Solar Physics

, 294:51 | Cite as

Nonlinear Evolution of Ion Kinetic Instabilities in the Solar Wind

  • Leon OfmanEmail author
Part of the following topical collections:
  1. Solar Wind at the Dawn of the Parker Solar Probe and Solar Orbiter Era


In-situ observations of the solar wind (SW) plasma from 0.29 to 1 AU show that the protons and \(\alpha \) particles are often non-Maxwellian, with evidence of kinetic instabilities, temperature anisotropies, differential ion streaming, and associated magnetic fluctuations spectra. The kinetic instabilities in the SW multi-ion plasma can lead to preferential heating of \(\alpha \) particles and the dissipation of magnetic fluctuation energy, affecting the kinetic and global properties of the SW. Using for the first time a three-dimensional hybrid model, where ions are modeled as particles using the Particle-In-Cell (PIC) method and electrons are treated as fluid, we study the onset, nonlinear evolution and dissipation of ion kinetic instabilities. The Alfvén/ion cyclotron, and the ion drift instabilities are modeled in the region close to the Sun (\(\sim 10R_{s}\)). Solar wind expansion is incorporated in the model. The model produces self-consistent non-Maxwellian velocity distribution functions (VDFs) of unstable ion populations, the associated temperature anisotropies, and wave spectra for several typical SW instability cases in the nonlinear growth and saturation stage of the instabilities. The 3D hybrid modeling of the multi-ion SW plasma could be used to study the SW acceleration region close to the Sun, which will be explored by the Parker Solar Probe mission.


Solar wind, theory: numerical modeling Instabilities Waves, plasma 



The author acknowledges support by NASA cooperative agreement NNG11PL10A 670.154 to the Catholic University of America. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center.

Disclosure of Potential Conflicts of Interest

The author declares he has no conflicts of interest.


