SpectralPlasmaSolver: a Spectral Code for Multiscale Simulations of Collisionless, Magnetized Plasmas

Venčels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco; Roytershteyn, V.

doi:10.1088/1742-6596/719/1/012022

Cited by 27 publications

(23 citation statements)

References 25 publications

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“…Within this approach, exact conservation laws in the discrete setting, i.e., discrete invariants in time for number of particles (mass, charge), momentum and energy, can be constructed from Hermite expansion's coefficients. Moreover, as pointed out in [57,56,24,45,46], expansions in Hermite basis functions are intrinsically multiscale, providing a natural connection between low-order moments of the plasma distribution function and typical fluid moments.…”

Section: Introductionmentioning

confidence: 98%

“…Semi-Lagrangian methods have been proposed in different frameworks such as the Finite Volume method [26,4], Discontinuous Galerkin method [2,3,39], finite difference methods based on ENO and WENO polynomial reconstructions [21], as well as in the propagation of solutions along the characteristics in an operator splitting context [1,17,20,28,27,52,23]. These methods offer an alternative to Particle-in-Cell (PIC) methods [22,58,59,12,18,19,42,43,47,53] and to the so called Transform methods based on spectral approximations [45,48,41,57,56]. PIC methods are very popular in the plasma physics community and are the most widely used methods because of their robustness and relative simplicity [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

Fatone

Funaro

Manzini

2019

Commun. Appl. Math. Comput.

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In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space-velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on the standard two-stream instability benchmark problem. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

Fatone

Funaro

Manzini

2019

Commun. Appl. Math. Comput.

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“…There are also numerical methods based on a full kinetic description 46,47 , often constrained by computational limitations. One possibility is to integrate the Vlasov equation for the dynamics of each species, coupled to Maxwell's equations for the electric and magnetic fields 47 .…”

Section: Introductionmentioning

confidence: 99%

Turbulent electromagnetic fields at sub-proton scales: Two-fluid and full-kinetic plasma simulations

et al. 2019

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Plasma dynamics is a multi-scale problem that involves many spatial and temporal scales. Turbulence connects the disparate scales in this system through a cascade that is established by nonlinear ineteractions. Most astrophysical plasma systems are weakly collisional, making a fully kinetic Vlasov description of the system essential. Use of reduced models to study such systems is computationally desirable but careful benchmarking of physics in different models is needed. We perform one such comparison here between fully kinetic Particle-In-Cell (PIC) model and a two-fluid model that includes Hall physics and electron inertia, with a particular focus on the sub-proton scale electric field. We show that in general the two fluid model captures large scale dynamics reasonably well. At smaller scales the Hall physics is also captured reasonably well by the fluid code but electron features show departures from the fully kinetic model. Implications for use of such fluid models are discussed.

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“…In order to verify these conclusions, we perform numerical simulations with the SpectralPlasmaSolver (SPS) Vlasov code (Delzanno, ; Roytershteyn & Delzanno, ; Vencels et al, ). SPS uses a spectral decomposition of the plasma distribution function in terms of Hermite polynomials in velocity space, a Fourier decomposition in physical space, and an implicit time discretization.…”

Section: Radiation From a Pulsed Beammentioning

confidence: 99%

“…Note that in addition to the finite width, other physical effects that regularize the resonances at lh and uh , such as thermal effects, collisions, and nonlinear effects, may be important depending on specific conditions. In order to verify these conclusions, we perform numerical simulations with the SpectralPlasmaSolver (SPS) Vlasov code (Delzanno, 2015;Roytershteyn & Delzanno, 2018;Vencels et al, 2016). SPS uses a spectral decomposition of the plasma distribution function in terms of Hermite polynomials in velocity space, a Fourier decomposition in physical space, and an implicit time discretization.…”

Section: Radiation From a Pulsed Beammentioning

confidence: 99%

High‐Frequency Plasma Waves and Pitch Angle Scattering Induced by Pulsed Electron Beams

Delzanno

Roytershteyn

2019

JGR Space Physics

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Cherenkov radiation from a pulse of charge propagating along the magnetic field in a magnetized plasma is analyzed using theory and fluid‐kinetic simulations. Besides radiation into whistler modes, the subject of many previous investigations in laboratory and space, radiation can occur through extraordinary (X) modes. Theory and simulations demonstrate that X mode radiation efficiencies can be orders of magnitude higher than those into whistler modes. Test particle simulations of the dynamics of energetic electrons in the beam‐generated wavefield show that X modes can also induce pitch angle scattering much more efficiently than whistlers. While coherence effects associated with spreading of realistic beam pulses may limit the size of the X mode source region, a simple model of beam dynamics suggests that the size of this region could be substantial (hundreds of meters for ionospheric conditions). These results have potentially important implications for many problems, including understanding losses in the near‐Earth environment and radiation belt remediation.

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SpectralPlasmaSolver: a Spectral Code for Multiscale Simulations of Collisionless, Magnetized Plasmas

Cited by 27 publications

References 25 publications

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

Turbulent electromagnetic fields at sub-proton scales: Two-fluid and full-kinetic plasma simulations

High‐Frequency Plasma Waves and Pitch Angle Scattering Induced by Pulsed Electron Beams

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