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Title: A finite mass based method for Vlasov–Poisson simulations

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Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
AC52-07NA27344; FC52-08NA28752
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 284; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-07-04 09:24:00; Journal ID: ISSN 0021-9991
Country of Publication:
United States

Citation Formats

Larson, David J., and Young, Christopher V. A finite mass based method for Vlasov–Poisson simulations. United States: N. p., 2015. Web. doi:10.1016/
Larson, David J., & Young, Christopher V. A finite mass based method for Vlasov–Poisson simulations. United States. doi:10.1016/
Larson, David J., and Young, Christopher V. 2015. "A finite mass based method for Vlasov–Poisson simulations". United States. doi:10.1016/
title = {A finite mass based method for Vlasov–Poisson simulations},
author = {Larson, David J. and Young, Christopher V.},
abstractNote = {},
doi = {10.1016/},
journal = {Journal of Computational Physics},
number = C,
volume = 284,
place = {United States},
year = 2015,
month = 3

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/

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Cited by: 2works
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  • This paper deals with the approximation of Vlasov-Poisson and Vlasov-Maxwell equations. We present two coupled particle-finite volume methods which use the properties of Delaunay-Voronoi meshes. These methods are applied to benchmark calculations and engineering problems such as simulation of electron injector devices. 42 refs., 13 figs.
  • In this paper the study of relativistic plasma double layers is described through the solution of the one-dimensional, unmagnetized, steady-state Poisson--Vlasov equations and by means of one-dimensional, unmagnetized, particle-in-cell simulations. The thickness versus potential-drop scaling law is extended to relativistic potential drops and relativistic plasma temperatures. The transition in the scaling law for strong'' double layers suggested by analytical two-beam models by Carlqvist (Astrophys. Space Sci. {bold 87}, 21 (1982)) is confirmed, and causality problems of standard double-layer simulation techniques applied to relativistic plasma systems are discussed.
  • The problem of a weak (n{sub b}/n{sub e}{approx}10{sup -3}) electron beam interaction with plasma is investigated by means of linear dispersion theory and electrostatic Vlasov simulations. In the case of a warm electron beam only Langmuir-type modes in a finite wavelength band are excited. Cold beams undergo rapid heating, after which the long-wavelength Langmuir and electron-acoustic modes are damped. As the waves decelerate and heat the beam, new modes with larger wave numbers and smaller phase velocities are excited, while the fastest-growing modes saturate at a finite level. The superposition of these modes with frequencies near electron plasma frequency {omega}{submore » pe} and broad k spectrum results in long quasiregular wave packets. The wave packets propagate slowly with group velocities typically 30 times smaller than the phase velocities and are weakly damped by the background electrons.« less
  • We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development ofmore » Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.« less
  • The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used,more » an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.« less