3. S. Y. Huang. 1. , F. Sahraoui. 2. , X. H. Deng. 1,3. , J. S. He. 4. , Z. G. Yuan ... found that clear spectral breaks exist near the electron scale, which separate two.
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Kinetic Turbulence in the Terrestrial Magnetosheath: Cluster
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Observations
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S. Y. Huang1, F. Sahraoui2, X. H. Deng1,3, J. S. He4, Z. G. Yuan1, M. Zhou3, Y. Pang3,
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H. S. Fu5
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1
School of Electronic and Information, Wuhan University, Wuhan, China.
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Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique-UPMC, Palaiseau, France
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3
Institute of Space Science and Technology, Nanchang University, Nanchang, China
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School of Earth and Space Sciences, Peking University, Beijing, China.
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5
Space Science Institute, School of Astronautics, Beihang University, Beijing, China.
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Abstract
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We present a first statistical study of subproton and electron scales turbulence in the
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terrestrial magnetosheath using the Cluster Search Coil Magnetometer (SCM)
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waveforms of the STAFF instrument measured in the frequency range [1,180] Hz. It is
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found that clear spectral breaks exist near the electron scale, which separate two
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power-law like frequency bands referred to as the dispersive and the electron
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dissipation ranges. The frequencies of the breaks fb are shown to be well correlated
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with the electron gyroscale ρe rather than with the electron inertial length de. The
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distribution of the slopes below fb was found to be narrow and peaks near -2.9, while
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that of the slopes above fb was found broader, peaks near -5.2 and has values as low as
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-7.5. This is the first time that such steep power-law spectra are reported in space
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plasma turbulence. These observations provide strong constraints on theoretical
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modeling of kinetic turbulence and dissipation in collisionless magnetized plasmas.
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Introduction
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Turbulence is ubiquitous in astrophysical plasmas such as accretion disks, the
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interstellar medium, the near-Earth space [1-4], and laboratory plasmas such as those
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of fusion devices [5]. Turbulence plays a fundamental role in mass transport, energy
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dissipation and particle acceleration or heating, in particular at kinetic scales [6].
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Therefore, it is crucial to determine the properties of kinetic turbulence (e.g. scaling
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law, anisotropy) experimentally, which should help to better understand the actual
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processes of energy dissipation (e.g., wave-particle interactions, coherent structures).
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In the solar wind (SW), turbulence has been studied for decades in particular at
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MHD scales (L>>ρi~100km, the ion gyroradius) using data from different spacecraft
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(e.g., Voyager, Wind, Helios). In recent years the interest of the space community has
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shifted toward kinetic scales, i.e., subproton and electron scales, where key processes
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such as energy dissipation and particles heating occur [7-13]. Parallel to these
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observational work to determine the properties of turbulence at kinetic scales, large
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theoretical and numerical efforts have been done to tackle this challenging problem
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[6,14-19]. Despite all those efforts, several aspects of kinetic scale turbulence remain
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very controversial such as: i) the nature of the plasma modes that carry the turbulence
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cascade: Kinetic Alfvén Wave (KAW) [6,9,12-14] or whistler and/or other type of
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turbulence [16-20]; ii) the nature of the dissipative processes: resonant wave-particle
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interactions [13,14], coherent-like dissipation –e.g., magnetic reconnection [21-23]; iii)
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the actual scaling of the magnetic energy spectra, exponential [26] or power-law
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[12,13].
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From the observational view point, the main obstacle that prevents one from fully
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addressing the previous controversies is the difficulty to measure the low amplitude
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electric and magnetic fluctuations in the SW at electron scales, because of the limited
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sensitivity of the current wave instruments [24,25]. Despite this limitation a few
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statistical studies have been conducted recently focusing on data intervals where the
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magnetic fluctuations have a high Signal-to-Noise-Ratio (SNR) [25,26]. In a ten years
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survey of the Cluster SCM burst mode waveforms in the SW, Sahraoui et al. [25]
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reported that spectral breaks occur near the Taylor-shifter electron gyroscale fρe
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followed by steeper power-law spectra. The distribution of the slopes below fρe was
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found narrow and peaked around -2.8, while that of the slopes above fρe was broader
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and peaked near -4. The break model used in Alexandrova et al. [26] yield similar
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results for 30% of the analyzed spectra, while the rest of the spectra were shown to be
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better fit with a curved (exponential) model (see discussion in [25]).
