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Challenges for modelling fusion plasmas

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GCS - Geometry, compatibility and structure preservation in computational differential equations

Modelling fusion plasmas presents many challenges, so that it is reasonable
that many modelling codes still use simple nite di erence representations that make
it relatively easy to explore new physical processes and preserve numerical stability [1].
However, October 2019 announcements by UK government have given UKAEA the
challenge of designing a nuclear fusion reactor in the next 5 years, plus a funding element
for upgrading existing software both for Exascale and to meet the design challenge. One
option under examination is the use of high order 'spectrally accurate' elements.
The biggest modelling problem is still that of turbulence mostly at relatively low plasma
collisionality. Speci cally non-dissipative issues are the tracking of plasma particle orbits
between collisions, sometimes reducing to tracing lines of divergence-free magnetic
eld. These particles then build into a Maxwell{Vlasov solver, for which many di erent
numerical representations, exploiting low collisonality and the presence of a strong,
directed magnetic eld have been explored [2]. One such is ideal MHD , where I have
explored the use of the Lie derivative [3, 4]. Some further speculations as to the likely
role of Lie (and spectral accuracy) in solving Vlasov{Maxwell, its approximations and
their ensembles, and interactions between the di erent approximations, in the Exascale
era will be presented.
This work was funded by the RCUK Energy Programme and the European Communities under the
contract of Association between EURATOM and CCFE .
[1] B.D. Dudson, A. Allen, G. Breyiannis, E. Brugger, J. Buchanan, L. Easy, S. Farley, I. Joseph,
M. Kim, A.D. McGann, et al. BOUT ++: Recent and current developments. Journal of Plasma
Physics, 81(01):365810104, 2015.
[2] W. Arter. Numerical simulation of magnetic fusion plasmas. Reports on Progress in Physics,
58:1{59, 1995.
[3] W. Arter. Potential Vorticity Formulation of Compressible Magwnetohydrodynamics. Physical
Review Letters, 110(1):015004, 2013.
[4] W. Arter. Beyond Linear Fields: the Lie{Taylor Expansion. Proc Roy Soc A, 473:20160525, 2017.

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