Ph.D. position (M/F) in high-temperature plasma modelling

Job Description

Thesis Subject

This thesis is focussed on the theoretical and numerical modelling of plasma dynamics far from thermal equilibrium. Modelling high-temperature plasmas remains a computational challenge. In fact, due to the rapid decrease of the Rutherford cross section, binary interactions among, close, charged particles become completely negligible at high temperature, with respect to their collective interaction. This leads to systems far from thermodynamic equilibrium, for which the typical dynamical time, related to the collective behaviour, if far shorter than the thermalization time. The more common approach, is to describe these plasmas using kinetic equations, that are very expensive from a computational point of view. Adopting a fluid approach is far less expensive, but needs for including in the fluid model the different behaviours for ions (massive) and electrons (lighter), and taking into account different closure equations determining their pressures. Depending on the physical ingredients taken into account, such models are known as Two-fluid model, or Two-temperature MagnetoHydroDynamics [1,2].

When discretizing these models, a problem arises as soon as the physical ingredients go beyond the usual single-temperature MHD, in particular for super(magneto)sonic regimes. Indeed, the jump conditions for physical quantities at the shock discontinuities that naturally develop in such regimes, are not correctly determined in Two-fluid or Two-temperature models, due to the presence of non-conservative terms in their equations. In numerical code, this leads to jumps at shocks that strongly depend on the numerical scheme adopted for the discretization. A way for avoiding that problem has been developed at the "Institut de Mathématiques de Bordeaux", by Stéphane Brull and colleagues. Instead of directly discretizing the fluid equations, it is possible to find their underlying kinetic model, discretize this model and recover the already discretized fluid equation, in the hydrodynamic limit [3,4]. The advantage of this procedure is that the underlying kinetic model is conservative, and thus its discretization is well posed. As a consequence, the jumps at shocks are correctly determined in the discretized fluid system.

The aims of this Ph.D. thesis are 1) to determine the underlying kinetic models for fluid models, gradually increasing their complexity (from Two-temperature MHD to a Two-fluid model, eventually including electron inertia), taking into account the evolution of the magnetic field in 3D configurations, 2) To recover the discretized fluid equations from the underlying kinetic ones and to develop a numerical code 3) To investigate plasma instabilities, and their non-linear evolution, in super(magneto)sonic regimes, that have rarely been characterized due to the computational difficulties of current numerical codes. In particular the Ph.D. student will focus on the magnetized Kelvin-Helmholtz instability, that develops at the Earth's magnetospheric flanks [4], determining an important plasma transport across the flanks, for “fast solar wind” periods (leading to super(magneto)sonic conditions in the near tail [5]).

[1] S. Guisset et al., Communications in Computational Physics, 19, 301 (2016).
[2] M. Faganello et al., Phys. Rev. Lett. 101, 175003, (2008).
[2] S. Brull et al., Kinetic and Related Models 4, 991 (2011)
[3] D. Aregba–Driollet et al., ESAIM : Mathematical Modelling and Numerical Analysis, 52, 1353 (2018).
[4] M. Faganello et al., Journal of Plasma Physics 83, 535830601 (2017).
[5] F. Palermo et al., J. Geophys. Res. 116, A04223 (2011).

Your Work Environment

The Ph.D student will spend the first part of her/his thesis work (~1.5 years) in Bordeaux, at the "Institut de Mathématiques de Bordeaux", for investigating the mathematical properties of the different fluid models, their underlying kinetic models, discretize them, and developing a numerical code. The second part (~1.5 years) will be spent in Marseille, at the "Physique des Interactions Ioniques et Moléculaires" laboratory (PIIM), for testing the new numerical tool in well-known configurations, and for investigating plasma instabilities. This Ph.D. work is funded by the "Centre National de la Recherche Scientifique" (CNRS), via its "Mission pour les Initiatives Transverses et Interdisciplinaires" (MITI). This funding also provides an advantageous environment, by funding summer schools, conferences, the organization of a workshop at the interface between Plasma Physics and Applied Mathematics, and several missions Marseille-Bordeaux, for regular meetings between the student, her/his supervisors, and collaborators.

Constraints and risks

Working on screens.

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

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