Dynamics of Complex Magnetic Fields: From the corona to the solar wind

Lead Research Organisation: University of Dundee
Department Name: Mathematics

Abstract

This project, entitled "Dynamics of Complex Magnetic Fields: From the corona to the solar wind'', is a continuation of a successful collaboration between the researchers of the Universities of Dundee and Durham on the entangled nature of magnetic fields in the solar atmosphere. The corona, the outer atmosphere of the Sun, 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 lead to major space weather events at Earth, creating the Northern and Southern lights but also having the potential for damaging economic impacts on engineered systems, ranging from satellites and communication systems to power grids and pipelines. It is becoming apparent that forecasting the occurrence and impact of space weather events cannot rely on static extrapolation models but requires a deep understanding of the dynamical behaviour of the Sun's magnetic field. Details of the complex, three-dimensional magnetic fields in the Sun's corona are a critical part of the space weather chain of events. At the same time, it is important to understand the manner in which these magnetic structures evolve in the solar wind as they are carried out towards Earth. This consortium aims to address these questions, as part of a wider goal in the scientific community of understanding the formation of structures in astrophysical plasmas.

Different projects within the consortium will focus on different aspects of the chain of events. We will address problems such as: How can we best model the build-up of coronal magnetic structure over time? What is the nature of the twisted magnetic "flux ropes" that form in the corona, and how does their structure evolve as they erupt and form coronal mass ejections? Where is the source of the non-steady slow component of the solar wind? What is the mechanism that makes the Sun's corona so hot? What controls the lowest energy state to which the coronal magnetic field can relax, and therefore how much energy is available to heat the plasma? Can we predict the equilibrium structure of the corresponding relaxed states? Common to each of these questions is the challenge of understanding dynamical, multi-scale processes in the Sun's coronal magnetic field.

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. Importantly, the modelling will take input from the latest generation of solar telescopes - several of our models will be directly "data-driven", and observations will be used to validate output (from global simulations of the coronal magnetic field to predictions of the slow solar wind and structure of magnetic clouds at Earth). Combined, the results will help to predict and explain events in the solar corona and to 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?"), as well as 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 be taken against the aforementioned effects.)

Project 1.1, examining the dynamics of the global solar corona, will allow for significantly improved simulations of the Sun's magnetic field on global scales. This will have potential impacts both on short-term space weather forecasting and 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. Similarly Projects 1.2 and 1.3, on the slow solar wind and the structure of magnetic flux ropes ejected from the Sun, will both help to improve our knowledge of the space weather in proximity of the Earth.

Projects 1.4 and 1.5 investigate the dynamics and structure of complex magnetic fields, a fundamental problem of astrophysical and laboratory plasmas (e.g., in controlled thermonuclear fusion). This research in particular - and the other projects to a lesser extent - 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 methods 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 Impact Plan document.

Publications

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Akhmet'ev P (2018) Minimum quadratic helicity states in Journal of Plasma Physics

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Berger M (2018) A generalized poloidal-toroidal decomposition and an absolute measure of helicity in Journal of Physics A: Mathematical and Theoretical

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Candelaresi S (2017) Magnetic field line braiding in the solar atmosphere in Proceedings of the International Astronomical Union

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Candelaresi S (2017) Quantifying the tangling of trajectories using the topological entropy. in Chaos (Woodbury, N.Y.)

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Candelaresi S (2021) Topological constraints in the reconnection of vortex braids in Physics of Fluids

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Liu Y (2019) SOTE: A Nonlinear Method for Magnetic Topology Reconstruction in Space Plasmas in The Astrophysical Journal Supplement Series

 
Description Both projects funded by this grant, "Coronal heating by magnetic braiding" and "Interchange reconnection and the slow solar wind", were successful, met their objectives and in many aspects surpassed our own expectations.

In the project "Interchange reconnection and the slow solar wind" we analysed the structure of the Sun's magnetic field with the aim of understanding the role of interchange reconnection in determining the properties of the solar wind. As both Parker Solar Probe and Solar Orbiter send back in situ data from the inner heliosphere, the theoretical models developed in the project work provide a framework for interpreting these data. Key results and outputs include the development of a new method for determining structures that may participate in interchange reconnection and associated theory to allow the interpretation of such analyses (see publications "Magnetic structures at the boundary of the closed corona: interpretation of s-web arcs", Scott et al 2018). A survey of potential field models throughout a full solar cycle was undertaken. Finally, MHD simulations revealed the process by which pseudo-streamers are formed (paper in press) - these pseudo-streamers being one of the major sources of slow wind. These results will be of direct relevance to scientists who are analysing data from new space missions. The project also lead to a new analysis tool, the foundations of which are described in "On the Magnetic Squashing Factor and the Lie Transport of Tangents", Scott et al. 2017.

