GRANUL Projet financé par l'ANR


Maxime Lesur Alejandro Guillevic Photo Photo Photo Photo
Maxime Lesur Alejandro Guillevic Postdoc Etienne Gravier Alain Ghizzo Thierry Réveillé
Principal Investigator PhD student Postdoc Participant (25%) Participant (10%) Participant (10%)
Research topics


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.

Objectives, scientific and technical barriers

The overall objective is to uncover the role of fine scales structures in velocity (or energy) space on turbulent processes, which impact the efficiency of energy generation in the core of magnetic fusion experiments. We will focus on the turbulent processes, which:
1. are not satisfyingly understood yet,
2. are known to originate from microscopic turbulence (as shown reliably by experimental evidences), and
3. have essential, macroscopic impacts on fusion power.
We aim to improve their theoretical understanding, in order to discover new ways to mitigate unwanted processes (e.g. turbulent mixing); and enhance beneficial processes (e.g. formation of internal transport barriers). Ultimately, we aim to improve the predictive capabilities of turbulence simulation codes, which will be required to design successful operating scenarios in present and near-future magnetic fusion experiments, and to develop an efficient fusion reactor in the long-term.

The main scientific barrier is the numerical treatment of this multi-scale problem. The nonlinear terms in the governing equations couple a large range of disparate scales in space, time, but also in energy space. In the conventional approach, the effort is focused on accuracy in real space. Our goal is to resolve fine-scales in energy space as well, which is not yet accessible to brute-force numerical simulations.
To overcome this barrier, we isolate one type of low-frequency turbulence, as a prototype for more general turbulence in fusion plasmas. This justifies a reduction in dimensionality from 5D to 3D. More precisely, by focusing on electrostatic modes driven by resonance with the toroidal precession motion of deeply trapped particles, and by adopting a model derived in action-angle formalism, the dimensionality is reduced from 5D gyrokinetics to a 2D phase-space (radial coordinate and toroidal precession angle) parameterized by an energy invariant. This prototype sacrifices some aspects, such as the coupling between several kinds of turbulence. However it includes the essential ingredients of more general turbulence in fusion plasmas: a wide range of scales, with energy flowing between scales, effects of toroidal geometry and resonances, competition between free energy and dissipation, etc. Finally, its numerical implementation (in the TERESA code) is orders-of-magnitude lighter than conventional brute-force (gyrokinetic) simulations.
This approach will allow the first numerical investigation of fine-scale structures in phase-space in magnetic fusion plasmas.

Another scientific barrier is the theoretical interpretation from simulation data of the fully-nonlinear, turbulent mechanisms. To overcome this barrier, the reduction of dimensionality in the model we adopt is crucial. Furthermore, analytic theory known as granulation theory provides guidelines for both the input parameters that need to be explored, and the expected mechanisms we will uncover.

There are many technical challenges associated with the development of a new simulation code. However, we have already overcome them: the TERESA code has been developed, parallelized, optimized, and tested during the last few years.

The main technical barriers concern the last two steps of the GRANUL project.
1. Direct observation of granulation is yet inaccessible to measurements in magnetic fusion experiments. Although theory predicts that granulation has major impacts on observed macroscopic phenomena, the predicted scales of granulation are too small to be measured today. To overcome this barrier, we resort to indirect measurement. Our numerical simulations will help us identify unambiguous signatures of granulation in available experimental data.
2. Based on our novel understanding of granulation, we plan to attempt to identify it in one brute-force simulation with enough accuracy in both real space and energy space. This will require a large amount of computing time, which we will have to secure.

Scientific, technological and economic benefits

The main application of GRANUL is to improve the efficiency of magnetic confinement fusion. This mode of energy production answers the axis 1 ("Fundamental, exploratory research, and breakthrough") of Challenge 2 ("Clean, safe and efficient energy") of the ANR. Magnetic fusion is:
1. Clean. It involves no high-activity nor long-lived nuclear waste, unlike nuclear fission. It involves no fossil fuel, nor carbon emission.
2. Safe. Unlike nuclear fission, the process is inherently safe. The fuel is a plasma of hydrogen in a void, weighting less than a gram, which cools down immediately when disturbed.
3. Not efficient enough yet. Indeed, no experiment has ever reached break-even, which is extracting more energy from fusion reactions than the energy to sustain the plasma.
The largest magnetic fusion experiment, ITER, is being built in France. It aims at reaching break-even for the first time in 2035, generating 500 MW from an input of 50 MW. To design successful operating scenarios, and to design a commercial fusion reactor, controlling turbulence is key.
The main role of the GRANUL project is to work on the issue of efficiency. By improving our understanding of turbulence, we will open avenues for new methods of control, and better designs.

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 will uncover 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. Thus, GRANUL targets orientations 9 and 10 of the National Research Strategy (SNR).

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:
1. inertial confinement. This is an alternative approach to fusion, where a small solid target is impacted by an array of powerful lasers and becomes a hot plasma. Control of turbulence is key in this approach too.
2. space weather. Improved understanding of turbulence is required to provide early warnings of solar radiation storms and geomagnetic storms, which affect electronics.
3. electric propulsion. Predicting the impact of plasma turbulence on thrusters (anomalous erosion) would expedite their design, and lead to an increase in range of space missions.
4. radiation from the Van Allen belts. Turbulence in these belts may interact with the phase-space structures in the solar wind and auroral plasmas, and produce radiation, endangering the health of space travelers.
5. other astrophysical contexts, such as the anomalous heating in the solar corona, or intermittent turbulence in the solar wind.

Numerical codes

Main results




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