find that 2fp radio emissivity shows nonlinear relation to the foreshock Langrnuir wave activity in the diffusion in the region distant from the shock (Figure 1) and the relation with the solar wind kinetic energy flux (Kasaba et al., 2000). It suggests that the radiation mechanism is non-linear process. However, both candidate processes are non-linear; so that this cannot distinguish two models. Another evidence is typical wave spectrum in the electron foreshock (Figure 2). At the most leading region of the foreshock, there is enhancement like electrostatic ~ and low-frequency ion acoustic wave associated with intense Langmuir wave (Lacombe et al., 1988; Kasaba et al., 2000). We do not have a confidence for the existence of electrostatic 2fp wave because the harmonic noise can be generated with the saturation by intense Langrnuir wave,~ On the other hand, low-frequency electrostatic wave seems real, because different instruments aboard GEOTAIL (PWI and EFD) get them independently. Although we are not convincing yet that this wave is ion acoustic mode, these results favor the direct conversion model associated with backscattering of Langrnuir wave. We have tried to generate 2fp waves in self-consistent PIC code simulations (Kasaba et al., 2001). Figure 3 are ?-k diagrams of ~ and B~ in one- and two-dimensional cases. Magnetic field and electron beam is along the Xaxis. In both cases, the electron beam generates intense Langmuir wave in positive wave number (L). Langrnuir wave backscattered by ion is also found in negative wave number (L'). Electrostatic ~ wave (ES-2~) appears at twice the wave number of beam-excited Langmuir wave. We find that this wave is enhanced in the early stage and independent of electromagnetic 2fp wave with slower growth rate. This result suggests that electrostatic 2fp wave is directly generated from beam-excited Langmuir waves and independent of electromagnetic 2fp radiation. On the other hand, electromagnetic ~Cpwave (EM-2fp) is only excited in two-dimensionalcase. The growth of electromagnetic ~p is slow and related to the backscattering process of Langrnuir wave. In our results, backward Langrnuir wave is correlated to the product of beam-excited Langmuir wave and ion acoustic wave (ES-LF). And electromagnetic ~p wave is correlated to the product of beam-excited and backward Langmuir waves. They are favorable to the direct conversion based on successive two processes, the back-scattering of Langmuir wave by electron-ion coupling and the wave-wave coupling between beam-excited and backscattered Langmuir waves. Generation through the strong instability by extreme Langmuir wave is not supported in our simulation. In this work, the growth rate problem is not fully resolved yet by two problems: 1) Large beam energy generates the waves about 2-3 orders stronger than the values observed in the foreshock region. 2) Insufficient number of particles in cell enhanced backscattering process. They are originated from the limitation of running time and memory size. The reality of the most delicate processes related to electrostatic 2fp wave and backscattered Langrnuir wave will be solved by future low-noise simulations (ex. electromagnetic 2-D Vlasov code). ELECTRON ACCELERATION Electron acceleration at perpendicular shock is another problem. We started the investigation of the origin of "weak 2fp radio activity" near the quasi-perpendicular shock (Figure 1). We had three ideas for this weakness: First is the evolution of electron beam in the foreshock. "Time of flight" and "electric field driW' effects generate and enhance 'bump' in the electron velocity space, and induce strong wave instability (cf. Fitzenreiter, 1995). Therefore, electron beam instability might not be induced enough in the region very close to the shock surface, if electrons initially ejected from the quasi-perpendicular shock do not have a clear bump yet. The second idea is "quadrupole directivity of ~p radiation". Quadrupole pattern is predicted in the excitation model;, supported in the simulation (Kasaba et al., 2001), and suggested in some solar burst observations (Thejappa, 2002). Quadrupole pattern is not confirmed in the terrestrial foreshock observation yet, but the weakness in the direction perpendicular to the tangential IMF line might cause observed weak flux near the shock. The third idea is the lack of accelerated electrons near perfectly perpendicular shock. The classic al electron acceleration model, "loss-cone type" electrons are produced from nearly perpendicular shock (Leroy and Mangeney, 1984). Its distribution function depends on the angle between the shock normal and magnetic field, 6113n. Near the perfectly perpendicular shock, energy per charge increases exponentially, but electron flux drastically decreases. Product of the normalized flux and energy per charge becomes maximum at 6)B, "- 86-87 ~
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Fig. 1. The distribution of the amplitude of plasma waves and the population of energetic electrons: (a) 2fp radiation; (b) Langmuir wave; (c) electrons from 1 to 3 keV. [Spatial resolution: 2x2 RE]
Fig. 2. Electric field spectrum (top) and electron population (bottom) around the electron foreshock observed by GEOTAIL on Apr. 6, 1995.
