Articles | Volume 36, issue 2
https://doi.org/10.5194/angeo-36-527-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/angeo-36-527-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Regular paper
| 
29 Mar 2018
Regular paper |
| 29 Mar 2018
| 29 Mar 2018
Three-dimensional density and compressible magnetic structure in solar wind turbulence
ESA/ESTEC SCI-S, Keplerlaan 1, 2201 AZ, Noordwijk, the Netherlands
Yasuhito Narita
Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria
C.-Philippe Escoubet
ESA/ESTEC SCI-S, Keplerlaan 1, 2201 AZ, Noordwijk, the Netherlands
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Martin Volwerk, David Mautner, Cyril Simon Wedlund, Charlotte Goetz, Ferdinand Plaschke, Tomas Karlsson, Daniel Schmid, Diana Rojas-Castillo, Owen W. Roberts, and Ali Varsani
Ann. Geophys., 39, 239–253, https://doi.org/10.5194/angeo-39-239-2021, https://doi.org/10.5194/angeo-39-239-2021, 2021
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The magnetic field in the solar wind is not constant but varies in direction and strength. One of these variations shows a strong local reduction of the magnetic field strength and is called a magnetic hole. These holes are usually an indication that there is, or has been, a temperature difference in the plasma of the solar wind, with the temperature along the magnetic field lower than perpendicular. The MMS spacecraft data have been used to study the characteristics of these holes near Earth.
Owen W. Roberts, Yasuhito Narita, and C.-Philippe Escoubet
Ann. Geophys., 36, 47–52, https://doi.org/10.5194/angeo-36-47-2018, https://doi.org/10.5194/angeo-36-47-2018, 2018
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To investigate compressible plasma turbulence in the solar wind on proton kinetic scales, a high time resolution measurement of the density is obtained from the spacecraft potential. Correlation between the magnetic field strength and the density is investigated as is the rotation sense of the magnetic field. The analysis reveals that compressible fluctuations are characteristic of kinetic Alfvén waves or a mixture of kinetic Alfvén and kinetic slow waves which counter-propagate.
O. W. Roberts, X. Li, and L. Jeska
Geosci. Instrum. Method. Data Syst., 3, 247–254, https://doi.org/10.5194/gi-3-247-2014, https://doi.org/10.5194/gi-3-247-2014, 2014
Yasuhito Narita, Daniel Schmid, and Simon Toepfer
Ann. Geophys., 42, 79–89, https://doi.org/10.5194/angeo-42-79-2024, https://doi.org/10.5194/angeo-42-79-2024, 2024
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The magnetosheath is a transition layer surrounding the planetary magnetosphere. We develop an algorithm to compute the plasma flow velocity and magnetic field for a more general shape of magnetosheath using the concept of potential field and suitable coordinate transformation. Application to the empirical Earth magnetosheath region is shown in the paper. The developed algorithm is useful when interpreting the spacecraft data or simulation of the planetary magnetosheath region.
Yasuhito Narita, Simon Toepfer, and Daniel Schmid
Ann. Geophys., 41, 87–91, https://doi.org/10.5194/angeo-41-87-2023, https://doi.org/10.5194/angeo-41-87-2023, 2023
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Magnetopause is a shielding boundary of planetary magnetic field. Many mathematical models have been proposed to describe or to reproduce the magnetopause location, but they are restricted to the real-number functions. In this work, we analytically develop a magnetopause model in the complex-number domain, which is advantageous in deforming the magnetopause shape in a conformal (angle-preserving) way, and is suited to compare different models or map one model onto another.
Daniel Schmid and Yasuhito Narita
Ann. Geophys. Discuss., https://doi.org/10.5194/angeo-2022-30, https://doi.org/10.5194/angeo-2022-30, 2023
Revised manuscript not accepted
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Here we present a useful tool to diagnose the bow shock condition around planets on basis of magnetic field observations. From the upstream and downstream shock normal angle of the magnetic field, it is possible to approximate the relation between compression ratio, Alfvenic Mach number and the solar wind plasma beta. The tool is particularly helpful to study the solar wind conditions and bow shock characteristics during the planetary flybys of the ongoing BepiColombo mission.
