A numerical solution to the Vlasov equation

Fijalkow, E.

doi:10.1016/s0010-4655(98)00146-5

Cited by 113 publications

(68 citation statements)

References 7 publications

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“…3. The time evolution of a beam instability with a low dissipation a ͑v Ͼ v ͒ = 0.002 0 and a small external damping ␥ d = 0.002 0 , for increasing grid resolution, is compared to a reference run for each of five schemes: flux-balance ͑FB͒, 25 CIP, 17 CIP with rational function interpolation ͑R-CIP͒, 26 CIP-CSL, and rational-CIP-CSL ͑R-CIP-CSL͒ schemes. 27 The reference run is obtained with a high resolution N x ϫ N v = 256ϫ 4096 using CIP-CSL.…”

Section: B Convergence Propertiesmentioning

confidence: 99%

Fully nonlinear features of the energetic beam-driven instability

2009

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The so-called Berk-Breizman model is applied to a cold bulk, weak warm beam, one-dimensional plasma, to investigate the kinetic instability arising from the resonance of a single electrostatic wave with an energetic particle beam. A Vlasov code is developed to solve the initial value problem for the full-f distribution, and the nonlinear evolution is categorized in the whole parameter space as damped, steady-state, periodic, chaotic, or chirping. The saturation level of steady-state solutions and the bifurcation between steady-state and periodic solutions near marginal stability match analytic predictions. The limit of a perturbative numerical approach when the resonant region extends into the bulk is shown. Frequency sweeping is observed, with time-evolution approaching theoretical results. A new method to extract the dissipation rate from frequency diagnostics is proposed. For small collision rates, instabilities are observed in the linearly barely stable region.

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Section: B Convergence Propertiesmentioning

confidence: 99%

Fully nonlinear features of the energetic beam-driven instability

2009

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“…The main step is now to choose an efficient method to reconstruct the distribution function from the cell average on each cell C i . In [8], the author used simple linear interpolation. Unfortunately this approach does not give a positive scheme and does not control spurious oscillations.…”

Section: Let Us Consider the Vlasov Equation Written In The Formmentioning

confidence: 99%

High order numerical methods for the space non-homogeneous Boltzmann equation

Filbet

Russo

2003

Journal of Computational Physics

102

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“…It consists in discretizing the Vlasov equation on a mesh of the phase space that remains fixed in time. The flux balance method (FBM) [23] uses a finite volume method for computing the average of the Vlasov equation on each cell on a fixed grid. More recently, the positive flux conservative (PFC) method [24] have been improved by introducing a slope limiter for the reconstruction of the distribution function to preserve the positivity and the mass.…”

Section: Introductionmentioning

confidence: 99%