Viviane Pierrard

Ulysses electron distributions fitted with Kappa functions

We fit Kappa functions to 16,000 velocity distribution functions measured in the solar wind by the electron plasma instrument on board Ulysses. Statistically, the electron distributions are observed to have important high velocity tails in the fast solar wind but are closer to a Maxwellian in the slow wind. We also discuss how this result could support a recent kinetic model of the solar wind proposed by Maksimovic, Pierrard and Lemaire [1997].

Kappa Distributions: Theory and Applications in Space Plasmas

The plasma particle velocity distributions observed in the solar wind generally show enhanced (non-Maxwellian) suprathermal tails, decreasing as a power law of the velocity and well described by the family of Kappa distribution functions. The presence of non-thermal populations at different altitudes in space plasmas suggests a universal mechanism for their creation and important consequences concerning plasma fluctuations, the resonant and nonresonant wave – particle acceleration and plasma heating. These effects are well described by the kinetic approaches where no closure requires the distributions to be nearly Maxwellian. This paper summarizes and analyzes the various theories proposed for the Kappa distributions and their valuable applications in coronal and space plasmas.

Lorentzian ion exosphere model

Since observed velocity distributions of particles in the magnetosphere generally have a suprathermal tail instead of an exponential one, we propose to recalculate the density and temperature distributions in a nonrotating ion exosphere with a Lorentzian velocity distribution function (VDF) instead of a Maxwellian. The number density, the flux of particles, parallel and perpendicular pressures, and energy flux of the different classes of particles in the exosphere have been determined for any value of the index κ characterizing the Lorentzian VDF. The barometric density and temperature distributions for a Maxwellian VDF and for a Lorentzian VDF are compared. It is shown that for particles in an attractive potential, the barometric density decreases more slowly with altitude for the Lorentzian VDF. Furthermore, the temperature increases with altitude in this case, while for a Maxwellian VDF, it is independent of altitude. It is suggested that positive gradients of the ion and electron temperatures observed between the topside ionosphere and the outer plasmasphere can be explained by this effect, that is, a non-Maxwellian VDF with an enhanced suprathermal tail.

A low altitude trapped proton model for solar minimum conditions based on SAMPEX/PET data

We present a low altitude (below about 600 km) trapped proton model for solar minimum conditions (1994-1995), based on measurements made by the Proton/Electron Telescope onboard the SAMPEX satellite. Substantial differences are found with the low altitude part of the AP-8 MIN model: low energy fluxes appear to be overestimated by AP-8 MIN, while the new model predicts higher fluxes than AP-8 MIN for energies above about 30 MeV.

Self‐consistent model of solar wind electrons

We model the transformation of the steady state electron velocity distribution function in the collisional transition region of the solar wind by solving the Fokker-Planck equation. Alongside the proton and electron Coulomb collisions, effects of gravitational and electric and magnetic forces are also considered. The Coulomb collision term is calculated for any background velocity distribution function using a spectral method that we have developed and applied previously [Pierrard et al., 1999], Consistent treatment of electron self collisions is obtained using an iterative numerical method to match the velocity distribution functions of “test” and “background” electron distributions. Electron collisions with background solar wind protons are also taken into account. We find that Coulomb collisions have important effects on angular scattering of the electrons [i.e., on the pitch angle distribution] without changing their average density or mean radial temperature distribution. Finally, the importance of boundary conditions on the solution of the Fokker-Planck equation is discussed and emphasized.

Coronal heating and solar wind acceleration for electrons, protons, and minor ions obtained from kinetic models based on kappa distributions

Astrophysical and space plasmas are commonly found to be out of thermal equilibrium; i.e., the velocity distribution functions of their particles are not well described by Maxwellian distributions. They generally have more suprathermal particles in the tail of the distribution. The kappa distribution provides a generalization to successfully describe such plasmas with tails decreasing as a power law of the velocity. In the present work, we improve the solar wind model developed on the basis of such kappa distributions by incorporating azimuthally varying 1 AU boundary conditions to produce a spatially structured view of the solar wind expansion. By starting from the top of the chromosphere to the heliosphere and by applying relevant boundary conditions in the ecliptic plane, a global model of the corona and the solar wind is developed for each particle species. The model includes the natural heating of the solar corona automatically appearing when an enhanced population of suprathermal particles is present at low altitude in the solar (or stellar) atmosphere. This applies not only for electrons and protons but also for the minor ions which then have a temperature increase proportional to their mass. Moreover, the presence of suprathermal electrons contributes to the acceleration of the solar wind to high bulk velocities when Coulomb collisions are neglected. The results of the model are illustrated in the solar corona and in solar wind for the different particle species and can now be directly compared in two dimensions with spacecraft observations in the ecliptic plane. Key Points Kappa distributions successfully describe plasmas out of thermal equilibrium A global kinetic model of the solar corona and solar wind is described The model is extended by incorporating azimuthally varying boundary conditions