Fig. 3. ? -k diagrams of Ex and Bz in (a) oneand (b) two-dimensional cases.
Fig. 4. (left) Foreshock electric field spectrum and electron energy distribution at 5 shock crossings (Yellow arrow) observed by GEOTAIL on 5 Apr. 1995. (right)A schematic view of the electron foreshock. Red line is the region connected to quasi-perpendicular shocks with 6)B, = 80~ ~
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Therefore, energetic electrons are supplied from nearly perpendicular, but not truly perpendicular shock region. Figure 4 shows some examples of the energy distribution of foreshock electrons just after the acceleration at the shock. Left lands show electric field spectrum and electron distributions around 5 shock crossings with different Oan angles. GEOTAIL was in the upstream of the shock in 16:55-17:14, 17:27-17:36, and 17:54(-18:00). At 3 almost perfectly perpendicular shocks with Oan > 85~ (89.4~ at 16:55, 88.2~ at 17:27, and 89.6~ at 17:54), no Langrnuir and electron enhancements are found in the upstream region just in front of the bow shock With Oa, = 800--85~ (84.5~ at 17:36), narrow-band intense Langmuir wave becomes evident, and high-energy field-aligned electrons are supplied from the bow shock. When Oan is less than 80~ (76.8~ 17:14), Langrnuir wave becomes weak and wide-band. It is not shown in Figure 4, but low frequency magnetic field turbulence is also found. Right panel of Figure 4 is a schematic view of the electron foreshock derived from 46 shock crossings. In this panel, "the electron foreshock" (red area), with keV-order electrons and large amplitude Langmuir waves, is assumed in the area connected to the quasi-perpendicuhr shock region x4th r = 800"85 ~ Although the upper and lower limits of Oa~ is not quantitatively evaluated because the accuracy of OBn determination is not enough, "no-active region" in this case appears at about several Re around the perfectly perpendicular shocks. Namely, the third idea seems qualitatively enough to account for "weak 2fp radio activity" near the shock in Figure 1. If all the features of the electron acceleration are matched with the Leroy and Mangeney's model, it is the end of the electron acceleration studies at the Earth's shock. But, in the recent two-dimensional PIC simulation with curved shock (Savoini and Lembege, 2000), field-aligned component was also found in the expected loss cone distributions. It might be generated by the interaction with strong wave turbulence at the shock surface. We will do the further quantitative studies in wave and electron observations just upstream of the shock: 1) precise determination of Oan at the strongest Langrnuir wave generation, and 2) the detailed electron distribution function and wave features along the IMF lines from quasi- and perfectly perpendicular shocks.
ACKNOWLEDGMENTS We gratefully acknowledge whole GEOTAIL team for successful operations. The computer simulation was done on the KDK system at Radio Science Center for Space and Atmosphere (RASC), Kyoto University. REFERENCES
Fitzenreiter, IL J.,The electron foreshock, Adv.SpaceRes., 15, 9, 1995. Lacombe, C., C. C. Harvey, S. Hoang, A. Mangeney, J.-L. Steinberg. and D. Burgess, ISEE observations of emission at twice the solar wind plasma frequency, Ann. Geophys., 1, 113, 1988. Leroy, M. M., and A. Mangeney, A theory of energization of solar wind electrons by the Earth's bow shock, Ann. Geophys., 2, 4, 449, 1984. Kasaba, Y., H. Matsumoto, and R. R. Anderson, GEOTAIL observation of ~ emission around the terrestrial foreshock region, Adv. SpaceRes., 20, 5, 699-702, 1997. Kasaba, Y., H. Matsumoto, Y. Omura, R. R. Anderson, T. Mukai, Y. Saito, T. Yamamoto, and S. Kokubun, Statistical studies of plasma waves and backstreaming electrons in the terrestrial electron foreshock observed by Geotail,J.Geophys.Res., 105, A1, 7%103, 2000. Kasaba, Y., H. Matsumoto, and Y. Omura, One- and two-dimensional simulations of electron beam instability: Generation of electrostatic and electromagnetic 2fp waves,,/. Geophys.Res., 106, 18693-18711, 2001. Reiner, M. J., Y. Kasaba, M. L. Kaiser, H. Matsumoto, I. Nagano, and J.-L. Bougeret, 2fp radio source location determined from WIND/GEOTAIL triangulation, Geophys.Res.Lett., 24, 91%22, 1997. Savoini, P., and B. Lembege, B., Two-dimensional simulations of a curved shock: self-consistent formation of the electron foreshock, J. Geophys. Res., 106, 12975, 2001. Thejappa, G., private communication, 2002. Yoon, P. H., C.S. Wu, A. F.-Vinus, M. J. Reiner, J. Fainberg, and R. G. Stone, Theory of Roperadiation induced by the bow shock,,/. Geophys.Res., 99, 23481-23488, 1994. E-mail address ofY.Kasaba kasabat~,sto.isas.ac.jo
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ABSTRACT We have studied several topics related to the ~ radiation generated in the terrestrial electron foreshock. Our investigation started from the macroscopic geometry d" the radio source, and is expanding to the microscopic processes. In this paper, we present a summary of latter studies, especially about the generation mechanism of electrostatic and electromagnetic 2fp waves and the electron acceleration at the quasi-perpendicular shock.
