Dudkovskaia, A. V., Garbet, X., Lesur, M. et al. (1 more author) (2019) Stability analysis of secondary modes, driven by the phase space island. Nuclear Fusion. 086010. ISSN 1741-4326
Abstract
We present a new theoretical approach, based on the Hamiltonian formalism, to investigate the stability of islands in phase space, generated by trapping of energetic particles (EPs) in plasma waves in a tokamak. This approach is relevant to MHD modes driven by EPs (EP-MHD) such as toroidal Alfvén eigenmodes (TAEs), EP-driven geodesic acoustic modes (EGAMs) or fishbones. A generic problem of a single isolated EP-MHD mode is equivalent to and hence can be replaced by a 2D Hamiltonian dynamics in the vicinity of the phase space island. The conventional Langmuir wave/bump-on-tail problem is then used as a representative reduced model to describe the dynamics of the initial EP-MHD. Solving the Fokker-Planck equation in the presence of pitch angle scattering, velocity space diffusion and drag and retaining plasma drifts in a model, we find a 'perturbed' equilibrium, associated with these phase space islands. Its stability is then explored by addressing the Vlasov/Fokker-Planck-Poisson system. The Lagrangian of this system provides the dispersion relation of the secondary modes and allows an estimate of the mode onset. The secondary instabilities have been confirmed to be possible but under certain conditions on the primary island width and in a certain range of mode numbers. The threshold island width, below which the mode stability is reached, is calculated. The secondary mode growth rate is found to be maximum when the associated resonant velocity approaches the boundary of the primary island. This, in turn, leads to a conclusion that the onset of the secondary mode can be prevented provided the primary wave number is the lowest available.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 IAEA, Vienna. Accepted manuscript available online 9th May 2019. |
Keywords: | bump-on-tail instability,energetic particles,Hamiltonian formalism,phase space island,secondary modes,stability analysis,toroidal Alfven eigenmodes |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > York Institute for Materials Research The University of York > Faculty of Sciences (York) > Physics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 28 Aug 2019 10:20 |
Last Modified: | 16 Oct 2024 15:58 |
Published Version: | https://doi.org/10.1088/1741-4326/ab2077 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1088/1741-4326/ab2077 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150154 |