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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 reasonablethat many modelling codes still use simple nite di erence representations that makeit relatively easy to explore new physical processes and preserve numerical stability [1].However, October 2019 announcements by UK government have given UKAEA thechallenge of designing a nuclear fusion reactor in the next 5 years, plus a funding elementfor upgrading existing software both for Exascale and to meet the design challenge. Oneoption under examination is the use of high order 'spectrally accurate' elements.The biggest modelling problem is still that of turbulence mostly at relatively low plasmacollisionality. Speci cally non-dissipative issues are the tracking of plasma particle orbitsbetween collisions, sometimes reducing to tracing lines of divergence-free magnetic eld. These particles then build into a Maxwell{Vlasov solver, for which many di erentnumerical representations, exploiting low collisonality and the presence of a strong,directed magnetic eld have been explored [2]. One such is ideal MHD , where I haveexplored the use of the Lie derivative [3, 4]. Some further speculations as to the likelyrole of Lie (and spectral accuracy) in solving Vlasov{Maxwell, its approximations andtheir ensembles, and interactions between the di erent approximations, in the Exascaleera will be presented.This work was funded by the RCUK Energy Programme and the European Communities under thecontract 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 PlasmaPhysics, 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. PhysicalReview 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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