I N T R O D U C T I O N : M A C R O S C O P I C V I E W O F 2~ RADIOSOURCE "2fp radiation" is frequently observed in the terrestrial upstream region at twice the electron plasma frequency. Its source is thought at the electron foreshock. Energetic electrons are accelerated at quasi-perpendicular shocks and backstreaming along the interplanetary magnetic field (IMF) lines. These electrons generate Langrnuir waves by electron beam instability. Electromagnetic 2fp radiation is finally generated from these Langmuir waves. The geometry of this radio source has been estimated by two indirect methods. One is "direction finding analysis", statistics based on single spacecraft observation (Kasaba et al., 2000) and the triangulation by two spacecraft (Reiner et al., 1997). Another method is "frequency variation" (Kasaba et al., 1997). Associated with the fluctuation of the plasma density at the radio source, new 2fp line at twice the new plasma frequency appears and the old 2fp line vanishes. The extension of the radio source can be estimated by the timing of these variations. These results indirectly suggest that the radio source should be the electron foreshoclc Direct evidence is provided by the first global mapping of 2fp radio flux around the foreshock (Kasaba et al., 2000). Figure 1 shows that the center of 2fp flux density is superposed on the region along the IMF lines connected to the quasi-perpendicular shocks in which strong Langrnuir waves and energetic electrons are confined. The 2fp radio flux distribution also leads to two questions. One is the different diffusion rate at the region distant from the shock. The decrease rate of the Langrnuir wave and electron flux is smaller than that in 2fp radio flux. The other is weak ~ radio flux in the region near the perpendicular shock. Quasi-perpendicular shock region supplies energetic electrons to the foreshock, but the region near the shock seems not to have strongest radio emissivity. These questions are related to microscopic views. The former is concerning to the generation mechanism of the radiation. The radiation near the electron plasma frequency is common in solar and stellar radio burst, but its mechanism has not been established enough. The latter is concerning to the acceleration of electron beam. Electron acceleration at quasi-perpendicular shock is common in interplanetary and interstellar shocks. The electron foreshock provides us a natural laboratory for fundamental processes related to these phenomena. GENERATION MECHANISM Several mechanisms have been proposed for 2fp radiation [Ref: in Kasaba et al., 2001]. Strong instability (ex. Langrnuir soliton) was not supported by observations, so two weak instability models are remained, "modeconversion' and "direct-conversion'. The former is based on the conversion from electrostatic ~ wave, but its
-247-
excitation and the conversion to electromagnetic 2fp in space plasma are not established The latter is based on the conversion from Langmuir wave. It consists of two processes: Backscattering of Langmuir wave by the interaction with ion acoustic waves, and the coupling of the backscattered and primary Langrnuir waves to the electromagnetic 2fp. However, the expected growth rate is too small to account for the production of 2fp waves in the foreshock [cf. Yoon et al., 1994]. There are two observational evidences for the radiation mechanism. First is the relation between 2fp radio flux and Langmuir wave activity. We find that 2fp radio emissivity shows nonlinear relation to the foreshock Langrnuir wave activity in the diffusion in the region distant from the shock (Figure 1) and the relation with the solar wind kinetic energy flux (Kasaba et al., 2000). It suggests that the radiation mechanism is non-linear process. However, both candidate processes are non-linear; so that this cannot distinguish two models. Another evidence is typical wave spectrum in the electron foreshock (Figure 2). At the most leading region of the foreshock, there is enhancement like electrostatic ~ and low-frequency ion acoustic wave associated with intense Langmuir wave (Lacombe et al., 1988; Kasaba et al., 2000). We do not have a confidence for the existence of electrostatic 2fp wave because the harmonic noise can be generated with the saturation by intense Langrnuir wave,~ On the other hand, low-frequency electrostatic wave seems real, because different instruments aboard GEOTAIL (PWI and EFD) get them independently. Although we are not convincing yet that this wave is ion acoustic mode, these results favor the direct conversion model associated with backscattering of Langrnuir wave. We have tried to generate 2fp waves in self-consistent PIC code simulations (Kasaba et al., 2001). Figure 3 are ?