Simon Toepfer, Ida Oertel, Vanita Schiron, Yasuhito Narita, Karl-Heinz Glassmeier, Daniel Heyner, Patrick Kolhey, and Uwe Motschmann
Ann. Geophys., 40, 91–105, https://doi.org/10.5194/angeo-40-91-2022, https://doi.org/10.5194/angeo-40-91-2022, 2022
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Revealing the nature of Mercury’s internal magnetic field is one of the primary goals of the BepiColombo mission. Besides the parametrization of the magnetic field contributions, the application of a robust inversion method is of major importance. The present work provides an overview of the most commonly used inversion methods and shows that Capon’s method as well as the Tikhonov regularization enable a high-precision determination of Mercury’s internal magnetic field up to the fifth degree.
Yasuhito Narita
Ann. Geophys., 39, 759–768, https://doi.org/10.5194/angeo-39-759-2021, https://doi.org/10.5194/angeo-39-759-2021, 2021
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The concept of electromotive force appears in various electromagnetic applications in geophysical and astrophysical fluid studies. The electromotive force is being recognized as a useful tool to construct a more complete picture of turbulent space plasma and has the potential to test for the fundamental processes of dynamo mechanism in space.
Daniel Schmid, Yasuhito Narita, Ferdinand Plaschke, Martin Volwerk, Rumi Nakamura, and Wolfgang Baumjohann
Ann. Geophys., 39, 563–570, https://doi.org/10.5194/angeo-39-563-2021, https://doi.org/10.5194/angeo-39-563-2021, 2021
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In this work we present the first analytical magnetosheath plasma flow model for the space environment around Mercury. The proposed model is relatively simple to implement and provides the possibility to trace the flow lines inside the Hermean magnetosheath. It can help to determine the the local plasma conditions of a spacecraft in the magnetosheath exclusively on the basis of the upstream solar wind parameters.
Martin Volwerk, David Mautner, Cyril Simon Wedlund, Charlotte Goetz, Ferdinand Plaschke, Tomas Karlsson, Daniel Schmid, Diana Rojas-Castillo, Owen W. Roberts, and Ali Varsani
Ann. Geophys., 39, 239–253, https://doi.org/10.5194/angeo-39-239-2021, https://doi.org/10.5194/angeo-39-239-2021, 2021
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The magnetic field in the solar wind is not constant but varies in direction and strength. One of these variations shows a strong local reduction of the magnetic field strength and is called a magnetic hole. These holes are usually an indication that there is, or has been, a temperature difference in the plasma of the solar wind, with the temperature along the magnetic field lower than perpendicular. The MMS spacecraft data have been used to study the characteristics of these holes near Earth.
Horia Comişel, Yasuhito Narita, and Uwe Motschmann
Ann. Geophys., 39, 165–170, https://doi.org/10.5194/angeo-39-165-2021, https://doi.org/10.5194/angeo-39-165-2021, 2021
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Identification of a large-amplitude Alfvén wave decaying into a pair of
ion-acoustic and daughter Alfvén waves is one of the major goals in the
observational studies of space plasma nonlinearity.
Growth-rate maps
may serve as a useful tool for predictions of the wavevector spectrum of density
or magnetic field fluctuations in various scenarios for the
wave–wave coupling processes developing at different stages in
space plasma turbulence.
Yasuhito Narita, Ferdinand Plaschke, Werner Magnes, David Fischer, and Daniel Schmid
Geosci. Instrum. Method. Data Syst., 10, 13–24, https://doi.org/10.5194/gi-10-13-2021, https://doi.org/10.5194/gi-10-13-2021, 2021
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The systematic error of calibrated fluxgate magnetometer data is studied for a spinning spacecraft. The major error comes from the offset uncertainty when the ambient magnetic field is low, while the error represents the combination of non-orthogonality, misalignment to spacecraft reference direction, and gain when the ambient field is high. The results are useful in developing future high-precision magnetometers and an error estimate in scientific studies using magnetometer data.
Simon Toepfer, Yasuhito Narita, Daniel Heyner, Patrick Kolhey, and Uwe Motschmann
Geosci. Instrum. Method. Data Syst., 9, 471–481, https://doi.org/10.5194/gi-9-471-2020, https://doi.org/10.5194/gi-9-471-2020, 2020
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The Capon method serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. Besides the analysis of waves, the method can be used in a generalized way to compare actual measurements with theoretical models, such as Mercury's magnetic field analysis. In view to the BepiColombo mission this work establishes a mathematical basis for the application of Capon's method to analyze Mercury's internal magnetic field in a robust and manageable way.
