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## Marie-Christine Firpo

CNRS research director.

Member of the board of the "Nonlinear Physics" division of Société Française de Physique https://www.sfpnet.fr/thematique/ph...

Web page on ResearchGate !

**News:**

**Make tokamak plasmas rotate by small axisymmetric magnetic disturbances**

https://www.lpp.polytechnique.fr/Ma...

“Breaking up-down symmetry with magnetic perturbations in tokamak plasmas: Increase of axisymmetric steady-state velocities”, H. Oueslati and M.-C. Firpo, Physics of Plasmas (2020). https://aip.scitation.org/doi/10.10...

**Coexisting crystal and liquid-like properties in a 2D long-range self-consistent model: Snapshots of the positions of the particles during the quasi-stationary state**

SCIENTIFIC REPORTS **Coexisting crystal and liquid-like properties in a 2D long-range self-consistent model** https://rdcu.be/92i9.

A two-dimensional class of mean-field models serving as a minimal frame to study long-range interaction in two space dimensions is considered. In the case of an anisotropic mixed attractive-repulsive interaction, an initially spatially homogeneous cold fluid is dynamically unstable and evolves towards a quasi-stationary state in which the less energetic particles get trapped into clusters forming a Bravais-like lattice, mimicking a crystalline state. Superimposed to this, one observes in symplectic numerical simulations a flux of slightly more energetic particles channeling through this crystalline background. The resultant system combines the rigidity features of a solid, as particles from a displaced core are shown to snap back into place after a transient, and the dynamical diffusive features of a liquid for the fraction of channeling and free particles. The combination of solid and liquid properties is numerically observed here within the classical context. The quantum transposition of the model may be experimentally reached using the latest ultracold atoms techniques to generate long-range interactions.

Invited talk, ICPP2016, Taïwan.

Review Editor in Interdisciplinary Physics, part of the journal **Frontiers in Physics**.

Member of the editorial board of the journal *Discontinuity, Nonlinearity, and Complexity* https://lhscientificpublishing.com/....

Wahb Ettoumi’s thesis award : *Prix Le Monde de la recherche universitaire 2014* https://www.polytechnique.edu/fr/wa...;

Recent works :

**Magnetic reconnection : the role of chaotic magnetic field lines**

### Impact of the Eulerian chaos of magnetic field lines in magnetic reconnection

http://aip.scitation.org/doi/10.106...

### Evidence and relevance of spatially chaotic magnetic field lines in MCF devices

https://doi.org/10.1088/1361-6587/aa570d

**A way to detect out-of-equilibrium phase transitions :**

*, Physica A*

**Entropy–complexity analysis in some globally-coupled systems****460**, 162-173 (2016) http://www.sciencedirect.com/scienc....

* Microtearing turbulence: magnetic braiding and disruption limit*, Phys. Plasmas

**22**, 122511 (2015) http://scitation.aip.org/content/ai....

A realistic reduced model involving a large poloidal spectrum of microtearing modes is used to probe the existence of some stochasticity of magnetic field lines. Stochasticity is shown to occur even for the low values of the magnetic perturbation delta_B/B devoted to magnetic turbulence that have been experimentally measured. Because the diffusion coefficient may strongly depend on the radial (or magnetic-flux) coordinate, being very low near some resonant surfaces, and because its evaluation implicitly makes a normal diffusion hypothesis, one turns to another indicator appropriate to diagnose the confinement: the mean residence time of magnetic field lines. Their computation in the microturbulence frame points to the existence of a disruption limit, namely of a critical order of magnitude of delta_B/B above which stochasticity is no longer benign yet leads to a macroscopic loss of confinement in some tens to hundred of electron toroidal excursions. Since the level of magnetic turbulence delta_B/B has been measured to grow with the plasma electron density this would also be a density limit.