-k diagrams of ~ and B~ in one- and two-dimensional cases. Magnetic field and electron beam is along the Xaxis. In both cases, the electron beam generates intense Langmuir wave in positive wave number (L). Langrnuir wave backscattered by ion is also found in negative wave number (L'). Electrostatic ~ wave (ES-2~) appears at twice the wave number of beam-excited Langmuir wave. We find that this wave is enhanced in the early stage and independent of electromagnetic 2fp wave with slower growth rate. This result suggests that electrostatic 2fp wave is directly generated from beam-excited Langmuir waves and independent of electromagnetic 2fp radiation. On the other hand, electromagnetic ~Cpwave (EM-2fp) is only excited in two-dimensionalcase. The growth of electromagnetic ~p is slow and related to the backscattering process of Langrnuir wave. In our results, backward Langrnuir wave is correlated to the product of beam-excited Langmuir wave and ion acoustic wave (ES-LF). And electromagnetic ~p wave is correlated to the product of beam-excited and backward Langmuir waves. They are favorable to the direct conversion based on successive two processes, the back-scattering of Langmuir wave by electron-ion coupling and the wave-wave coupling between beam-excited and backscattered Langmuir waves. Generation through the strong instability by extreme Langmuir wave is not supported in our simulation. In this work, the growth rate problem is not fully resolved yet by two problems: 1) Large beam energy generates the waves about 2-3 orders stronger than the values observed in the foreshock region. 2) Insufficient number of particles in cell enhanced backscattering process. They are originated from the limitation of running time and memory size. The reality of the most delicate processes related to electrostatic 2fp wave and backscattered Langrnuir wave will be solved by future low-noise simulations (ex. electromagnetic 2-D Vlasov code). ELECTRON ACCELERATION Electron acceleration at perpendicular shock is another problem. We started the investigation of the origin of "weak 2fp radio activity" near the quasi-perpendicular shock (Figure 1). We had three ideas for this weakness: First is the evolution of electron beam in the foreshock. "Time of flight" and "electric field driW' effects generate and enhance 'bump' in the electron velocity space, and induce strong wave instability (cf. Fitzenreiter, 1995). Therefore, electron beam instability might not be induced enough in the region very close to the shock surface, if electrons initially ejected from the quasi-perpendicular shock do not have a clear bump yet. The second idea is "quadrupole directivity of ~p radiation". Quadrupole pattern is predicted in the excitation model;, supported in the simulation (Kasaba et al., 2001), and suggested in some solar burst observations (Thejappa, 2002). Quadrupole pattern is not confirmed in the terrestrial foreshock observation yet, but the weakness in the direction perpendicular to the tangential IMF line might cause observed weak flux near the shock. The third idea is the lack of accelerated electrons near perfectly perpendicular shock. The classic al electron acceleration model, "loss-cone type" electrons are produced from nearly perpendicular shock (Leroy and Mangeney, 1984). Its distribution function depends on the angle between the shock normal and magnetic field, 6113n. Near the perfectly perpendicular shock, energy per charge increases exponentially, but electron flux drastically decreases. Product of the normalized flux and energy per charge becomes maximum at 6)B, "- 86-87 ~
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Fig. 1. The distribution of the amplitude of plasma waves and the population of energetic electrons: (a) 2fp radiation; (b) Langmuir wave; (c) electrons from 1 to 3 keV. [Spatial resolution: 2x2 RE]
Fig. 2. Electric field spectrum (top) and electron population (bottom) around the electron foreshock observed by GEOTAIL on Apr. 6, 1995.
Fig. 3. ? -k diagrams of Ex and Bz in (a) oneand (b) two-dimensional cases.
