Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit
KAUST Grant NumberKUK-C1-013-04
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AbstractCopyright © Cambridge University Press 2015. We study Landau damping in the 1+1D Vlasov-Poisson system using a Fourier-Hermite spectral representation. We describe the propagation of free energy in Fourier-Hermite phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetic theory. We derive a free energy equation that relates the change in the electric field to the net Hermite flux out of the zeroth Hermite mode. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterized by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK, modified to solve the 1+1D Vlasov-Poisson system. This captures Landau damping via Hou-Li filtering in velocity space. Therefore the code is applicable even in regimes where phase mixing and filamentation are dominant.
CitationParker JT, Dellar PJ (2015) Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit. Journal of Plasma Physics 81. Available: http://dx.doi.org/10.1017/S0022377814001287.
SponsorsThe authors are grateful for fruitful conversations with I. Abel, G. Colyer, S. Cowley, W. Dorland, M. Fox, G. Hammett, E. Highcock, A. Kanekar, G. Plunk, C. Roach, A. Schekochihin, F. van Wyk, and A. Zocco. This work was supported by the UK Engineering and Physical Sciences Research Council through a Doctoral Training Grant award to J.T.P. and an Advanced Research Fellowship [grant number EP/E054625/1] to P.J.D., with additional support from Award No KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). Some of the results of this research were obtained using the PRACE-3IP project (FP7 RI-312763) resource FIONN based in Ireland at the DJEI/DES/SFI/HEA Irish Centre for High-End Computing (ICHEC). Our work also made use of the IRIDIS High Performance Computing Facility provided by the Science & Engineering South (SES) Centre for Innovation, the UK HECToR HPC facility [grant number EP/H002081/1], and the BlueJoule early access programme at the UK Science and Technology Facilities Council's Hartree Centre.
PublisherCambridge University Press (CUP)
JournalJournal of Plasma Physics