Solar Physics

, Volume 288, Issue 1, pp 355–368 | Cite as

Modification of Proton Velocity Distributions by Alfvénic Turbulence in the Solar Wind

  • V. Pierrard
  • Y. Voitenko


In the present paper, the proton velocity distribution function (VDF) in the solar wind is determined by numerically solving the kinetic evolution equation. We compare the results obtained when considering the effects of external forces and Coulomb collisions with those obtained by adding effects of Alfvén wave turbulence. We use Fokker–Planck diffusion terms to calculate the Alfvénic turbulence, which take into account observed turbulence spectra and kinetic effects of the finite proton gyroradius. Assuming a displaced Maxwellian for the proton VDF at the simulation boundary at 14 solar radii, we show that the turbulence leads to a fast (within several solar radii) development of the anti-sunward tail in the proton VDF. Our results provide a natural explanation for the nonthermal tails in the proton VDFs, which are often observed in-situ in the solar wind beyond 0.3 AU.


Solar wind Space plasmas Turbulence Waves 



The research leading to these results has received funding from the Belgian Federal Science Policy in the framework of the program Interuniversitary Attraction Pole for the project P7/08 CHARM and from the European Commission’s FP7 Program for the STORM (313038) and SWIFF projects (263340, We thank the referee for his/her useful suggestions.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Solar-Terrestrial Centre of Excellence, Space PhysicsBelgian Institute for Space AeronomyBrusselsBelgium
  2. 2.Georges Lemaître Centre for Earth and Climate Research (TECLIM)Université Catholique de LouvainLouvain-la-NeuveBelgium

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