A finite element code for the simulation of one-dimensional vlasov plasmas. II. Applications

Zaki, S.I.; Boyd, T. J. M.; Gardner, L. R. T.

doi:10.1016/0021-9991(88)90011-3

Cited by 32 publications

(26 citation statements)

References 5 publications

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“…Grant and Feix 1967;Cheng and Knorr 1976;Zaki et al 1988;Manfredi 1997;Nakamura and Yabe 1999;Filbet et al 2001;Heath et al 2012). Grant and Feix 1967;Cheng and Knorr 1976;Zaki et al 1988;Manfredi 1997;Nakamura and Yabe 1999;Filbet et al 2001;Heath et al 2012).…”

Section: Nonlinear Landau Dampingmentioning

confidence: 99%

Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit

Parker

Dellar

2015

J. Plasma Phys.

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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.

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Section: Nonlinear Landau Dampingmentioning

confidence: 99%

Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit

Parker

Dellar

2015

J. Plasma Phys.

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“…The method, which has successfully simulated the Landau damping phenomenon with machine precision [33], is high order in phase space and time, and could resolve sharp interfaces without oscillations by adaptively assigning weights to neighboring reconstruction stencils. Other well-developed methods for the VP system include finite element [32,31] as well as spectral methods. The bottleneck of all of these methods, when applied to the VP system, is the CFL time step restriction.…”

Section: Introductionmentioning

confidence: 99%

A conservative high order semi-Lagrangian WENO method for the Vlasov equation

Qiu

Christlieb

2010

Journal of Computational Physics

132

126

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“…Various techniques have been investigated and we refer the reader to [10][11][12]15,16,23,26,27,30,32,33] for plasma physics applications, and to [1,31] for other applications. Among these Eulerian methods, the semi-Lagrangian method consists in computing directly the distribution function on a Cartesian grid of the phase space, by integrating the characteristic curves backward at each time step and interpolating the value at the feet of 0021-9991/$ -see front matter Ó 2008 Elsevier Inc. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%