Daniel Schmid, Ferdinand Plaschke, Yasuhito Narita, Daniel Heyner, Johannes Z. D. Mieth, Brian J. Anderson, Martin Volwerk, Ayako Matsuoka, and Wolfgang Baumjohann
Ann. Geophys., 38, 823–832, https://doi.org/10.5194/angeo-38-823-2020, https://doi.org/10.5194/angeo-38-823-2020, 2020
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Recently, the two-spacecraft mission BepiColombo was launched to explore Mercury. To measure the magnetic field precisely, in-flight calibration of the magnetometer offset is needed. Usually, the offset is evaluated from magnetic field observations in the solar wind. Since one of the spacecraft will remain within Mercury's magnetic environment, we examine an alternative calibration method. We show that this method is applicable and may be a valuable tool to determine the offset accurately.
Horia Comişel, Yasuhito Narita, and Uwe Motschmann
Ann. Geophys., 37, 835–842, https://doi.org/10.5194/angeo-37-835-2019, https://doi.org/10.5194/angeo-37-835-2019, 2019
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Here we present a scenario that the decay of a field-aligned Alfvén wave can occur simultaneously at various angles to the mean magnetic field, generating a number of second-order fluctuations or waves (after the pump wave as the first-order fluctuation). We refer to the simultaneous decay as
multi-channel couplingsfollowing the notion in scattering theory. Our goal is to study the hypothesis of the multi-channel coupling by running a three-dimensional hybrid plasma simulation.
Yasuhito Narita, Wolfgang Baumjohann, and Rudolf A. Treumann
Ann. Geophys., 37, 825–834, https://doi.org/10.5194/angeo-37-825-2019, https://doi.org/10.5194/angeo-37-825-2019, 2019
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Scaling laws and energy spectra for the electric field, magnetic field, flow velocity, and density are theoretically derived for small-scale turbulence in space plasma on which the electrons behave as a fluid but the ions more as individual particles due to the difference in the mass (the Hall effect). Our theoretical model offers an explanation for the small-scale turbulence spectra measured in near-Earth space.
Christoph Lhotka and Yasuhito Narita
Ann. Geophys., 37, 299–314, https://doi.org/10.5194/angeo-37-299-2019, https://doi.org/10.5194/angeo-37-299-2019, 2019
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The interplanetary magnetic field is a consequence of the solar magnetic field and the solar wind. Different magnetic field models exist in literature that allow us to better understand how the solar field extends throughout the solar system. We highlight different aspects of these different interplanetary magnetic field models and discuss possible applications. Verification of these models will become possible using data from the Parker Solar Probe and BepiColombo space mission.
Rudolf A. Treumann, Wolfgang Baumjohann, and Yasuhito Narita
Ann. Geophys., 37, 183–199, https://doi.org/10.5194/angeo-37-183-2019, https://doi.org/10.5194/angeo-37-183-2019, 2019
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Occasional deviations in density and magnetic power spectral densities in an intermediate frequency range are interpreted as an ion-inertial-range response to either the Kolmogorov or Iroshnikov–Kraichnan inertial-range turbulent velocity spectrum.
Ferdinand Plaschke, Hans-Ulrich Auster, David Fischer, Karl-Heinz Fornaçon, Werner Magnes, Ingo Richter, Dragos Constantinescu, and Yasuhito Narita
Geosci. Instrum. Method. Data Syst., 8, 63–76, https://doi.org/10.5194/gi-8-63-2019, https://doi.org/10.5194/gi-8-63-2019, 2019
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Raw output of spacecraft magnetometers has to be converted into meaningful units and coordinate systems before it is usable for scientific applications. This conversion is defined by 12 calibration parameters, 8 of which are more easily determined in flight if the spacecraft is spinning. We present theory and advanced algorithms to determine these eight parameters. They take into account the physical magnetometer and spacecraft behavior, making them superior to previously published algorithms.
