GRANDPA · GeometRic ANalysis of Dilute PlasmAs
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2018-07-01 → 2020-06-30
- EU contribution
- €195,455
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
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Results in brief
GeometRic ANalysis of Dilute PlasmAs
The goal of this project was to study the long-time behaviour of dilute plasmas governed by the relativistic Vlasov-Maxwell (RVM) system of equations. The importance of this has several facets. First, plasmas make up 99% of the known universe. Plasmas are also important in many applications, such as television sets. However, perhaps most importantly in the 21st century is the prospect of clean energy produced in fusion reactors: these reactors hold a plasma heated to millions of degrees which (it is hoped) can produce vast amounts of clean energy (the process is similar to the processes that generate the heat in the sun). Understanding how the RVM system behaves is an integral part of the overall research into plasmas, which encompases engineers, physicists, applied mathematicians and pure mathematicians.
Data: CORDIS, © European Union
Project objective
The ultimate goal of this Fellowship is to understand the long time behaviour of plasmas governed by the relativistic Vlasov-Maxwell system (RVM). The main difficulty is the hyperbolic nature of Maxwell's equations (the electromagnetic fields propagate at the speed of light): particles that travel close to the speed of light nearly interact with their own fields. It is not currently known whether particles can be accelerated to such speeds, and, if so, whether this necessarily leads to development of singularities. This is a major open problem.My expertise in the analysis of hyperbolic equations and in microlocal analysis, complemented by my host's expertise in kinetic theory will put us in a unique position to make progress on this problem. As an integral part of this Fellowship I will train in kinetic theory, and my host and I will share our mutual networks in Europe and around the world to help us study this major open problem.To this end, I have identified several workpackages with intermediate objectives to facilitate the progression:WP1: TOY MODEL. First I will analyse a toy model of RVM that preserves the hyperbolic nature, yet is simpler to handle.WP2: THE LINEARISED SYSTEM. I will then analyse the linearised RVM system using novel tools from microlocal analysis.WP3: PARTICLE TRAJECTORIES. Returning to the RVM system, I will use the previous results, together with further hyperbolic techniques (such as Strichartz estimates) to improve existing a priori estimates for particle trajectories.I also have robust career development and public outreach agendas, to complement the scientific aspects of this proposal. Combined, all these elements will establish me as a prominent research leader upon my return to the Beijing Institute of Technology, with extensive links throughout Europe.
Original text from CORDIS.
Participants
- CARDIFF UNIVERSITY · CARDIFFCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union