Phase-space GRANULation in fusion plasmas – GRANUL

For decades, large efforts have been invested in increasingly detailed numerical simulations. This brute-force approach continues to uncover additional interplaying ingredients, but robust agreement (even qualitative) with experiments remains elusive. Recently, the essential role of fine-scale structures in real space has been uncovered. Our objective is to uncover the role of fine-scale structures in both real-space AND velocity-space, in turbulent fusion plasmas.

In hot plasmas, collisions are so rare that vortex-like fine scale structures develop in the phase-space (PS) of the particle distribution: coupling both real space and velocity space. Many PS vortices of various sizes can form and interact, leading to a new type of turbulence: phase-space turbulence. PS structures and PS turbulence are well known in some contexts, such as coherent, large-scale waves in astrophysical plasmas.
We propose to extend these concepts to fusion plasmas. In the context of fusion, the PS is expected to corrugate, as a result of a competition between microscopic PS vortices and background micro-turbulence. An analytic theory of this granulation, under development since the 1970s, promises to solve many longstanding issues of hot plasma turbulence. However, this theory remains untested numerically, because granulation involves fine-scales in both real-space and velocity-space, which are still inaccessible to a brute force approach.

The GRANUL project is based on a lighter approach, which isolates one type of low-dimensional turbulence, as a fundamental paradigm for more general turbulence. With this approach, granulation can be resolved numerically, taking advantage of a new reduced simulation code. We can then analyze the properties of granulation, its macroscopic impacts, and how it depends on plasma parameters.

Our preliminary data indicates the presence of granulation, which survives significant background turbulence, as well as a regime where transport is dominated by the dynamics of phase-space structures.
A component of particle motion called as curvature drift, which was until recently neglected in our model, turns out to play an important qualitative role in the dynamics of phase-space structures. We are currently completing a task which consists in improving the model, the associated numerical codes, and documenting the effects of curvature drift. In particular, we verified the impact of this term by studying its effect on low-concentration impurities, which allows one to separate the effects on transport from the effect on turbulence.

Analytic theory indicates that granulation has essential impacts on the mean fields in magnetic fusion plasmas, such as
1. diffusive and non-diffusive transport of particle, momentum and heat
2. formation of mesoscale and macroscale structures such as internal transport barriers and zonal flows
3. coupling between different directions of mean flows.
The GRANUL project uncovers how these effects depend on plasma parameters. This will lead to new methods of control, where one acts on granulation to improve the efficiency of fusion power.
Furthermore, we expect our evidences of essential impacts of fine-scale structures in phase-space to trigger a shift of efforts from increasingly detailed models to more balanced efforts including fine-scales in the energy dimensions, as well as clarification of seemingly complex phenomena in terms of fundamental processes in the phase-space.
Another, lighter approach, may emerge. We envision that it will be possible to incorporate the results from the GRANUL project into brute-force simulations, as an additional term in the equations to model at low cost the effects of granulation.
In the long term, by adding this missing ingredient in the conventional approach, we will improve our predictive capabilities. This will help optimize the design of future commercial reactors, which for the moment have to rely on extrapolations of empirical scaling laws of turbulence, which were obtained by measurements in much smaller devices.

Furthermore, the GRANUL project will provide the essential building blocks, and first steps, toward a more comprehensive, fully nonlinear turbulence theory. This will impact, in addition to magnetic fusion plasmas, other applications of turbulent hot plasmas, such as inertial confinement, space weather, electric propulsion, radiation from the Van Allen belts, anomalous heating in the solar corona, or intermittent turbulence in the solar wind.

Monograph:
1. M. Lesur, «Nonlinear features of instabilities, turbulence and transport in hot plasmas«, HDR (Habilitation à Diriger des Recherches) thesis, Lorraine University (2020), hal.archives-ouvertes.fr/tel-02882428v2

