Complex magnetic fields: An enigma of solar plasmas (Dundee-Durham Consortium)
Lead Research Organisation:
University of Dundee
Department Name: Mathematics
Abstract
The outer atmosphere of the Sun, the solar corona, is a dynamic plasma permeated by a magnetic field. This magnetic field is responsible for creating long-lived structures such as coronal loops, for heating the corona to its multi-million degree temperatures, and for explosive events such as solar flares and coronal mass ejections. These powerful explosions can greatly influence the Earth and its surrounding environment. They create the Northern and Southern lights, but also have the potential to damage satellites, power grids and pipelines, disrupt communications systems, and endanger astronauts. Understanding how these explosive processes take place requires a detailed understanding of the behaviour of the Sun's magnetic field, which is characterised by its complex three-dimensional structure. Gaining such an understanding is the aim of this work programme and is part of a wider goal in the scientific community of understanding the formation of structures in astrophysical plasmas.
Recent observational advances are providing us with a more and more detailed view of the Sun's magnetic field. But each increase in spatial resolution reveals finer scale magnetic structures, down to the resolution limit of even the most advanced telescopes. What is more, each increase in time cadence reveals more complex dynamics that shape the magnetic field and plasma on all scales. The over-arching theme of this consortium proposal is to explore the physical consequences of this magnetic complexity. We aim to understand how such complex magnetic fields are formed, how they evolve, and how they can build up and explosively release extreme amounts of energy. These questions are challenging, but must be addressed if we are to understand the full implications of what we are now observing.
We will address problems such as: What is the mechanism that makes the solar corona so hot? How do explosive events occur in the Sun's atmosphere? Can we develop new tools to help analyse these complex magnetic fields, and can we apply these tools to the evolution of the corona on global scales? What controls the lowest energy state to which the magnetic field of the corona can relax, and therefore how much energy is available to heat the plasma? How are particles accelerated in particular complex magnetic field structures?
We will use a combination of numerical simulations and mathematical modelling to tackle these questions, primarily using the non-linear partial differential equations of magnetohydrodynamics. The modelling will take input from the latest generation of solar telescopes, using various observations to verify and refine the theory. Combined, the results should help not only to explain and predict events in the solar corona and help answer STFC's Science Roadmap Challenge B:2 ("How does the Sun influence the environment of the Earth and the rest of the Solar System?") but also to understand some of the basic plasma physical processes that go on throughout the Universe.
Recent observational advances are providing us with a more and more detailed view of the Sun's magnetic field. But each increase in spatial resolution reveals finer scale magnetic structures, down to the resolution limit of even the most advanced telescopes. What is more, each increase in time cadence reveals more complex dynamics that shape the magnetic field and plasma on all scales. The over-arching theme of this consortium proposal is to explore the physical consequences of this magnetic complexity. We aim to understand how such complex magnetic fields are formed, how they evolve, and how they can build up and explosively release extreme amounts of energy. These questions are challenging, but must be addressed if we are to understand the full implications of what we are now observing.
We will address problems such as: What is the mechanism that makes the solar corona so hot? How do explosive events occur in the Sun's atmosphere? Can we develop new tools to help analyse these complex magnetic fields, and can we apply these tools to the evolution of the corona on global scales? What controls the lowest energy state to which the magnetic field of the corona can relax, and therefore how much energy is available to heat the plasma? How are particles accelerated in particular complex magnetic field structures?
We will use a combination of numerical simulations and mathematical modelling to tackle these questions, primarily using the non-linear partial differential equations of magnetohydrodynamics. The modelling will take input from the latest generation of solar telescopes, using various observations to verify and refine the theory. Combined, the results should help not only to explain and predict events in the solar corona and help answer STFC's Science Roadmap Challenge B:2 ("How does the Sun influence the environment of the Earth and the rest of the Solar System?") but also to understand some of the basic plasma physical processes that go on throughout the Universe.
Planned Impact
Eruptive magnetic storms on the Sun (Coronal Mass Ejections) regularly reach the Earth's space environment. The economic consequences of this space weather can be severe, and include damage to satellites and power grids, corrosion of oil and gas pipelines and disruption of communication systems. Furthermore, these events may endanger the health of astronauts and those onboard high-flying aircraft. The proposed research seeks to develop an understanding of how complex magnetic structures in the Sun's atmosphere change and interact, with these interactions being a critical part of the chain of events that generates solar eruptions. As such, a possible major impact of the proposed research will be on the international effort to develop reliable space-weather forecasting systems (given notice, defensive measures can the taken against the aforementioned effects).
