Abstract
This paper provides an overview of recent results on two distinct studies exploiting the non-linear model for ideal ballooning modes with potential applications to edge-localized modes (ELMs). The non-linear model for tokamak geometries was developed by Wilson and Cowley in 2004 and consists of two differential equations that characterize the temporal and spatial evolution of the plasma displacement. The variation of the radial displacement along the magnetic field line is described by the first equation, which is identical to the linear ballooning equation. The second differential equation is a two-dimensional non-linear ballooning-like equation, which is often second order in time but can involve a fractional time derivative depending on the geometry. In the first study, the interaction of multiple filamentary eruptions is addressed in a magnetized plasma in a slab geometry. Equally sized filaments evolve independently in both the linear and non-linear regimes. However, if filaments are initiated with slightly different heights from the reference flux surface, they interact with each other in the non-linear regime: lower filaments are slowed down and are eventually completely suppressed, while the higher filaments grow faster because of the non-linear interaction. In the second study, this model of non-linear ballooning modes is examined quantitatively against experimental observations of ELMs in Mega Amp Spherical Tokamak (MAST) geometries. The results suggest that experimentally relevant results can only be obtained using modified equilibria.
Original language | English |
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Pages (from-to) | 6-20 |
Number of pages | 15 |
Journal | Contributions to Plasma Physics |
Volume | 58 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2018 |
Externally published | Yes |
Funding
Part of this work was funded by the German National Academic Foundation (Studienstiftung des deutschen Volkes), the German Academic Exchange Service (DAAD—Stipendium für Doktoranden). We would also like to mention that this work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement No. 633053 and from the RCUK Energy Programme (grant number EP/I501045). The views and opinions expressed herein do not necessarily reflect those of the European Commission. 1Max-Planck-Institut für Plasmaphysik, Greifswald, Germany 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK 3Corpus Christi College, Oxford, UK 4Department of Physics, York Plasma Institute, University of York, Heslington, UK * Correspondence Sophia A. Henneberg, Max-Planck-Institut für Plasmaphysik, Wendelsteinstr. 1, 17489 Greifswald, Germany. Email: [email protected] Funding Information This research was supported by the German National Academic Foundation (Studienstiftung des deutschen Volkes). German Academic Exchange Service (DAAD—Stipendium für Doktoranden). RCUK Energy Programme, EP/I501045.
Funders | Funder number |
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Euratom research and training programme 2014–2018 | |
Horizon 2020 Framework Programme | 633053 |
Research Councils UK | EP/I501045 |
Deutscher Akademischer Austauschdienst | |
Studienstiftung des Deutschen Volkes |
Keywords
- ELMs
- MHD
- non-linear ballooning model