Communications in international conferences:
1. M. Lesur, E. Gravier, K. Lim, C. Djerroud, M. Idouakass, et X. Garbet, «Impurity transport in collisionless trapped-particle-driven turbulence«, 28th IAEA Fusion Energy Conference, Nice, France, 14/05/2021 (poster, après sélection par les pairs) conferences.iaea.org/event/214/contributions/17618/
2. M. Lesur, E. Gravier, K. Lim, C. Djerroud, M. Idouakass, et X. Garbet, «Impurity transport in collisionless trapped-particle-driven turbulence«, Proc. 28th IAEA Fusion Energy Conference, Nice, France (proceeding)
3. M. Lesur, E. Gravier, K. Lim, C. Djerroud, M. Idouakass, X. Garbet et Y. Sarazin, «Impurity transport driven by trapped-particle turbulence in tokamak plasmas«, 47th EPS Plasma Physics conference, Sitges, Spain, 24/06/2021 (poster).
4. M. Lesur, E. Gravier, K. Lim, C. Djerroud, M. Idouakass, X. Garbet et Y. Sarazin, «Impurity transport driven by trapped-particle turbulence in tokamak plasmas«, Proc. of 47th EPS Plasma Physics conference (proceeding)

Broader conferences:
1. A. Guillevic, M. Lesur, F. Brochard, J. Estiez, S. Chouchene, E. Gravier, T. Réveillé, et A. Ghizzo, «Turbulent transport in the granulation regime in fusion plasmas«, Scientific Day of Institut Jean Lamour, Nancy, 20/05/2021 (poster).

Other:
1. A. Guillevic, “Nonlinear kinetic dynamics of electron holes in phase-space”, Master 2 internship report, Lorraine University, August 2020, hal.archives-ouvertes.fr/hal-03273113

Thermonuclear fusion is an ideal solution to the energy crisis: a clean, safe, global, abundant and sustainable source of energy. A promising approach is to heat an ionized gas (a plasma) of hydrogen isotopes at 150 million degrees, and confine it in a donut-shaped magnetic field. After decades of progress, this is routinely done in several devices (tokamaks and stellerators) around the world, albeit not efficiently enough, yet. The largest magnetic fusion experiment, ITER, which is being built in France, aims at demonstrating in 2035 the scientific feasibility of this approach, with a ten-fold return on energy. To ensure its success, and to design a commercial fusion reactor, we need to overcome some remaining scientific challenges. In particular, understanding and controlling plasma turbulence is key in the future of magnetic confinement fusion energy.
In magnetic fusion devices, the tremendous temperature gradient between the hot core and the cool edge makes the plasma inevitably turbulent. Turbulence drives the transport of particles and energy from the core to the edge, which degrades the confinement of the hot plasma. Turbulence cannot be completely suppressed, however it can be mitigated or channeled. Some methods of control have been discovered empirically. A better theoretical understanding of turbulence would lead to new methods of control.

Our target for turbulence theory is a robust predictability of macroscopic impacts of turbulence (mainly transport, or turbulent mixing). However, this target remains elusive.
Turbulence theories attempt to model the statistics of the fluctuations of the whole plasma and fields. This is challenging, because hot (collisionless) plasmas are dominated by multi-scale, nonlinear mechanisms.
For decades, large efforts have been invested in increasingly detailed numerical simulations. This brute-force approach continues to uncover additional interplaying ingredients, but robust agreement (even qualitative) with experiments remains elusive. Recently, the essential role of fine-scale structures in real space has been uncovered. My objective is to uncover the role of fine-scale structures in both real-space AND velocity-space, in turbulent fusion plasmas.

In hot plasmas, collisions are so rare that vortex-like fine scale structures develop in the phase-space (PS) of the particle distribution: coupling both real space and velocity space. Many PS vortices of various sizes can form and interact, leading to a new type of turbulence: phase-space turbulence. PS structures and PS turbulence are well known in some contexts, such as coherent, large-scale waves in astrophysical plasmas.
I propose to extend these concepts to fusion plasmas. In the context of fusion, the PS is expected to corrugate, as a result of a competition between microscopic PS vortices and background micro-turbulence. An analytic theory of this granulation, under development since the 1970s, promises to solve many longstanding issues of hot plasma turbulence. However, this theory remains untested numerically, because granulation involves fine-scales in both real-space and velocity-space, which are still inaccessible to a brute force approach.

My proposal is based on a lighter approach, which isolates one type of low-dimensional turbulence, as a fundamental paradigm for more general turbulence. With this approach, granulation can be resolved numerically, taking advantage of a new reduced simulation code. Our preliminary data indicates the presence of granulation, which survives significant background turbulence. I will lead a team, including one PhD student and one postdoc, to analyze the properties of granulation, its macroscopic impacts, and how it depends on plasma parameters.

This unique approach will provide the building blocks towards a more comprehensive turbulence theory, with academic and socioeconomic applications, not only in fusion energy, but in astrophysics, space weather, and space exploration as well.