A collisional kinetic model of the polar wind

The effects of Coulomb collisions in the transition region between the collision-dominated regime at low altitudes and the collisionless regime at high altitudes have been taken into account to study the escape of H+ ions in the polar wind. A specialized spectral method is used to solve the steady state Fokker-Planck equation describing the diffusion and upward bulk motion of H+ ions through a background of O+ ions. The H+ ion velocity distribution function is determined as a function of altitude for realistic initial conditions in the whole velocity space. We emphasize the importance for a correct choice of the boundary conditions at v = 0 to obtain regular mathematical solutions. The results of this kinetic model are compared with results of earlier polar wind models based on different approximations of the plasma transport equations.

Comparison between two theoretical mechanisms for the formation of the plasmapause and relevant observations

The plasmapause formation physical mechanisms are recalled: (i) the MHD convection mechanism, based on the original idea that the plasmapause coincides with the last closed equipotential (LCE) of the magnetospheric convection electric field or with the last closed streamline (LCS) of the equatorial plasma, and (ii) the interchange mechanism, which is based on peeling off the plasmasphere as a result of substorm associated enhancements of the night side convection velocity, leading to an enhanced centrifugal acceleration in the outermost layers of the plasmasphere. The plasmapause positions, predicted by these alternative theories, were numerically determined for two different magnetospheric empirical electric field models: (i) the Volland-Stern-Maynard-Chen (VSMC) and (ii) McIlwain E5D models, both of which are Kp-dependent. The predicted positions and overall shape of the equatorial plasmapause cross-sections are confronted to those derived from decades of whistler and satellite observations including the EUV observations during the substorm of June 27, 2001. It is found that the VSMC electric field model and the LCS plasmapause formation theory less correspond to whistler measurements and in-situ satellite observations than the E5D model and the interchange plasmapause formation mechanism.

Collisionless model of the solar wind in a spiral magnetic field

We present a kinetic collisionless model of the solar wind generalized to take into account the spiral structure of the interplanetary magnetic field. This model, which also includes Kappa velocity distributions, calculates self-consistently the electric potential profile and derives the solar wind speed and the temperatures of the medium. We study how the inclusion of the spiral geometry changes the plasma parameters compared to the case of a radial magnetic field. Whereas the interplanetary electric potential, the wind density and bulk speed are not significantly changed, we show that the electron and proton temperatures are modified; in particular, we find a decrease of the proton temperature and of its anisotropy, and an increase of the electron temperature. We discuss these results and the validity of the model.

Exospheric model of the plasmasphere

Abstract ISEE observations indicate that after prolonged quiet periods, the saturated equatorial density decreases exponentially with the radial distance in the plasmasphere. No hydrostatic barometric models fit the saturated equatorial density profiles, since those obtained with barometric maxwellian or lorentzian kinetic models decrease more slowly with the radial distance. Orbits of trapped particles are in complete thermal equilibrium with the escaping and ballistic ones only when the Coulomb collision time is much smaller than the inter-hemispheric flight time of the ions and electrons. At large radial distances and in the outermost flux tubes (i.e. for large L-parameters), this condition is not always fulfilled. It is shown that hydrostatic exospheric models with an unsaturated and L-dependent population of trapped particles can be used to fit the observed density profiles. Such hydrostatic exospheric models with unsaturated population of trapped particles can therefore be used to construct empirical 3D models of the density distribution in the plasmasphere. At small L and low altitudes, trapped orbits are saturated, while at large distances, these orbits are almost completely depleted. The fraction η(L) of required trapped particles necessary to obtain a good fit to observed equatorial density profiles is a function of L. We have determined this function by fitting our hydrostatic theoretical equatorial electron density profiles to that observed by Carpenter and Anderson (1992) from L=2 to 8 after a prolonged period of quiet conditions. Differences between maxwellian and lorentzian hydrostatic barometric models and exospheric hydrostatic models for different values of the kappa index are presented.