**Some results** (partial)

**On the issue of confinement in magnetic confinement devices**

*N*of degrees of freedom. However, one may wonder whether the

*effective*number of degrees of freedom behind turbulence is not much smaller, as the large

*N*limit may regularize the dynamics. In this framework, why not consider, as a first approach to address the issue of turbulence and confinement in magnetic confinement devices, a one-and-a-half degrees of freedom description as a

*minimal skeleton for chaos*? Such a system is naturally given by the equations for the magnetic field lines. So doing, one addresses the issue of plasma confinement through the deeper, more fondamental issue of the confinement of magnetic field lines.

Some related publications :

L. Nasi and M.-C. Firpo, *Enhanced confinement with increased extent of the low magnetic shear region in tokamak plasmas*, Plasma Physics and Controlled Fusion **51** 045006, 2009.http://iopscience.iop.org/0741-3335...

M.-C. Firpo and D. Constantinescu, *Study of the interplay between magnetic shear and resonances
using Hamiltonian models for the magnetic field lines*, Physics of Plasmas

**18**032506, 2011.http://pop.aip.org/resource/1/phpae...

D. Constantinescu and M.-C. Firpo, *Modifying locally the safety profile to improve the confinement of magnetic field lines in tokamak plasmas*, Nucl. Fusion **52** 054006, 2012. http://iopscience.iop.org/0029-5515...

**Early nonlinear regime of the m=1 internal mode**

*m=1*resistive mode, whose destabilization governs the sawteeth phenomenon of small tokamaks, is predicted. This problem is addressed by realizing that

*two*small parameters are involved: one is the resistivity, assumed to be constant in time, the other one is the mode amplitude

*A*, which is time dependent. An amplitude expansion is derived. The entrance into the nonlinear regime is shown to proceed through successive phases, separated by thresholds in amplitude given by power laws in the resistivity. This happens to be a general feature in the dynamics of magnetic reconnection, as observed in experiments or numerical simulations.

Some related publications :

M.-C. Firpo and B. Coppi, *Dynamical Analysis of the Nonlinear Growth of the m=n=1 Resistive Internal Mode*, Phys. Rev. Lett. **90**, 095003 (2003). http://prl.aps.org/abstract/PRL/v90...

M.-C. Firpo, *Onset of the nonlinear regime and finite-resistivity effects for the resistive kink instability*, Phys. Plasmas. **11**, 970 (2004).http://pop.aip.org/resource/1/phpae...

**A statistical mechanics viewpoint on nonlinear Landau damping**

The question of the long-time fate of the electric field in the case of initial conditions subject to Landau damping has been much debated. Under the ergodic hypothesis, this may be answered through an equilibrium statistical mechanics approach of the finite-dimensional wave-particle Hamiltonian model.

*In the case of damping of a single Langmuir wave*, O’Neil’s threshold, that separates nonzero time-asymptotic wave amplitude states from zero ones, is associated to a second order phase transition [2]. *In the general case of a continuum of waves*, in which the ergodic hypothesis is the most likely to be satisfied, the wave spectrum is predicted to collapse towards small wavelengths together with the escape of initially resonant particles towards low bulk plasma thermal speeds. This study [3] reveals the fundamental discrepancy between the long-time dynamics of single waves, that can support finite amplitude steady states, and of wave spectra, that cannot.

[1] Y. Elskens and D. F. Escande, Microscopic Dynamics of Plasmas and Chaos (IOP, Bristol, 2002).

[2] M.-C. Firpo and Y. Elskens, *
Phase Transition in the Collisionless Damping Regime for Wave-Particle Interaction*, Phys. Rev. Lett.

**84**, 3318 (2000).http://prl.aps.org/abstract/PRL/v84...

[3] M.-C. Firpo, F. Leyvraz and G. Attuel, *Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction*, Phys. Plasmas **13**, 122302 (2006).http://pop.aip.org/resource/1/phpae...

**Beam-plasma interactions for fast ignition applications**

*Linear theory of the beam/return plasma equilibrium setting*, done

*without any restriction on the wave vector orientation*, reveals that filamentation is mainly triggered by an oblique mode belonging to the two-stream/filamentation branch.