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Here we propose to analyze another collisionless magnetized space plasma that is
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the terrestrial magnetosheath, i.e. part of the SW downstream of the bow shock. We
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take advantage of the high SNR available in the magnetosheath to overcome the
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limitation discussed above and to probe into the electron scales. In comparison with
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SW turbulence, magnetosheath turbulence is poorly known and only a handful of
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studies have been carried out in recent years [e.g. 3,27-34]. Two main similarities with
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SW turbulence emerged from those studies: i) A strong anisotropy (k//10. However, as we increase the threshold on the SNR we
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observe a decreasing correlation: C~0.19 and C~0.1 for SNR>20 and SNR>25,
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respectively. We can see furthermore that slopes20, which were extremely rare in the SW [25]. From the above observations
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one may conclude that SNR higher than 20 are needed in the SW to fully address the
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scaling on the magnetic energy spectra at electron scales. This result sets up an
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instrumental requirement that the future space mission dedicated to SW turbulence
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need to fulfill. We note that we also investigated the possible dependence of the
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scaling on the plasma parameters, such as ion βe, and found no significant low
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correlation (not shown here).
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Above we used the Taylor assumption to link the observed breaks in frequency
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with the spatial scales of ions and electrons, similarly to what has been used in
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previous magnetosheath [30] and SW studies [12,25,6]. While this assumption is
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generally valid at MHD scales (where MA=Vsw/VA>>1, the Alfvén Mach number) it
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may fail at electron scales (both in the W of magnetosheath) if high frequency or
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dispersive modes are present (e.g. whistlers). Sahraoui et al. [17] have proposed a
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simple test based on estimating the ratio between the break frequencies of electron to
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ion (formula 15 therein). This test was performed on the present data (not shown here)
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and showed that most of the intervals used here reasonably fulfill the Taylor
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assumption even at electron scales. A complete study of this problem is being
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published elsewhere [Huang et al., 2014].
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Conclusions
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Strong controversies exist about the scaling and the nature of the turbulence at
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electron scales in the SW. Due the low amplitude fluctuations of the electric and the
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magnetic fields in the SW, the current sensitivity of the instruments do not allow one
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to fully address electron scale turbulence, and thus to remove part of the existing
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controversies. Magnetosheath turbulence presents another alternative to explore
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electron scale turbulence in collisionless magnetized plasmas. The statistical results
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shown above confirm the presence of the spectral breaks near the electron gyroscale
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ρe, followed by steep power-law like spectra with slopes as high as -7.5. This suggests
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that ρe plays the role of the dissipation scale, as previously found in SW turbulence.
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The steepest spectra reported here have not been predicted so far by any existing
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theoretical or numerical studies. The present results provide strong observational
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constraints on the current theoretical efforts to understand the problem of energy
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cascade and dissipation in collisionless magnetized plasmas. Some important
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questions, such as the nature of the plasma modes involved in the cascade at electron
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scales and the degree of anisotropy of the turbulence, will be investigated in future
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studies.
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Acknowledge
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The data used in this work come from the ESA/Cluster Active Archive (CAA) and
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AMDA (IRAP, France). This research was supported by the National Natural Science
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Foundation of China (NSFC) under grants 40890163, 41174147 and 41004060. F.
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Sahraoui acknowledges support from the THESOW project funded by ANR (Agence
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Nationale de la Recherche).
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Reference
178
[1] C. Y. Tu, & E. Marsch, Space Sci. Rev., 73, 1 (1995).
179
[2] R. Bruno & V. Carbone, Living Rev. Solar Phys. 2, 4 (2005).
180
[3] F. Sahraoui et al., Phys. Rev. Lett. 96, 075002 (2006).
181
[4] S. Y. Huang et al., Geophys. Res. Lett., 39, L11104 (2012).
182
[5] S. J. Zweben, et al., Phys. Rev. Lett., 42, 1720 (1979).
183
[6] A. A. Schekochihin, et al., Astrophys. J. Suppl. Ser., 182, 310 (2009).
184
[8] C. H. K. Chen, et al., Phys. Rev. Lett., 104, 255002 (2010).
185
[9] C. H. K. Chen, et al., Phys. Rev. Lett., 110, 225002 (2013).