The project on "Coronal heating by magnetic braiding" looked into the viability of the Parker braiding model for heating the solar corona. We investigated how the motion of photospheric plasma can braid the magnetic field in the solar corona and how this energy in the magnetic field is then subsequently released to heat the coronal plasma to temperatures of over a million degree Kelvin. The key results were published in a series of papers (see publications section) highlighting the different aspects of the problem:

a) We investigated the dependence of the turbulence in the corona on certain properties of the photospheric driver, such as its ability to mix (braid) the magnetic field and twist the magnetic field lines. These properties where measured by the topological entropy of the driver and the magnetic helicity transport into the corona (Ritchie et al 2016).The results showed that a high mixing efficiency of the driver yields many small scale energy releases, resulting in a very homogenous heating of the corona. On the other hand a driver which injects a lot of helicity leads to fewer but bigger energy releases. In the process of our investigations we also developed new computational tools, for instance an efficient method to calculate the topological entropy. These methods were published separately in Candelaresi et al. 2017.

b) The efficiency of the photospheric driver to heat the corona also depends on the topology of coronal field itself. Closed flux regions low down in the corona can prevent the energy flux from reaching higher parts of the atmosphere. However, our simulations demonstrated that the photospheric driver can quickly shred regions of closed magnetic flux and turn them into open flux and thereby alter the field structure to still allow the energy flux to reach the higher corona. This has been shown in "Effects of fieldline topology on energy propagation in the corona", Candelaresi et al. 2016.

c) We looked into the question whether braided magnetic fields can be in equilibrium or how the structure of magnetic field in the corona can drive initial instabilities, which then lead to magnetic reconnection and subsequently to turbulence and heating of the plasma. We showed that even complex braided fields can be in equilibrium (force-free) but contain many small scale current sheets and are unstable to small perturbations, triggering magnetic reconnection. "Braided magnetic fields: equilibria, relaxation and heating" Pontin et al. 2016.

d) We examined the question how energy releases in braided magnetic loops would show up in current observations. To this end we created synthetic emission images and energy spectra and compared them with existing observations. The results showed that the emissions do not necessarily show the complex underlying field structure but look rather smooth and only in rare cases does the braiding become visible in observations. This would explain why the current observations rarely find unambiguous signatures of magnetic braids ("Observable Signatures of Energy Release in Braided Coronal Loops" Pontin et al. 2017).

Both projects have let to further investigations into the response of the corona to photospheric motions supported by a subsequent STFC grant for the same Consortium.
Exploitation Route The most immediate beneficiaries of this work will be fellow researchers in solar physics. The results significantly advance the community's understanding of structure formation and energy release processes in the corona. Away from solar and heliospheric physics, researchers in astrophysics and laboratory plasma physics are also potentially interested in the results on braided magnetic fields as similar structures can occur in accretion discs, jets and in the outer layers of a tokamak plasma. Our project on "Interchange reconnection and the slow solar wind" directly contributes to our understanding of the slow solar wind and can help to improve our knowledge of the space weather in proximity of the Earth. As such, a possible major long-term impact of the proposed research can be on the international effort to develop reliable space-weather forecasting systems.
Sectors Education,Energy,Environment

 
Description Australian Research Council Discovery Project
Amount $375,000 (AUD)
Funding ID DP210100709 
Organisation Australian Research Council 
Sector Public
Country Australia
Start 04/2021 
End 04/2024
 
Description IAU travel support for S. Candelaresi
Amount € 740 (EUR)
Funding ID IAU327 
Organisation International Astronomical Union 
Sector Learned Society
Country France
Start 10/2016 
End 10/2016
 
Description IAU travel support for S. Candelaresi
Amount £652 (GBP)
Organisation International Astronomical Union 
Sector Learned Society
Country France
Start 10/2016 
End 10/2016
 
Description INI visitor support
Amount £500 (GBP)
Organisation Isaac Newton Institute for Mathematical Sciences 
Sector Academic/University
Country United Kingdom
Start 08/2017 
End 09/2017
 
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 Rankin-Sneddon Research Fellow for Sc
Amount £110,000 (GBP)
Organisation University of Glasgow 
Sector Academic/University
Country United Kingdom
Start 09/2019 
End 08/2022
 