Horia Comişel, Yasuhiro Nariyuki, Yasuhito Narita, and Uwe Motschmann
Ann. Geophys., 36, 1647–1655, https://doi.org/10.5194/angeo-36-1647-2018, https://doi.org/10.5194/angeo-36-1647-2018, 2018
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Space plasmas are assumed to be highly active and dynamic systems including waves and turbulence. Electromagnetic waves such as Alfven waves interact with one another, producing daughter waves. In our study based on three-dimensional hybrid simulations, we emphasize the role of obliquely propagating daughter waves in particle heating in low-temperature (or low-beta) plasmas. The evolutions of plasma turbulence, wave dissipation, and heating are essential problems in astrophysics.
Yasuhito Narita and Uwe Motschmann
Ann. Geophys., 36, 1537–1543, https://doi.org/10.5194/angeo-36-1537-2018, https://doi.org/10.5194/angeo-36-1537-2018, 2018
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Venus has no intrinsic magnetic field. On the other hand, we discover that an interplanetary magnetic field may nevertheless penetrate the planetary ionosphere by the diffusion process and reach the planetary surface when the solar wind condition remains for a sufficiently long time, between 12 and 54 h, depending on the condition of ionosphere.
Gurbax S. Lakhina, Bruce T. Tsurutani, George J. Morales, Annick Pouquet, Masahiro Hoshino, Juan Alejandro Valdivia, Yasuhito Narita, and Roger Grimshaw
Nonlin. Processes Geophys., 25, 477–479, https://doi.org/10.5194/npg-25-477-2018, https://doi.org/10.5194/npg-25-477-2018, 2018
Yasuhito Narita and Zoltán Vörös
Ann. Geophys., 36, 101–106, https://doi.org/10.5194/angeo-36-101-2018, https://doi.org/10.5194/angeo-36-101-2018, 2018
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Electromotive force plays a central role in the dynamo mechanism amplifying the magnetic field in turbulent plasmas and electrically conducting fluids. An algorithm is developed to measure the electromotive force using spacecraft data, and it is applied to a magnetic cloud event in interplanetary space. The electromotive force is enhanced when the magnetic cloud passes by the spacecraft, indicating local amplification of the magnetic field.
Owen W. Roberts, Yasuhito Narita, and C.-Philippe Escoubet
Ann. Geophys., 36, 47–52, https://doi.org/10.5194/angeo-36-47-2018, https://doi.org/10.5194/angeo-36-47-2018, 2018
Short summary
Short summary
To investigate compressible plasma turbulence in the solar wind on proton kinetic scales, a high time resolution measurement of the density is obtained from the spacecraft potential. Correlation between the magnetic field strength and the density is investigated as is the rotation sense of the magnetic field. The analysis reveals that compressible fluctuations are characteristic of kinetic Alfvén waves or a mixture of kinetic Alfvén and kinetic slow waves which counter-propagate.
Yasuhito Narita and Zoltán Vörös
Nonlin. Processes Geophys., 24, 673–679, https://doi.org/10.5194/npg-24-673-2017, https://doi.org/10.5194/npg-24-673-2017, 2017
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A method is proposed to determine the temporal decay rate of turbulent fluctuations, and is applied to four-point magnetic field data in interplanetary space. The measured decay, interpreted as the energy transfer rate in turbulence, is larger than the theoretical estimate from the fluid turbulence theory. The faster decay represents one of the differences in turbulent processes between fluid and plasma media.
Yasuhito Narita
Nonlin. Processes Geophys., 24, 203–214, https://doi.org/10.5194/npg-24-203-2017, https://doi.org/10.5194/npg-24-203-2017, 2017
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Various methods in the single-spacecraft data analysis are reviewed to determine physical properties of waves, turbulent fluctuations, and wave-wave and wave-particle interactions in the space plasma environment using the magnetic field, the electric field, and the plasma data.
Yasuhito Narita, Yoshihiro Nishimura, and Tohru Hada
Ann. Geophys., 35, 639–644, https://doi.org/10.5194/angeo-35-639-2017, https://doi.org/10.5194/angeo-35-639-2017, 2017
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An algorithm is proposed to estimate the spectral index of the turbulence energy spectrum directly in the wavenumber domain using multiple-sensor-array data. In contrast to the conventional method using time series data and Fourier transform of the fluctuation energy onto the frequency domain, the proposed algorithm does not require the assumption of Taylor's frozen inflow hypothesis, enabling direct comparison of the spectra in the wavenumber domain with various theoretical predictions.
