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Numerical Methods for Three-dimensional Magnetohydrostatic Equilibria

School of Mathematics and Statistics

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Prof Thomas Neukirch No more applications being accepted Awaiting Funding Decision/Possible External Funding
St Andrews United Kingdom Applied Mathematics Astrophysics Physics Theoretical Physics

About the Project

Static solutions of the magnetohydrodynamic (MHD) equations are often used to model magnetic fields of astrophysical systems in a relatively simple way, for example to interpret observational data or as a starting point for theoretical investigations.

This PhD project on magnetohydrostatic (MHS) equilibria will focus on 3D MHS equilibria with an emphasis on numerical methods and applications to magnetic fields in the solar corona. In particular, the project aim would be to develop and use a 3D numerical continuation method code to calculate sequences of MHS equilibria, determine their bifurcation properties and apply the results to, for example, models of solar eruptions.

A PhD project on this topic would involve extending previous work (see references) based on a continuation method for 2D (symmetric) MHS equilibria. This project requires an aptitude for coding and an interest in numerical methods.

For more details about the group, please visit our website: http://www-solar.mcs.st-and.ac.uk/.

For information about the School and the application procedure in general, please see: https://www.st-andrews.ac.uk/mathematics-statistics/prospective/pgr/

Funding Notes

Applicants should have (or be about to complete) an undergraduate degree and/or taught postgraduate degree in (applied) mathematics or (theoretical) physics. Successful applicants usually have a very good UK First Class Honours degree (or equivalent).

Eligible applicants will be considered for UK research council funding (STFC) if available.

Applicants graduating from a Scottish university may be eligible to apply for a Carnegie PhD Scholarship (for details see https://www.st-andrews.ac.uk/study/fees-and-funding/postgraduate/scholarships/carnegie-caledonian/, please note the deadline of 12 January 2021).

Applicants with Chinese citizenship may be eligible for funding by the China Scholarship Council (for details see https://www.st-andrews.ac.uk/study/fees-and-funding/postgraduate/scholarships/china-scholarship-council/ , deadline 7 January 2021).


J. D. B. Hodgson and T. Neukirch, "A combined theory for magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear", Journal of Physics A: Mathematical and Theoretical, 50, 105501-1 - 105501-25 (2017).
J. D. B. Hodgson and T. Neukirch,"On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear", Geophysical and Astrophysical Fluid Dynamics, 109, 524 - 537 (2015).
M. K.-H. Kiessling and T. Neukirch, "Negative Specific Heat of a Magnetically Self-Confined Plasma Torus,'' Proceedings of the National Academy of Sciences of the United States of America, 100, 1510-1514 (2003).
Z. Romeou and T. Neukirch, "On the Application of Numerical Continuation Methods to the Calculation of Magnetostatic Equilibria", Journal of Atmospheric and Solar-Terrestrial Physics, 64, 639-644 (2002)
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