Post-Doctoral Research Visit F/M Campagne postdoc 2024 - Stellarator design: Foliations of toroidal domains by harmonic fields

Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

Context

The posdoc witll be co-supervised by Mario Sigalotti (Inria) and Ugo Boscain (CNRS)

Assignment

Nuclear fusion differs from conventional fission in that, instead of splitting large nuclei like Uranium and producing radioactive waste, it fuses light nuclei like Hydrogen isotopes. Its sole direct byproducts are Helium and neutrons. These reactions occur in relatively dense, very hot plasmas that are either compressed by powerful lasers (inertial confinement) or confined by strong magnetic fields. Magnetic confinement devices of the tokamak type have produced the largest amounts of fusion power to date, and a tokamak – the large ITER under construction in Provence – is projected to achieve net power for the first time in 2035. Tokamaks however, require an intense electrical current in the plasma. As a result, they are inherently pulsed and subject to instabilities called disruptions.

The stellarator is another magnetic confinement approach, alternative to the tokamak. It is naturally steady-state and immune from disruptions because it does not require a plasma current to confine the plasma: it obtains the same effect (helical fields) by means of specially deformed magnetic coils. The downside is the complexity of the coils’ shape. One could summarize by saying that tokamaks are relatively simple to build but difficult to operate, whereas stellarators are simple to operate but difficult to build. While today’s funding is mainly devoted to tokamak development, advances in 3D modeling and manufacturing have recently accelerated stellarator progress.

The stellarator design opens many technological and mathematical research challenges. The core issue considered by the proposed project is the design of coils generating a magnetic field in a toroidal domain (a domain diffeomorphic to a torus) whose integral lines are sufficiently twisted to allow the confinement and guarantee stability [1, 2]. Such twist is needed to counteract natural drifts of the plasma towards the exterior of the stellarator. Our main objective consists in understanding the topological properties of phase portraits of magnetic fields in toroidal domains.

 

 [1]  G. Grieger, W. Lotz, P. Merkel, J. Nuhrenberg, J. Sapper, E. Strumberger, H. Wobig, R. Burhenn, V. Erckmann, U. Gasparino, L. Giannone, H. J. Hartfuss, R. Jaenicke, G. Ku ̈hner, H. Ringler, A. Weller, and F. Wagner. Physics optimization of stellarators. Physics of Fluids B: Plasma Physics, 4(7):2081–2091, 1992.

 [2] J. Nuhrenberg and R. Zille. Quasi-helically symmetric toroidal stellarators. Physics Letters A, 129(2):113–117, 1988.

Main activities

This main goal of the postdoc will consist in designing a foliation of a given toroidal domain in integral lines of a harmonic (divergence-free and curl-free) vector field with specific properties of twisting and density of the integral curves. Such properties are required to compensate the natural drift of the particle trajectories towards the exterior of the stellarator.

The main object to study is the shape of the integral lines of the magnetic field: the ideal situation is the one in which the toroidal domain is foliated by 2D topological tori, invariant for the flow of the magnetic field (a onion-like toroidal foliation). In this case on each 2D leaf the line field is either ergodic or contains periodic orbits. Another possibility is the presence of a discrete (finite or infinite) sequence of invariant 2D tori creating regions of confinement. We stress that this project focuses on the topological and Frobenius integrability properties of the phase portrait of the magnetic field and not on the plasma dynamics. When the case of harmonic vector fields is understood, we could consider as next step Beltrami vector fields, i.e., eigenvector fields of the curl operator. Harmonic fields describe magnetic fields in the void, while Beltrami fields are stationary solutions of the equations of ideal magnetohydrodynamics in the context of a resting plasma and constant pressure.

Skills

The candidate should have a strong mathematical background. Knowledge in nonlinear control theory, differential geometry, and geometric analysis will be highly appriciated.  

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking
  • Flexible organization of working hours (after 12 months of employment)
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Remuneration

According to civil service salary scales