Project 1.2, examining the consequences of complex magnetic fields in the global solar corona, will allow for significantly improved simulations of the Sun's magnetic field on global scales. A potential impact here will be on reconstructions of the Sun's magnetic field in the past which, in turn, will affect reconstructions of the Earth's climate in the past.
The proposed research should be seen in the wider framework of the analysis of complex multi-scale systems which we encounter in many areas of science: the weather, cellular networks, material sciences, neurosciences, nuclear sciences, etc. The theoretical tools and method created for investigating astrophysical plasmas have both benefited from and contributed to progress in these areas via exchanges of ideas, software and human resources.
More generally, astronomy has a strong cultural impact. Due to the Sun's close proximity and the stunning images being gathered by new satellites, solar physics has a great capacity to get young people interested in science, contributing to UK's skilled labour market. We will engage with schools and the general public on our research findings through the Schools Outreach Programme of the Division of Mathematics in Dundee, via press releases, articles in popular science magazines and public events such as the Dundee Science Festival. These methods are further documented in the Outreach section of the Pathways to Impact document.
Project 1.2, examining the consequences of complex magnetic fields in the global solar corona, will allow for significantly improved simulations of the Sun's magnetic field on global scales. A potential impact here will be on reconstructions of the Sun's magnetic field in the past which, in turn, will affect reconstructions of the Earth's climate in the past.
The proposed research should be seen in the wider framework of the analysis of complex multi-scale systems which we encounter in many areas of science: the weather, cellular networks, material sciences, neurosciences, nuclear sciences, etc. The theoretical tools and method created for investigating astrophysical plasmas have both benefited from and contributed to progress in these areas via exchanges of ideas, software and human resources.
More generally, astronomy has a strong cultural impact. Due to the Sun's close proximity and the stunning images being gathered by new satellites, solar physics has a great capacity to get young people interested in science, contributing to UK's skilled labour market. We will engage with schools and the general public on our research findings through the Schools Outreach Programme of the Division of Mathematics in Dundee, via press releases, articles in popular science magazines and public events such as the Dundee Science Festival. These methods are further documented in the Outreach section of the Pathways to Impact document.
Publications
Beg R
(2022)
Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers
in The Astrophysical Journal
Berger M
(2018)
A generalized poloidal-toroidal decomposition and an absolute measure of helicity
in Journal of Physics A: Mathematical and Theoretical
Candelaresi S
(2016)
EFFECTS OF FIELD-LINE TOPOLOGY ON ENERGY PROPAGATION IN THE CORONA
in The Astrophysical Journal
Candelaresi S
(2014)
Mimetic Methods for Lagrangian Relaxation of Magnetic Fields
in SIAM Journal on Scientific Computing
Candelaresi S
(2015)
MAGNETIC FIELD RELAXATION AND CURRENT SHEETS IN AN IDEAL PLASMA
in The Astrophysical Journal
Candelaresi S
(2020)
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium
in The Astrophysical Journal
Craig I
(2014)
CURRENT SINGULARITIES IN LINE-TIED THREE-DIMENSIONAL MAGNETIC FIELDS
in The Astrophysical Journal
Kerr G
(2016)
SIMULATIONS OF THE MG ii K AND CA ii 8542 LINES FROM AN ALFVÉN WAVE-HEATED FLARE CHROMOSPHERE
in The Astrophysical Journal
Pontin D
(2020)
The Parker problem: existence of smooth force-free fields and coronal heating
in Living Reviews in Solar Physics
Description | Key results are a) A new computer code has been developed for finding force-free equilibria in plasmas. The code follows an ideal relaxation towards a force-free equilibrium. The code is a significant improvement over previous codes of the same kind. It has by construction no dissipation and hence is ideally suited for the problems of magnetic relaxation in plasmas with high magnetic Reynolds numbers. It also uses GPU's for fast processing, has been tested, documented and is publicly available. b) Significant progress has been made towards a theoretical predicition of the end state of the (non-ideal) relaxation of a plasma with a braided magnetic field. This is a major stepping stone in understanding the structure of magnetic fields in astrophysical plasmas. Several papers have been published and further publications are in progress. c) Magnetic reconnection is a key process which triggers almost all eruptive phenomena in solar and astrophysical plasmas. The process of current sheet formation in a plasma with complex magnetic fields, which is key for the onset of magnetic reconnection, has been investigated and an important scaling law has been discovered. The results have been published. d) A new mathematical concept, the field line helicity, has been developed as an analytic tool to investigate the dynamics of plasmas. This tool is in particular capable to explain deviations between results of numerical simulations of relaxed plasma states and the predictions which the Taylor hypothesis makes about these states. |
