A numerical scheme for the integration of the Vlasov–Poisson system of equations, in the magnetized case

Numerical and experimental evidence is given for the occurrence of the plateau states and\ud concomitant corner modes proposed in Valentini et al. [Phys. Plasmas 19, 092103 (2012)]. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in Schamel [Phys. Plasmas 20, 034701 (2013)]

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“…4, we make use of a Eulerian code [5][6][7] that solves the Vlasov-Poisson equations for one spatial and one velocity dimension…”

mentioning

confidence: 99%

Response to “Comment on ‘Undamped electrostatic plasma waves’” [Phys. Plasmas 20, 034701 (2013)]

et al. 2013

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“…[16][17][18]). The Poisson equation for the electrostatic potential is solved after the first spatial advection step.…”

Section: Mathematical Model and Numerical Approachmentioning

confidence: 99%

Eulerian simulations of collisional effects on electrostatic plasma waves

et al. 2013

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The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attach, both from the theoretical and the numerical point of view, and which requires in general to approximate the original collisional Landau integral by simplified differential operators in reduced dimensionality. In this paper, a Eulerian timesplitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear form. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column [M. W. Anderson and T. M. ONeil, Phys. Plasmas 14, 112110 (2007)]. A receipt to prevent the filamentation problem in Eulerian algorithms is provided by exploiting the property of velocity diffusion operators to smooth out small velocity scales.

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“…that are solved by the van Leer's upwind scheme (van Leer 1976;Harten 1982) described in Valentini et al (2005). This scheme is second order in space and time and is stable under the Courant condition.…”

Section: Numerical Integration Of the Cbementioning

confidence: 99%

“…(1981). We also refer the reader to the 1D2V Vlasov-Poisson resolution by Valentini et al (2005) (see also Mangeney et al 2002). Our numerical resolution of the CBE is based on their numerical analysis.…”

Section: Introductionmentioning

confidence: 99%

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

Bienaymé

2018

A&A

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We have studied the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carried out the analysis by developing a numerical resolution of the 2D2V (two-dimensional in the physical space, 2D, and two-dimensional in the velocity motion, 2V) collisionless Boltzmann equation (CBE) and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood. We recover similar results to those obtained by other authors using N-body simulations, but we are also able to numerically identify faint structures thanks to the cancelling of the Poisson noise. We find that the ratio of the bar pattern speed to the local circular frequency is in the range Ω B /Ω = 1.77 to 1.91. If the Galactic bar angle orientation is within the range from 24 to 45 degrees, the bar pattern speed is between 46 and 49 km.s −1 .kpc −1 .

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A numerical scheme for the integration of the Vlasov–Poisson system of equations, in the magnetized case

Cited by 30 publications

References 25 publications

Response to “Comment on ‘Undamped electrostatic plasma waves’” [Phys. Plasmas 20, 034701 (2013)]

Response to “Comment on ‘Undamped electrostatic plasma waves’” [Phys. Plasmas 20, 034701 (2013)]

Eulerian simulations of collisional effects on electrostatic plasma waves

Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

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