  1. Bale, S.D., Kasper, J.C., Howes, G.G., Quataert, E., Salem, C., Sundkvist, D.: 2009, Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211101. DOI. ADSCrossRefGoogle Scholar
  2. Borovsky, J.E.: 2016, The plasma structure of coronal hole solar wind: Origins and evolution. J. Geophys. Res. 121, 5055. DOI. ADS. CrossRefGoogle Scholar
  3. Borovsky, J.E., Gary, S.P.: 2014, How important are the alpha-proton relative drift and the electron heat flux for the proton heating of the solar wind in the inner heliosphere? J. Geophys. Res. 119, 5210. DOI. ADS. CrossRefGoogle Scholar
  4. Bourouaine, S., Marsch, E., Neubauer, F.M.: 2011a, On the relative speed and temperature ratio of solar wind alpha particles and protons: Collisions versus wave effects. Astrophys. J. 728, L3. DOI. ADS. ADSCrossRefGoogle Scholar
  5. Bourouaine, S., Marsch, E., Neubauer, F.M.: 2011b, Temperature anisotropy and differential streaming of solar wind ions. Correlations with transverse fluctuations. Astron. Astrophys. 536, A39. DOI. ADS. ADSCrossRefGoogle Scholar
  6. Bourouaine, S., Alexandrova, O., Marsch, E., Maksimovic, M.: 2012, On spectral breaks in the power spectra of magnetic fluctuations in fast solar wind between 0.3 and 0.9 AU. Astrophys. J. 749, 102. DOI. ADS. ADSCrossRefGoogle Scholar
  7. Bourouaine, S., Verscharen, D., Chandran, B.D.G., Maruca, B.A., Kasper, J.C.: 2013, Limits on alpha particle temperature anisotropy and differential flow from kinetic instabilities: Solar wind observations. Astrophys. J. Lett. 777, L3. DOI. ADS. ADSCrossRefGoogle Scholar
  8. Bruno, R., Carbone, V.: 2013, The solar wind as a turbulence laboratory. Living Rev. Solar Phys. 10, 2. DOI. ADS. ADSCrossRefGoogle Scholar
  9. Davidson, R.C., Ogden, J.M.: 1975, Electromagnetic ion cyclotron instability driven by ion energy anisotropy in high-beta plasmas. Phys. Fluids 18, 1045. ADS. ADSCrossRefGoogle Scholar
  10. Durovcová, T., Němeček, Z., Šafránková, J.: 2019, Evolution of the \(\alpha \)-proton differential motion across stream interaction regions. Astrophys. J. 873, 24. DOI. ADS. ADSCrossRefGoogle Scholar
  11. Fox, N.J., Velli, M.C., Bale, S.D., Decker, R., Driesman, A., Howard, R.A., Kasper, J.C., Kinnison, J., Kusterer, M., Lario, D., Lockwood, M.K., McComas, D.J., Raouafi, N.E., Szabo, A.: 2016, The solar probe plus mission: Humanity’s first visit to our star. Space Sci. Rev. 204, 7. DOI. ADS. ADSCrossRefGoogle Scholar
  12. Franci, L., Landi, S., Verdini, A., Matteini, L., Hellinger, P.: 2018, Solar wind turbulent cascade from MHD to sub-ion scales: Large-size 3D hybrid particle-in-cell simulations. Astrophys. J. 853, 26. DOI. ADS. ADSCrossRefGoogle Scholar
  13. Gary, S.P.: 1993, Theory of Space Plasma Microinstabilities, Cambridge University Press, New York. CrossRefGoogle Scholar
  14. Gary, S.P., Yin, L., Winske, D., Ofman, L.: 2001, Electromagnetic heavy ion cyclotron instability: Anisotropy constraint in the solar corona. J. Geophys. Res. 106, 10715. DOI. ADS. ADSCrossRefGoogle Scholar
  15. Gary, S.P., Yin, L., Winske, D., Ofman, L., Goldstein, B.E., Neugebauer, M.: 2003, Consequences of proton and alpha anisotropies in the solar wind: Hybrid simulations. J. Geophys. Res. 108, 1068. DOI. ADS. CrossRefGoogle Scholar
  16. Grappin, R., Velli, M.: 1996, Waves and streams in the expanding solar wind. J. Geophys. Res. 101, 425. DOI. ADS. ADSCrossRefGoogle Scholar