Exploitation Route | We developed a new numerical code for the relaxation of magnetic fields in plasmas, which has significant advantages over existing codes and uses state of the art technology (GPUs) for fast processing. This code is available to the community (https://github.com/SimonCan/glemur ) and could help to find force-free equilibria in a wide range of plasmas. We advertised the use of this code to the plasma physics community on a number of conferences and will continue to do this. The new analytic tools developed in this project for analysing the dynamics of complex plasmas could prove useful in the prediction of space weather. We continue to develop applications of these tools in order to demonstrate their applicability. |
Sectors | Energy,Environment |
URL | http://www.maths.dundee.ac.uk/mhd/index.shtml |
Description | The research of this project by the members of the consortium has impacted on the society via various outreach activities (see list of outreach activities), mainly by raising awareness of the plasma environment we are living in. One of the most prominent of these activities was the virtual reality project ``Traveling Through a Solar Storm: An immersive virtual Reality Experience", which was led by Dr M Janvier and to which various group members contributed. The website of the project is https://www-perso.ias.u-psud.fr/solarstormvr/ and this project was funded by STFC through grant ST/N002121/1 (http://gtr.rcuk.ac.uk/projects?ref=ST/N002121/1). |
First Year Of Impact | 2016 |
Sector | Other |
Impact Types | Societal |
Description | HECToR RAP - Application for access to the GPGPU testbed resource |
Amount | £1 (GBP) |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 10/2013 |
End | 03/2014 |
Description | IUTAM travel support for S. Candelaresi |
Amount | £280 (GBP) |
Organisation | International Union of Theoretical and Applied Mechanics |
Sector | Charity/Non Profit |
Country | Germany |
Start | 04/2016 |
End | 04/2016 |
Description | Leverhulme Research Grant |
Amount | £200,000 (GBP) |
Organisation | The Leverhulme Trust |
Sector | Charity/Non Profit |
Country | United Kingdom |
Start | 10/2015 |
End | 10/2018 |
Description | NSO travel support for S. Candelaresi |
Amount | £120 (GBP) |
Organisation | National Solar Observatory (NSO) |
Sector | Public |
Country | United States |
Start | 05/2016 |
End | 06/2016 |
Description | NVIDIA Corporation Hardware Donation Program (for HPC on GPUs) |
Amount | $5,000 (USD) |
Organisation | NVIDIA |
Sector | Private |
Country | Global |
Start | 03/2014 |
Description | STFC Public Engagement Awards |
Amount | £4,712 (GBP) |
Funding ID | ST/N002121/1 |
Organisation | Science and Technologies Facilities Council (STFC) |
Sector | Public |
Country | United Kingdom |
Start | 08/2015 |
End | 08/2016 |
Description | Support for Research Visit |
Amount | £770 (GBP) |
Organisation | Edinburgh Mathematical Society |
Sector | Academic/University |
Country | United Kingdom |
Start | 11/2015 |
End | 12/2015 |
Description | Travel support |
Amount | £500 (GBP) |
Organisation | University of Cambridge |
Sector | Academic/University |
Country | United Kingdom |
Start | 07/2015 |
End | 07/2015 |
Description | Northumbria University Solar Physics Research Group |
Organisation | Northumbria University |
Department | Department of Mathematics, Physics and Electrical Engineering |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | We contributed with our expertise in magnetic reconnection, in particular reconnection at magnetic null points, to a joint research project with the Solar Physics Group at Northumbria University on oscillatory magnetic reconnection in the solar atmosphere. The project is supported by the Leverhulme Trust (£200000 in total, Dundee contribution ca £70000) and supports a joint postdoc working on the project for 3 years. |
Collaborator Contribution | The Northumbria group contributed with their expertise in MHD waves to the project. |
Impact | Thurgood, J. O., Pontin, D. I. and McLaughlin, J. A. Three-dimensional Oscillatory Magnetic Reconnection, Astrophys. J., 844, 1 (2017). [doi:10.3847/1538-4357/aa79fa]; Thurgood, J. O., Pontin, D. I. and McLaughlin, J. A. Implosive Collapse about Magnetic Null Points: A Quantitative Comparison between 2D and 3D Nulls, Astrophys. J., 855, 50 (2018). [doi:10.3847/1538-4357/aab0a0] |
Start Year | 2015 |
Title | GLEMuR |
Description | The code performs a relaxation of a magnetic field towards a force-free state (Beltrami field) using a Lagrangian numerical scheme. The numerical method strictly preserves the magnetic flux and the topology of magnetic field lines. In contrast to other implementations we use mimetic operators for the spatial derivatives in order to improve accuracy for high distortions of the grid. The scheme runs on graphical processing units (GPU), which leads to an enhanced computing speed compared to previous relaxation codes. The code has been made open source. |
Type Of Technology | Software |