Yasuhito Narita
Ann. Geophys., 35, 325–331, https://doi.org/10.5194/angeo-35-325-2017, https://doi.org/10.5194/angeo-35-325-2017, 2017
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In situ spacecraft data in space plasma are obtained often as time series data. Using Taylor's frozen-in flow hypothesis, one can interpret the time series data as spatial variations swept by the slow and passing by the spacecraft. A quantitative method for estimating the error for Taylor's hypothesis is developed here.
Martin Volwerk, Daniel Schmid, Bruce T. Tsurutani, Magda Delva, Ferdinand Plaschke, Yasuhito Narita, Tielong Zhang, and Karl-Heinz Glassmeier
Ann. Geophys., 34, 1099–1108, https://doi.org/10.5194/angeo-34-1099-2016, https://doi.org/10.5194/angeo-34-1099-2016, 2016
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The behaviour of mirror mode waves in Venus's magnetosheath is investigated for solar minimum and maximum conditions. It is shown that the total observational rate of these waves does not change much; however, the distribution over the magnetosheath is significantly different, as well as the growth and decay of the waves during these different solar activity conditions.
Horia Comişel, Yasuhiro Nariyuki, Yasuhito Narita, and Uwe Motschmann
Ann. Geophys., 34, 975–984, https://doi.org/10.5194/angeo-34-975-2016, https://doi.org/10.5194/angeo-34-975-2016, 2016
Ferdinand Plaschke and Yasuhito Narita
Ann. Geophys., 34, 759–766, https://doi.org/10.5194/angeo-34-759-2016, https://doi.org/10.5194/angeo-34-759-2016, 2016
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Spacecraft-mounted magnetic field instruments (magnetometers) need to be routinely calibrated. This involves determining the magnetometer outputs in vanishing ambient magnetic fields, the so-called offsets. We introduce and test a new method to determine these offsets with high accuracy, the mirror mode method, which is complementary to existing methods. The mirror mode method should be highly beneficial to current and future magnetic field observations near Earth, other planets, and comets.
Rudolf A. Treumann, Wolfgang Baumjohann, and Yasuhito Narita
Ann. Geophys., 34, 673–689, https://doi.org/10.5194/angeo-34-673-2016, https://doi.org/10.5194/angeo-34-673-2016, 2016
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In support of low-frequency electromagnetic turbulence we formulate the inverse scattering theory of electromagnetic fluctuations in plasma. Its solution provides the turbulent response function which contains all information of the dynamical causes of the electromagnetic fluctuations. This is of basic interest in any electromagnetic turbulence. It requires measurement of magnetic and electric fluctuations but makes no direct use of the turbulent power spectral density.
Y. Narita, H. Comişel, and U. Motschmann
Ann. Geophys., 34, 591–593, https://doi.org/10.5194/angeo-34-591-2016, https://doi.org/10.5194/angeo-34-591-2016, 2016
Y. Narita, E. Marsch, C. Perschke, K.-H. Glassmeier, U. Motschmann, and H. Comişel
Ann. Geophys., 34, 393–398, https://doi.org/10.5194/angeo-34-393-2016, https://doi.org/10.5194/angeo-34-393-2016, 2016
Y. Narita, R. Nakamura, W. Baumjohann, K.-H. Glassmeier, U. Motschmann, and H. Comişel
Ann. Geophys., 34, 85–89, https://doi.org/10.5194/angeo-34-85-2016, https://doi.org/10.5194/angeo-34-85-2016, 2016
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Four-spacecraft Cluster observations of turbulent fluctuations in the magnetic reconnection region in the geomagnetic tail show for the first time an indication of ion Bernstein waves, electromagnetic waves that propagate nearly perpendicular to the mean magnetic field and are in resonance with ions. Bernstein waves may influence current sheet dynamics in the reconnection outflow such as a bifurcation of the current sheet.
