GeometRic ANalysis of Dilute PlasmAs

Informations projet

GRANDPA

N° de convention de subvention: 790623

DOI

10.3030/790623

Projet clôturé

Date de signature de la CE 16 Mars 2018

Date de début 1 Juillet 2018

Date de fin 30 Juin 2020

Financé au titre de

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coût total

€ 195 454,80

Contribution de l’UE

€ 195 454,80

Coordonné par

CARDIFF UNIVERSITY
United Kingdom

Periodic Reporting for period 1 - GRANDPA (GeometRic ANalysis of Dilute PlasmAs)

Période du rapport: 2018-07-01 au 2020-06-30

Résumé du contexte et des objectifs généraux du projet

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.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

The RVM system is notoriously difficult to analyze, and attempts at "solving" it have been made ever since the 1980s, if not earlier. That is why this project involved several steps, and the overall goal of analyzing the full RVM system remains an active project for many years to come. During the course of this project we analyzed a "toy model" which resembles the RVM system in many ways. This has led to a preprint which is available freely online. Separately, I worked on equations that resemble the RVM system in many aspects of their evolutions, such as the wave, Klein-Gordon, Dirac and Schrodinger equations. This led to 4 published works, as well as numerous preprints available freely to the public.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

The resolution of the toy problem - proposed by one of the leading mathematicians in the field - is a major step forward in our future endeavors to study the RVM system. The works on the wave, Klein-Gordon, Dirac and Schrodinger equations also provide important insights, and this is reflected in the high impact journals in which they appeared.

Project website