Implication of kinetic Alfvén waves to magnetic field turbulence spectra: Earth’s magnetosheath

  • N. K. DwivediEmail author
  • S. Kumar
  • P. Kovacs
  • E. Yordanova
  • M. Echim
  • R. P. Sharma
  • M. L. Khodachenko
  • Y. Sasunov
Original Article


In the present paper, we investigate the power-law behaviour of the magnetic field spectra in the Earth’s magnetosheath region using Cluster spacecraft data under solar minimum condition. The power spectral density of the magnetic field data and spectral slopes at various frequencies are analysed. Propagation angle, \(\theta_{kB}\), and compressibility, \(R_{\|}\), are used to test the nature of turbulent fluctuations. The magnetic field spectra have the spectral slopes, \(\alpha\), between −1.5 to 0 down to spatial scales of \(20\rho_{i}\) (where \(\rho_{i}\) is ion gyroradius), and show clear evidence of a transition to steeper spectra for small scales with a second power-law, having \(\alpha\) between −2.6 to −1.8. At low frequencies, \(f_{sc} <0.3 f_{ci}\) (where \(f_{ci}\) is ion gyro-frequency), \(\theta_{kB}\sim 90^{ \circ} \) to the mean magnetic field, \(B_{0}\), and \(R_{\|}\) shows a broad distribution, \(0.1 \le R_{\|} \le 0.9\). On the other hand at \(f_{sc} >10 f_{ci}\), \(\theta_{kB}\) exhibits a broad range, \(30^{ \circ} \le \theta_{kB} \le 90^{ \circ} \), while \(R_{\|}\) has a small variation: \(0.2 \le R_{\|} \le 0.5\). We conjecture that at high frequencies, the perpendicularly propagating Alfvén waves could partly explain the statistical analysis of spectra. To support our prediction of kinetic Alfvén wave dominated spectral slope behaviour at high frequency, we also present a theoretical model and simulate the magnetic field turbulence spectra due to nonlinear evolution of kinetic Alfvén waves. The present study also shows the analogy between the observational and simulated spectra.


Turbulence Magnetic field spectra Spectral slope Kinetic Alfvén wave Nonlinearity 



The authors would like to thank the entire members of Cluster fluxgate magnetometer team, and Cluster Science Archive for providing the data used in the present work. The magnetosheath data set was compiled in the frame of the STORM project (grant agreement No. 313038). The Austrian Science Foundation (FWF) (Project I2939-N27), Austrian Agency for International Cooperation in Education and Research Project No. IN 05/2018, and Austrian Academy of Sciences have supported this work. MLK acknowledges the support from the project S11606-N16 and partial support by the Ministry of Education and Science of Russian Federation (Grant No. RFMEFI61617X0084). RPS thanks DST and ISRO for the support.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • N. K. Dwivedi
    • 1
    Email author
  • S. Kumar
    • 2
    • 3
  • P. Kovacs
    • 4
  • E. Yordanova
    • 5
  • M. Echim
    • 6
  • R. P. Sharma
    • 7
  • M. L. Khodachenko
    • 1
    • 8
    • 9
  • Y. Sasunov
    • 1
    • 8
  1. 1.Space Research InstituteAustrian Academy of SciencesGrazAustria
  2. 2.School of Space ResearchKyung Hee UniversityYonginKorea
  3. 3.Shandong Provincial Key Laboratory of Optical Astronomy and Solar-terrestrial Environment, Institute of Space ScienceShandong UniversityWeihaiChina
  4. 4.Mining and Geological Survey of HungaryBudapestHungary
  5. 5.Swedish Institute of Space PhysicsUppsalaSweden
  6. 6.Institut Royale d’Aeronomie Spatiale de BelgiqueBrusselsBelgium
  7. 7.Centre for Energy StudiesIndian Institute of Technology DelhiDelhiIndia
  8. 8.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia
  9. 9.Institute of AstronomyRussian Academy of ScienceMoscowRussia

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