GeometRic ANalysis of Dilute PlasmAs

Información del proyecto

GRANDPA

Identificador del acuerdo de subvención: 790623

DOI

10.3030/790623

Proyecto cerrado

Fecha de la firma de la CE 16 Marzo 2018

Fecha de inicio 1 Julio 2018

Fecha de finalización 30 Junio 2020

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 195 454,80

Aportación de la UE

€ 195 454,80

Coordinado por

CARDIFF UNIVERSITY
United Kingdom

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

Período documentado: 2018-07-01 hasta 2020-06-30

Resumen del contexto y de los objetivos generales del proyecto

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.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

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.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

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