Electron velocity distributions measured in the solar wind exhibit significant departures from thermal equilibrium. These include the existence of power-law tails at high energies and the presence of a field-aligned, suprathermal component known as the “strahl.” These features arise from the complex dynamics of solar wind electrons in interplanetary space, under the action of the large-scale electromagnetic field, and of various scattering mechanisms, which may include Coulomb collisions, interactions with background turbulence, or scattering by waves self-consistently generated through plasma instabilities.

A Fokker-Planck numerical code solving for the so-called focused transport equation (FTE) was recently developed at LIRA to capture these complex dynamics. The FTE, a model initially developed to describe the transport of solar energetic particles and cosmic rays, proved to be highly effective in reproducing the suprathermal electrons pitch-angle distributions measured by the Solar Orbiter/EAS and Parker Solar Probe/SPAN-e electron analyzers. The use of this model, coupled to SolO and PSP measurements, enabled the first direct measurements of the solar wind electrons effective mean free path from 100 eV to 1 keV [Zaslavsky et al., 2024, 2025].

The proposed doctoral project builds upon these promising results. The numerical code presently solves the FTE in a two-dimensional phase space, assuming constant particle energy. A first objective will be to extend the code to a three-dimensional phase space, explicitly including particle energy as a variable. The upgraded model will incorporate the effects of the interplanetary electric field, Coulomb collisions at low energies, and energy diffusion due to Fermi-like acceleration processes. This extension will allow for a theoretical investigation of the formation of electron energy distribution functions in the solar wind, including the development of power-law tails at high energies – a fundamental problem of solar wind physics, unsolved for decades – and of the so-called “sunward electron cutoff”, which has been the subject of extensive debate since its initial detection by PSP in 2021 [Halekas et al, 2021].

In parallel with the numerical development, the project will involve a systematic comparison of model results with electron measurements from Parker Solar Probe and Solar Orbiter. This observational work will benefit from strong collaborations with the teams at University College London (responsible for the Solar Orbiter plasma analyzers) and the University of California, Berkeley (responsible for the Parker Solar Probe plasma analyzers). These partnerships will provide the student with in-depth knowledge of the instruments and data, facilitating an observational work that will provide robust constraints on the electron velocity diffusion coefficients – quantities that remain poorly characterized. The derived coefficients will, in turn, enable testing of theoretical models that predict their values.

Beyond advancing our understanding of solar wind physics, this project has broader implications for the study of energetic particle transport in astrophysical plasmas. For example, it can help to clarify the role of angular scattering in electron beams that are responsible for interplanetary type III radio bursts – and more generally help the modeling of cosmic ray transport in various astrophysical environments. The methodology and focus of this project will bridge the communities studying high-energy particle events and the broader evolution of the solar wind, by adapting approaches from the high-energy domain to investigate energy ranges that are less explored from this perspective. 

Finally, and importantly, note that the project is currently expanding rapidly, following several years of development, and the recent publication of two papers in 2024 and 2025. The novelty of the approach and the unique data currently gathered by PSP and SolO will guarantee direct and immediate publication opportunities to the student and the team.

Biblio :

Probing Turbulent Scattering Effects on Suprathermal Electrons in the Solar Wind: Modeling, Observations and Implications

A. Zaslavsky, J.C. Kasper, E. Kontar, D.E. Larson, M. Maksimovic, J.M.D.C Marques, G. Nicolaou, C. Owen, O. Romeo, P.L. Whittlesey, ApJ, 966, 60, 2024

Radial evolution of the strahl pitch-angle width

A. Zaslavsky, O. Romeo, E. Cherier, D.E. Larson, A&A, accepted, sept. 2025

The Sunward Electron Deficit: A Telltale Sign of the Sun’s Electric Potential

J.S. Halekas, L. Bercic, P. Whittlesey, D. E. Larson et al, ApJ 916, 1, 2021

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - arnaud.zaslavsky@obspm.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online before March 13th, 2026 Midnight Paris time!