GeometRic ANalysis of Dilute PlasmAs

Project Information

GRANDPA

Grant agreement ID: 790623

DOI

10.3030/790623

Project closed

EC signature date 16 March 2018

Start date 1 July 2018

End date 30 June 2020

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 195 454,80

EU contribution

€ 195 454,80

Coordinated by

CARDIFF UNIVERSITY
United Kingdom

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

Reporting period: 2018-07-01 to 2020-06-30

Summary of the context and overall objectives of the project

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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

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