Year Produced | 2014 |
Impact | Not yet applicable. |
URL | https://github.com/SimonCan/glemur |
Description | 2015 Women in Science Festival Dundee |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | General outreach event to celebrate the achievements of women in Science, Technology, Engineering and Maths (STEM) and attract more women to STEM subjects. A total of 45 family events, exhibitions, film screenings, fun days, talks and other events took place across the city in March, and the Festival was supported by many of the internationally acclaimed female scientists and researchers working at institutions in Dundee. The MHD group took part in demonstrating mathematical concepts and simple physical examples of magnetic interactions. The demonstrations were well received by the audience and triggered many discussions. |
Year(s) Of Engagement Activity | 2015 |
URL | http://www.dundee.ac.uk/news/2015/2015-women-in-science-festival-launches-with-a-bang.php |
Description | Dundee Science Festival 2013 |
Form Of Engagement Activity | Participation in an open day or visit at my research institution |
Part Of Official Scheme? | Yes |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | A full-day open day was held with hands-on activities (including a solar telescope and magnetism experiments) and discussions of the research in solar physics taking place in Dundee. Generated interest in Mathematics and Physics. |
Year(s) Of Engagement Activity | 2013 |
Description | Dundee Science Festival 2013 |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | General outreach event, organised by the Dundee Science Centre, where we presented hands-on activities to explore what a plasma is and how magnetic fields interact. The audience consisted of families, pupils, students and journalists. The demonstrations triggered interest in the field and led to discussions about science. |
Year(s) Of Engagement Activity | 2013 |
URL | http://www.dundeesciencecentre.org.uk/UserFiles/files/Dundee%20Science%20Festival%202013%20Report(2)... |
Description | Dundee Science Festival 2014 |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | Yes |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | "Dundee Science Festival", November, 2014. Public outreach activity. We presented examples from the fascinating world of magnetic fields by way of hands-on examples for pupils as well as examples of solar physics research. The Division of Mathematics, including the Solar MHD group, were awarded the main auditorium at the Dundee Science Centre and in total 16 staff manned 10 separate display stations with 681 guests passing through the centre. Each hands-on exhibit presented an interesting phenomenon related to our research. For example, the study of nonlinear oscillators (cell-synchrony) is a key research area in the division. The major concepts were brought to life by use of a physical device: a double pendulum. Visitors were invited to set it in motion, explore numerical simulations and discuss the relevant mathematical concepts (e.g. chaos) and how they are relevant to our daily lives. Another example is the use of magnets to demonstrate non-intuitive electromagnetic phenomena before presenting simulation results that communicate our research in the field of solar electromagnetism. Additionally, our display included five large television/computer monitors that displayed simulations from a range of research studies undertaken at the division (e.g. tumour, biofilm, root and fungal growth, decay of a magnetic trefoil knot, decay of a magnetic braid, dynamics of the interface of rising bubbles). We received excellent feedback regarding our participation at this event and have been informed that the Science Centre would like to include mathematical talks in their new programme for 2015. General positive feedback and interest from the public. |
Year(s) Of Engagement Activity | 2014 |
URL | http://www.dundeesciencefestival.org |
Description | Nature's Equations - D'Arcy Thompson and the Beauty of Mathematics |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | Public outreach activity which took place at the Dundee Science Centre to celebrate D'Arcy Thompson's life and work. The MHD group was represented with three members who visualised conformal mappings to the general public. |
Year(s) Of Engagement Activity | 2015 |
URL | http://www.dundee.ac.uk/museum/exhibitions/zoology/equations/ |
Description | Science in the Overgate |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | Outreach event, which took place in a local shopping centre, particularly designed to engage the local population with science and technology. |
Year(s) Of Engagement Activity | 2014 |
Description | Science in the Overgate |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | Yes |
Type Of Presentation | Workshop Facilitator |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | Mathematics games and activities (demonstrations and interactive games) as well as research of the department presented to wide ranging audience in Dundee's Overgate centre as part of Dundee's Women in Science Festival 2014. Generated enquiries relating to the Mathematics degree programme at the University. |
Year(s) Of Engagement Activity | 2014 |