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Kappa distributions in space plasmas

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Space plasmas are essentially collisionless gases out of thermal equilibrium, where enhanced populations of suprathermal particles are observed. The typical distributions are generally better described by kappa distributions than by Maxwellians, especially for electrons. This has large consequences, since the small electron mass makes them major agents for plasma energy transport. Suprathermal electrons have a critical role in the heating and acceleration of plasmas, especially in the solar corona and solar wind.
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Suprathermal tails

Non-thermal particle distributions are ubiquitously observed in space plasmas. Measurements confirmed by many interplanetary missions show enhanced populations of suprathermal electrons.

The electron velocity distribution functions in space plasmas obviously have non-Maxwellian suprathermal tails decreasing as a power law of the velocity. Such distributions can be approximated by the so-called kappa or generalized Lorentzian distributions. The typical velocity distribution function observed by WIND at 1 AU in the slow speed solar wind is illustrated in Figure 4. Maxwellian is in red for comparison.

Solar wind model

Exospheric models based on anisotropic kappa distributions have been developed to study the outflow of particles from planetary and stellar exospheres. Such models show that suprathermal electrons generate large ambipolar electric fields and heat flux along open magnetic flux tubes in solar/stellar coronae and in planetary ionospheres and thus contribute significantly to solar and stellar wind acceleration, outflow from planetary ionospheres and possibly even exoplanetary atmospheric loss.

In solar wind models, the velocity at 1 AU depends on the suprathermal tail of the escaping population and thus on the kappa value. A low altitude of the exobase also accelerates the wind. Using realistic boundary conditions, the model can be used for space weather prediction.


  • Dahlqvist, C.-H., Pierrard, V. (2018). Improvements for solar wind exospheric model through boundary conditions optimization. Submitted to Solar Physics.
  • Lazar, M., Pierrard, V., Shaaban, S. M., Fichtner, H., Poedts, S. (2017). Dual Maxwellian-Kappa modeling of the solar wind electrons: new clues on the temperature of Kappa populations. Astronomy & Astrophysics, 602, A44.
  • Moschou, S.-P., Pierrard, V., Keppens, R., Pomoell, J. (2017). Interfacing MHD Single Fluid and Kinetic Exospheric Solar Wind Models and Comparing Their Energetics. Solar Physics, 292(9), 139.
  • Pierrard, V., Meyer-Vernet, N. (2017). Electron Distributions in Space Plasmas. In Kappa Distributions (pp. 465–479). Elsevier.
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Figure 2: Solar wind velocity (color scale in km/s) obtained with the exospheric solar wind model based on kappa distributions for the electrons, as a function of the kappa index used for the escaping electrons and of the exobase radial distance in solar radii.(Credit: Pierrard and Meyer-Vernet, 2017).
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Figure 3: Kappa value associated to the solar wind velocity in the exospheric model, with larger kappa values in the neutral sheet of the heliosphere (Credit: Moschou et al., 2017).
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Figure 4: The typical velocity distribution function observed by WIND at 1 AU in the slow speed solar wind. Maxwellian is in red for comparison.