  17. Hellinger, P., Trávníček, P., Mangeney, A., Grappin, R.: 2003, Hybrid simulations of the expanding solar wind: Temperatures and drift velocities. Geophys. Res. Lett. 30, 1211. DOI. ADS. ADSCrossRefGoogle Scholar
  18. Hellinger, P., Velli, M., TráVníčEk, P., Gary, S.P., Goldstein, B.E., Liewer, P.C.: 2005, Alfvén wave heating of heavy ions in the expanding solar wind: Hybrid simulations. J. Geophys. Res. 110(A9), A12109. DOI. ADS. ADSCrossRefGoogle Scholar
  19. Jian, L.K., Russell, C.T., Luhmann, J.G., Strangeway, R.J., Leisner, J.S., Galvin, A.B.: 2009, Ion cyclotron waves in the solar wind observed by STEREO near 1 AU. Astrophys. J. 701, L105. DOI. ADS. ADSCrossRefGoogle Scholar
  20. Jian, L.K., Russell, C.T., Luhmann, J.G., Anderson, B.J., Boardsen, S.A., Strangeway, R.J., Cowee, M.M., Wennmacher, A.: 2010, Observations of ion cyclotron waves in the solar wind near 0.3 AU. J. Geophys. Res. 115, A12115. DOI. ADS. ADSCrossRefGoogle Scholar
  21. Jian, L.K., Wei, H.Y., Russell, C.T., Luhmann, J.G., Klecker, B., Omidi, N., Isenberg, P.A., Goldstein, M.L., Figueroa-Viñas, A., Blanco-Cano, X.: 2014, Electromagnetic waves near the proton cyclotron frequency: STEREO observations. Astrophys. J. 786, 123. DOI. ADS. ADSCrossRefGoogle Scholar
  22. Kasper, J.C., Lazarus, A.J., Gary, S.P.: 2008, Hot solar-wind helium: Direct evidence for local heating by Alfvén-cyclotron dissipation. Phys. Rev. Lett. 101(26), 261103. DOI. ADS. ADSCrossRefGoogle Scholar
  23. Kasper, J.C., Maruca, B.A., Stevens, M.L., Zaslavsky, A.: 2013, Sensitive test for ion-cyclotron resonant heating in the solar wind. Phys. Rev. Lett. 110(9), 091102. DOI. ADS. ADSCrossRefGoogle Scholar
  24. Kasper, J.C., Abiad, R., Austin, G., Balat-Pichelin, M., Bale, S.D., Belcher, J.W., Berg, P., Bergner, H., Berthomier, M., Bookbinder, J., Brodu, E., Caldwell, D., Case, A.W., Chandran, B.D.G., Cheimets, P., Cirtain, J.W., Cranmer, S.R., Curtis, D.W., Daigneau, P., Dalton, G., Dasgupta, B., DeTomaso, D., Diaz-Aguado, M., Djordjevic, B., Donaskowski, B., Effinger, M., Florinski, V., Fox, N., Freeman, M., Gallagher, D., Gary, S.P., Gauron, T., Gates, R., Goldstein, M., Golub, L., Gordon, D.A., Gurnee, R., Guth, G., Halekas, J., Hatch, K., Heerikuisen, J., Ho, G., Hu, Q., Johnson, G., Jordan, S.P., Korreck, K.E., Larson, D., Lazarus, A.J., Li, G., Livi, R., Ludlam, M., Maksimovic, M., McFadden, J.P., Marchant, W., Maruca, B.A., McComas, D.J., Messina, L., Mercer, T., Park, S., Peddie, A.M., Pogorelov, N., Reinhart, M.J., Richardson, J.D., Robinson, M., Rosen, I., Skoug, R.M., Slagle, A., Steinberg, J.T., Stevens, M.L., Szabo, A., Taylor, E.R., Tiu, C., Turin, P., Velli, M., Webb, G., Whittlesey, P., Wright, K., Wu, S.T., Zank, G.: 2016, Solar Wind Electrons Alphas and Protons (SWEAP) investigation: Design of the solar wind and coronal plasma instrument suite for solar probe plus. Space Sci. Rev. 204, 131. DOI. ADS. ADSCrossRefGoogle Scholar
  25. Liewer, P.C., Velli, M., Goldstein, B.E.: 2001, Alfvén wave propagation and ion cyclotron interactions in the expanding solar wind: One-dimensional hybrid simulations. J. Geophys. Res. 106, 29261. DOI. ADS. ADSCrossRefGoogle Scholar
  26. Maneva, Y.G., Ofman, L., Viñas, A.: 2015, Relative drifts and temperature anisotropies of protons and \(\alpha \) particles in the expanding solar wind: 2.5D hybrid simulations. Astron. Astrophys. 578, A85. DOI. ADS. ADSCrossRefGoogle Scholar
  27. Maneva, Y.G., Poedts, S.: 2018, Generation and evolution of anisotropic turbulence and related energy transfer in drifting proton-alpha plasmas. Astron. Astrophys. 613, A10. DOI. ADS. ADSCrossRefGoogle Scholar