Fig. 4. (left) Foreshock electric field spectrum and electron energy distribution at 5 shock crossings (Yellow arrow) observed by GEOTAIL on 5 Apr. 1995. (right)A schematic view of the electron foreshock. Red line is the region connected to quasi-perpendicular shocks with 6)B, = 80~ ~
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Therefore, energetic electrons are supplied from nearly perpendicular, but not truly perpendicular shock region. Figure 4 shows some examples of the energy distribution of foreshock electrons just after the acceleration at the shock. Left lands show electric field spectrum and electron distributions around 5 shock crossings with different Oan angles. GEOTAIL was in the upstream of the shock in 16:55-17:14, 17:27-17:36, and 17:54(-18:00). At 3 almost perfectly perpendicular shocks with Oan > 85~ (89.4~ at 16:55, 88.2~ at 17:27, and 89.6~ at 17:54), no Langrnuir and electron enhancements are found in the upstream region just in front of the bow shock With Oa, = 800--85~ (84.5~ at 17:36), narrow-band intense Langmuir wave becomes evident, and high-energy field-aligned electrons are supplied from the bow shock. When Oan is less than 80~ (76.8~ 17:14), Langrnuir wave becomes weak and wide-band. It is not shown in Figure 4, but low frequency magnetic field turbulence is also found. Right panel of Figure 4 is a schematic view of the electron foreshock derived from 46 shock crossings. In this panel, "the electron foreshock" (red area), with keV-order electrons and large amplitude Langmuir waves, is assumed in the area connected to the quasi-perpendicuhr shock region x4th r = 800"85 ~ Although the upper and lower limits of Oa~ is not quantitatively evaluated because the accuracy of OBn determination is not enough, "no-active region" in this case appears at about several Re around the perfectly perpendicular shocks. Namely, the third idea seems qualitatively enough to account for "weak 2fp radio activity" near the shock in Figure 1. If all the features of the electron acceleration are matched with the Leroy and Mangeney's model, it is the end of the electron acceleration studies at the Earth's shock. But, in the recent two-dimensional PIC simulation with curved shock (Savoini and Lembege, 2000), field-aligned component was also found in the expected loss cone distributions. It might be generated by the interaction with strong wave turbulence at the shock surface. We will do the further quantitative studies in wave and electron observations just upstream of the shock: 1) precise determination of Oan at the strongest Langrnuir wave generation, and 2) the detailed electron distribution function and wave features along the IMF lines from quasi- and perfectly perpendicular shocks.
ACKNOWLEDGMENTS We gratefully acknowledge whole GEOTAIL team for successful operations. The computer simulation was done on the KDK system at Radio Science Center for Space and Atmosphere (RASC), Kyoto University. REFERENCES
Fitzenreiter, IL J.,The electron foreshock, Adv.SpaceRes., 15, 9, 1995. Lacombe, C., C. C. Harvey, S. Hoang, A. Mangeney, J.-L. Steinberg. and D. Burgess, ISEE observations of emission at twice the solar wind plasma frequency, Ann. Geophys., 1, 113, 1988. Leroy, M. M., and A. Mangeney, A theory of energization of solar wind electrons by the Earth's bow shock, Ann. Geophys., 2, 4, 449, 1984. Kasaba, Y., H. Matsumoto, and R. R. Anderson, GEOTAIL observation of ~ emission around the terrestrial foreshock region, Adv. SpaceRes., 20, 5, 699-702, 1997. Kasaba, Y., H. Matsumoto, Y. Omura, R. R. Anderson, T. Mukai, Y. Saito, T. Yamamoto, and S. Kokubun, Statistical studies of plasma waves and backstreaming electrons in the terrestrial electron foreshock observed by Geotail,J.Geophys.Res., 105, A1, 7%103, 2000. Kasaba, Y., H. Matsumoto, and Y. Omura, One- and two-dimensional simulations of electron beam instability: Generation of electrostatic and electromagnetic 2fp waves,,/. Geophys.Res., 106, 18693-18711, 2001. Reiner, M. J., Y. Kasaba, M. L. Kaiser, H. Matsumoto, I. Nagano, and J.-L. Bougeret, 2fp radio source location determined from WIND/GEOTAIL triangulation, Geophys.Res.Lett., 24, 91%22, 1997. Savoini, P., and B. Lembege, B., Two-dimensional simulations of a curved shock: self-consistent formation of the electron foreshock, J. Geophys. Res., 106, 12975, 2001. Thejappa, G., private communication, 2002. Yoon, P. H., C.S. Wu, A. F.-Vinus, M. J. Reiner, J. Fainberg, and R. G. Stone, Theory of Roperadiation induced by the bow shock,,/. Geophys.Res., 99, 23481-23488, 1994. E-mail address ofY.Kasaba kasabat~,sto.isas.ac.jo
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