Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov–Maxwell system

Huot, F.; Ghizzo, A.; Bertrand, Pierre; Sonnendrücker, Éric; Coulaud, Olivier

doi:10.1016/s0021-9991(02)00079-7

Cited by 68 publications

(73 citation statements)

References 16 publications

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“…This subsection presents a more realistic test case from a physical of view since this fully relativistic model can be used for the modelling of laser-plasma interaction problems ( [14,15,16]). Since the previous numerical scheme is too diffusive (due to the creation of very thin structures), a more precise interpolation operator has to be employed.…”

Section: Fully Relativistic Vlasov-maxwell Modelmentioning

confidence: 99%

“…This model describes the motion of the electrons in the laser-plasma interaction context and has been recently introduced in the literature by the physicists [15]. To derive such a model, the key points are the following: starting from the Vlasov-Maxwell equations in one dimension in space (called x) and three dimensions in momentum, we make the assumption that the motions of interest are faster along the direction of propagation of the laser than in the associated transversal directions.…”

Section: Introductionmentioning

confidence: 99%

“…Some previous works were dealt with these Vlasov-Maxwell models from the numerical point of view (see [14,15]). The theoretical study of the above models has been performed in [8,6].…”

Section: Introductionmentioning

confidence: 99%

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Convergence of a semi-Lagrangian scheme for the reduced Vlasov–Maxwell system for laser–plasma interaction

Bostan

Crouseilles

2009

Numer. Math.

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The subject matter of this paper concerns the numerical approximation of reduced Vlasov-Maxwell models by semi-Lagrangian schemes. Such reduced systems have been introduced recently in the literature for studying the laserplasma interaction. We recall the main existence and uniqueness results on these topics, we present the semi-Lagrangian scheme and finally we establish the convergence of this scheme.

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Section: Fully Relativistic Vlasov-maxwell Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convergence of a semi-Lagrangian scheme for the reduced Vlasov–Maxwell system for laser–plasma interaction

Bostan

Crouseilles

2009

Numer. Math.

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“…We have performed numerical simulations of the 1D2V full kinetic Vlasov equation (V-model) given by Eq. (1) and then of the 1D reduced Vlasov equations (2), using a phase space code based on a splitting method and semi-lagrangian scheme [9][10][11] of the Vlasov equation. Both Vlasov models were solved in parallel with the Maxwell's equations.…”

Section: Numerical Comparison Between the 1d2v Full Kinetic Version Amentioning

confidence: 99%

Vlasov simulations of self generated strong magnetic fields in plasmas and laser-plasma interaction

Inglebert

Ghizzo

Réveillé

et al. 2013

EPJ Web of Conferences

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Abstract.A new formulation based on Hamiltonian reduction technique using the invariance of generalized canonical momentum is introduced for the study of relativistic Weibel-type instability. An example of application is given for the current filamentation instability resulting from the propagation of two counterstreaming electron beams in the relativistic regime of the instability. This model presents a double advantage. From an analytical point of view, the method is exact and standard fluid dispersion relations for Weibel or filamentation instabilies can be recovered. From a numerical point of view, the method allows a drastic reduction of the computational time. A 1D multi-stream Vlasov-Maxwell code is developed using such dynamical invariants in the perpendicular momentum space. Numerical comparison with a full VlasovMaxwell system has also been carried out to show the efficiency of this reduction technique.

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“…͑i͒ To keep the accuracy of the second order in time, time splitting between the phase space coordinates ͑ , 3 ͒ in the second equation ͑62͒ of the sequence of integration is not allowed in our Vlasov equation 36 because the advection field in each resulting split equation would be not divergence free. Therefore a direct two-dimensional advection is required.…”

Section: ͒mentioning

confidence: 99%

Streamer-induced transport in the presence of trapped ion modes in tokamak plasmas

et al. 2010

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Global gyrokinetic Vlasov simulations for trapped ion modes are performed by solving a Vlasov equation averaged over the cyclotron and bounce motions of trapped ions. The distribution function, for trapped ions, is then calculated in a two-dimensional phase space, parametrized by the longitudinal action ͑energy͒ and the magnetic moment in presence of magnetic shear. The physical mechanism of the saturation processes between streamerlike structures and zonal flows in relation to the suppression of turbulent transport is discussed. The magnetic shear is identified to play a key role in the dominant streamer-induced transport regime, which exhibits a Bohm-like scaling. The interaction of streamerlike structures with plasma turbulence is shown to produce the inverse cascade that condenses onto long-wavelength trapped ion structures, on the basis on wave triad interactions.

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Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov–Maxwell system

Cited by 68 publications

References 16 publications

Convergence of a semi-Lagrangian scheme for the reduced Vlasov–Maxwell system for laser–plasma interaction

Convergence of a semi-Lagrangian scheme for the reduced Vlasov–Maxwell system for laser–plasma interaction

Vlasov simulations of self generated strong magnetic fields in plasmas and laser-plasma interaction

Streamer-induced transport in the presence of trapped ion modes in tokamak plasmas

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