186
[10] K. H. Kiyani, et al., Phys. Rev. Lett., 103, 075006 (2009).
187
[11] K. H. Kiyani, et al., Astrophys. J., 763, 10 (2013).
188
[12] F. Sahraoui et al., Phys. Rev. Lett., 102, 231102 (2009).
189
[13] F. Sahraoui, et al., Phys. Rev. Lett., 105, 131101 (2010a).
190
[14] G. G. Howes, et al., Phys. Rev. Lett., 107, 035004 (2011).
191
[15] E. Camporeale, & Burgess., D., Astrophys. J., 730, 114 (2011).
192
[16] S. P. Gary et al., Astrophys. J., 755, 142 (2012).
193
[17] F. Sahraoui, et al., Astrophys. J., 748, 100, (2012).
194
[18] S. Boldyrev, et al., Astrophys. J. Lett, 758, L44. (2012).
195
[19] R. Meyrand, & S. Galtier, Phys. Rev. Lett., 109, 194501 (2012)
196
[20] J. J. Podesta, 2012. J. Geophys. Res., 117, 7101 (2012).
197
[21] D. Sundkvist, et al., Phys. Rev. Lett., 99, 025004 (2007).
198
[22] K. T. Osman, et al., Phys. Rev. Lett., 108, 261102 (2012).
199
[23] S. Perri, et al., Phys. Rev. Lett., 109, 191101 (2012).
200
[24] F. Sahraoui, et al., Plant. Space Science, 59, 585 (2010b).
201
[25] F. Sahraoui, et al., Astrophys. J., 777,15 (2013).
202
[26] O. Alexandrova, et al., Astrophys. J., 760, 121 (2012).
203
[27] F. Sahraoui, et al., J. Geophys. Res.,108, 1335 (2003).
204
[28] F. Sahraoui, et al., Ann. Geophys., 22, 2283 (2004).
205
[29] C. Lacombe, et al., Ann. Geophys., 24, 3523-3531(2006).
206
[30] A. Mangeney, et al., Ann. Geophys., 24, 3507 (2006).
207
[31] O. Alexandrova, et al., Ann. Geophys., 26, 3585 (2008).
208
[32] E. Yordanova, et al., Phys. Rev. Lett., 100, 205003 (2008).
209
[33] J. S. He, et al., J. Geophys. Res., 116, A06207 (2011).
210
[34] F. Sahraoui, Phys. Rev. E, 78, 026402 (2008).
211
[35] N. Cornilleau-Wehrlin et al., Ann. Geophys., 21, 437 (2003)
212
[36] Y. Narita, et al., Phys. Rev. Lett., 104, 171101 (2010).
213
[37] A. Balogh, et al., Ann. Geophys., 19, 1207 (2001).
214
[38] G. Gustafsson, et al., Ann. Geophys., 19, 1219– 1240 (2001).
215
[39] H. Rème, et al., Ann. Geophys., 19, 1303, (2001).
216 217
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Fig.1. SNR of total magnetic energy spectra at 30 Hz in the terrestrial magnetosheath
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turbulence.
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Fig. 2. Typical example of the studied Magnetosheath data: (a) electron spectrogram;
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(b) plasma flow velocity; (c) magnitude of the magnetic field; (d) ion density
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Fig. 3. The histograms of the mean plasma parameters for the magnetosheath
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observations: (a) electron plasma βe; (b) ion gyrofrequency; (c) plasma flow speed; (d)
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the ratio of ion and electron temperatures.
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Fig.4. Examples of analyzed magnetic spectra. The red dashed curve is the in-flight
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sensitivity of STAFF SCM instrument. The vertical black and green lines are the
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Taylor-shifted frequencies of electron gyroradius scale and electron inertial length.
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The horizontal red and cyan lines are the compensated spectra showing the quality of
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the power-law fits.
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Fig. 5. Correlations of the frequencies of the spectral breaks with (a) the
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Taylor-shifted electron gyroradius and (b) electron inertial length scale. Linear fits
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with corresponding functions are shown by blue dashed lines. Histograms of the
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spectral indices above (c) and below (d) the electron spectral breaks.
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Fig. 6. Correlation between the SNR and the slopes of the spectra above the spectral
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break fbe for the events having SNR>10 (a), SNR>20 (b) and SNR>25 (c).