Description Visiting Researcher Grant for Roger B Scott
Amount $1,432 (USD)
Organisation National Aeronautics and Space Administration (NASA) 
Sector Public
Country United States
Start 06/2018 
End 12/2018
 
Title Coronal Volume Segmentation 
Description Existing image segmentation techniques are applied to coronal volumes and used to identify magnetic domains using quasi-separatrix layers to define domain interfaces. The tool is available publicly at https://zenodo.org/record/3053417#.YEV5Ki0RpBy 
Type Of Material Improvements to research infrastructure 
Year Produced 2018 
Provided To Others? Yes  
Impact Method to be made available in 2018. We expect this method to impact the academic community when published. 
URL https://zenodo.org/record/3053417#.YEV5Ki0RpBy
 
Description International Team hosted by the International Space Sciences Institute 
Organisation Beihang University
Country China 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation National Center for Scientific Research (Centre National de la Recherche Scientifique CNRS)
Country France 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation Shandong University
Country China 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation Swedish Institute of Space Physics (IRF)
Country Sweden 
Sector Public 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation University of Calabria
Country Italy 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation University of Copenhagen
Department Niels Bohr Institute
Country Denmark 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation University of Leuven
Country Belgium 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description International Team hosted by the International Space Sciences Institute 
Organisation University of St Andrews
Country United Kingdom 
Sector Academic/University 
PI Contribution Participation in an International Team hosted by the International Space Sciences Institute (funded from 2017-2018) on topological structures in turbulent space plasmas
Collaborator Contribution Collaborative research team across different academic disciplines
Impact none
Start Year 2017
 
Description NASA Collaboration 
Organisation National Aeronautics and Space Administration (NASA)
Department Goddard Space Flight Center
Country United States 
Sector Public 
PI Contribution We are designing and running MHD simulations using the ARMS code (Adaptive Refinement MHD Solver) for the investigations of the slow solar wind. This investigation is of mutual interest for the team at NASA, Goddard, who developed the code, and ourselves.
Collaborator Contribution See above.
Impact Will appear under ``Publications".
Start Year 2017
 
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
 
Description High School Visit 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact An afternoon of outreach activities (scientific demonstrations and experiments) for the pupils of a local High School to raise interest in science and mathematics. The teacher gave positive feedback on the uptake of science subjects afterwards.
Year(s) Of Engagement Activity 2016
 
Description Maths Week Scotland 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact Researchers from the Universities of Abertay, Dundee, and St Andrews together gave a number of presentations to the general public to highlight how maths can be used to understand the world around us. This included also talks on the solar physics.
Year(s) Of Engagement Activity 2017
URL https://ima.org.uk/7163/maths-week-scotland/
 
Description Maths Week Scotland 2018 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact Researchers from the University of Dundee gave a number of presentations and hands-on workshops to high school students from the local area how maths can be used to understand the world around us. This included also talks on the solar physics.
Year(s) Of Engagement Activity 2018
 
Description Maths Week Scotland Public Lecture 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact Series of short lectures within the Maths Week Scotland, one of which was on Auroras, which is closely related to space weather and the scientific questions addressed in this STFC project.
Year(s) Of Engagement Activity 2017
URL http://www.maths.dundee.ac.uk/news/complexWorlds.pdf
 
Description School visit (Monifieth) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact Presentations were given to groups of school children, which sparked many questions and discussions. Subsequently the school reported increased interest in solar physics, astrophysics, space science
Year(s) Of Engagement Activity 2017
 
Description Schools Visit - Brechin 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact Presentations were given to groups of school children, which sparked many questions and discussions. Subsequently the school reported increased interest in solar physics, astrophysics, space science
Year(s) Of Engagement Activity 2017
 
Description Schools Visits - Monifieth, Carnoustie 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact Presentations were given to groups of school children, which sparked many questions and discussions. Subsequently the school reported increased interest in solar physics, astrophysics, space science
Year(s) Of Engagement Activity 2018
 
Description Wednesday Wonders 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact Public outreach activity, under the title ``Outer space - Inner space", to which we contributed demonstrations of magnetism and the Sun. This also included a presentation of the virtual reality immersive experience of a flight through the solar atmosphere.
Year(s) Of Engagement Activity 2017
URL http://www.leisureandculturedundee.com/sites/default/files/Activities-Events-Mills_Winter_17-18.pdf