  28. Marsch, E., Rosenbauer, H., Schwenn, R., Muehlhaeuser, K.-H., Neubauer, F.M.: 1982, Solar wind helium ions: Observations of the Helios solar probes between 0.3 and 1 AU. J. Geophys. Res. 87, 35. DOI. ADS. ADSCrossRefGoogle Scholar
  29. Maruca, B.A., Kasper, J.C., Bale, S.D.: 2011, What are the relative roles of heating and cooling in generating solar wind temperature anisotropies? Phys. Rev. Lett. 107(20), 201101. DOI. ADS. ADSCrossRefGoogle Scholar
  30. Maruca, B.A., Kasper, J.C., Gary, S.P.: 2012, Instability-driven limits on helium temperature anisotropy in the solar wind: Observations and linear Vlasov analysis. Astrophys. J. 748, 137. DOI. ADS. ADSCrossRefGoogle Scholar
  31. Ofman, L.: 2010, Hybrid model of inhomogeneous solar wind plasma heating by Alfvén wave spectrum: Parametric studies. J. Geophys. Res. 115(A14), 4108. DOI. ADS. CrossRefGoogle Scholar
  32. Ofman, L., Viñas, A.F.: 2007, Two-dimensional hybrid model of wave and beam heating of multi-ion solar wind plasma. J. Geophys. Res. 112(A11), 6104. DOI. ADS. CrossRefGoogle Scholar
  33. Ofman, L., Viñas, A.F., Maneva, Y.: 2014, Two-dimensional hybrid models of H+-He++ expanding solar wind plasma heating. J. Geophys. Res. 119, 4223. DOI. ADS. CrossRefGoogle Scholar
  34. Ofman, L., Viñas, A.-F., Moya, P.S.: 2011, Hybrid models of solar wind plasma heating. Ann. Geophys. 29, 1071. DOI. ADS. ADSCrossRefGoogle Scholar
  35. Ofman, L., Viñas, A.F., Roberts, D.A.: 2017, The effects of inhomogeneous proton-\(\alpha \) drifts on the heating of the solar wind. J. Geophys. Res. 122, 5839. DOI. ADS. CrossRefGoogle Scholar
  36. Ozak, N., Ofman, L., Viñas, A.-F.: 2015, Ion heating in inhomogeneous expanding solar wind plasma: The role of parallel and oblique ion-cyclotron waves. Astrophys. J. 799, 77. DOI. ADS. ADSCrossRefGoogle Scholar
  37. Perrone, D., Bourouaine, S., Valentini, F., Marsch, E., Veltri, P.: 2014, Generation of temperature anisotropy for alpha particle velocity distributions in solar wind at 0.3 AU: Vlasov simulations and Helios observations. J. Geophys. Res. 119, 2400. DOI. ADS. CrossRefGoogle Scholar
  38. Telloni, D., Bruno, R., Trenchi, L.: 2015, Radial evolution of spectral characteristics of magnetic field fluctuations at proton scales. Astrophys. J. 805, 46. DOI. ADS. ADSCrossRefGoogle Scholar
  39. Vasquez, B.J.: 2015, Heating rate scaling of turbulence in the proton kinetic regime. Astrophys. J. 806, 33. DOI. ADS. ADSCrossRefGoogle Scholar
  40. Vasquez, B.J., Markovskii, S.A., Chandran, B.D.G.: 2014, Three-dimensional hybrid simulation study of anisotropic turbulence in the proton kinetic regime. Astrophys. J. 788, 178. DOI. ADS. ADSCrossRefGoogle Scholar
  41. Wambecq, A.: 1978, Rational Runge–Kutta methods for solving systems of ordinary differential equations. Computing 20, 333. MathSciNetCrossRefGoogle Scholar
  42. Winske, D., Omidi, N.: 1993, In: Matsumoto, H., Omura, Y. (eds.) Computer Space Plasma Physics: Simulation Techniques and Sowftware, Terra Scientific Publishing, Tokyo, 103. Google Scholar
  43. Xie, H., Ofman, L., Viñas, A.: 2004, Multiple ions resonant heating and acceleration by Alfvén/cyclotron fluctuations in the corona and the solar wind. J. Geophys. Res. 109, A08103. DOI. ADS. ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhysicsCatholic University of AmericaWashingtonUSA
  2. 2.NASA Goddard Space Flight CenterGreenbeltUSA

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