Y. Narita
Ann. Geophys., 33, 1413–1419, https://doi.org/10.5194/angeo-33-1413-2015, https://doi.org/10.5194/angeo-33-1413-2015, 2015
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A lot of efforts have been put into understanding the turbulence structure in space and astrophysical plasmas, in particular how the filamentary structure develops as the length scale of the turbulent fluctuations changes from large to smaller ones. Motivated by the recent spacecraft observations in the solar wind, an analytic model is proposed to explain the nature of filament-formation processes in space plasma turbulence with a successful test against the spacecraft observations.
C. P. Escoubet, A. Masson, H. Laakso, and M. L. Goldstein
Ann. Geophys., 33, 1221–1235, https://doi.org/10.5194/angeo-33-1221-2015, https://doi.org/10.5194/angeo-33-1221-2015, 2015
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This paper presents recent highlights from the Cluster mission on solar wind turbulence, magnetopause asymmetries and magnetosheath density enhancements, dipolarisation currents, reconnection variability, FTE in greatest detail, plasmaspheric wind and re-filling of the plasmasphere, radiation belts, updates of magnetospheric electric and magnetic field models, and magnetosheath and magnetopause properties under low Mach number. Public access to all high-resolution data (CSA) is also presented.
H. Comişel, Y. Narita, and U. Motschmann
Ann. Geophys., 33, 345–350, https://doi.org/10.5194/angeo-33-345-2015, https://doi.org/10.5194/angeo-33-345-2015, 2015
O. W. Roberts, X. Li, and L. Jeska
Geosci. Instrum. Method. Data Syst., 3, 247–254, https://doi.org/10.5194/gi-3-247-2014, https://doi.org/10.5194/gi-3-247-2014, 2014
H. Comişel, Y. Narita, and U. Motschmann
Nonlin. Processes Geophys., 21, 1075–1083, https://doi.org/10.5194/npg-21-1075-2014, https://doi.org/10.5194/npg-21-1075-2014, 2014
D. Schmid, M. Volwerk, F. Plaschke, Z. Vörös, T. L. Zhang, W. Baumjohann, and Y. Narita
Ann. Geophys., 32, 651–657, https://doi.org/10.5194/angeo-32-651-2014, https://doi.org/10.5194/angeo-32-651-2014, 2014
M. Wilczek, H. Xu, and Y. Narita
Nonlin. Processes Geophys., 21, 645–649, https://doi.org/10.5194/npg-21-645-2014, https://doi.org/10.5194/npg-21-645-2014, 2014
Y. Narita
Nonlin. Processes Geophys., 21, 41–47, https://doi.org/10.5194/npg-21-41-2014, https://doi.org/10.5194/npg-21-41-2014, 2014
C. Perschke, Y. Narita, S. P. Gary, U. Motschmann, and K.-H. Glassmeier
Ann. Geophys., 31, 1949–1955, https://doi.org/10.5194/angeo-31-1949-2013, https://doi.org/10.5194/angeo-31-1949-2013, 2013
Y. Narita, R. Nakamura, and W. Baumjohann
Ann. Geophys., 31, 1605–1610, https://doi.org/10.5194/angeo-31-1605-2013, https://doi.org/10.5194/angeo-31-1605-2013, 2013
C. P. Escoubet, M. G. G. T. Taylor, A. Masson, H. Laakso, J. Volpp, M. Hapgood, and M. L. Goldstein
Ann. Geophys., 31, 1045–1059, https://doi.org/10.5194/angeo-31-1045-2013, https://doi.org/10.5194/angeo-31-1045-2013, 2013
C. P. Escoubet, J. Berchem, K. J. Trattner, F. Pitout, R. Richard, M. G. G. T. Taylor, J. Soucek, B. Grison, H. Laakso, A. Masson, M. Dunlop, I. Dandouras, H. Reme, A. Fazakerley, and P. Daly
Ann. Geophys., 31, 713–723, https://doi.org/10.5194/angeo-31-713-2013, https://doi.org/10.5194/angeo-31-713-2013, 2013
Short summary
In this study we use multi-point spacecraft measurements of magnetic field and electron density derived from spacecraft potential to investigate the three-dimensional structure of solar wind plasma turbulence. We see that there is a dependence on the plasma beta (ratio of thermal to magnetic pressure) as well as a dependence on the type of wind i.e. fast or slow.
In this study we use multi-point spacecraft measurements of magnetic field and electron density...
