A study of the numerical heating in electrostatic particle simulations

Ueda, Hiroko; Omura, Yoshiharu; Matsumoto, Hiroshi; Okuzawa, Takashi

doi:10.1016/0010-4655(94)90071-x

Cited by 30 publications

(22 citation statements)

References 14 publications

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“…Even though the present stability analysis alone is not expected to account for the complex issue of numerical self-heating [1,56], the results of Table 2 are found in reasonable agreement with the lower bound of the above heuristic range, as they indicate a complete stabilization of the system for v t Dt=Dx J 0:1 in case of a linear weigth factor and h f ¼ 1.…”

Section: Dispersion Relation Of Electrostatic Plasma Wavessupporting

confidence: 82%

Particle-in-cell modeling of relativistic laser–plasma interaction with the adjustable-damping, direct implicit method

Drouin

Grémillet

Adam

et al. 2010

Journal of Computational Physics

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a b s t r a c t Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable for modeling the interaction of high-intensity laser pulses with overcritical plasmas, in the case where the electrostatic modes in the denser regions are of negligible influence on the physical processes under study. To this goal, we have developed the new two-dimensional electromagnetic code ELIXIRS (standing for ELectromagnetic Implicit X-dimensional Iterative Relativistic Solver) based on the relativistic extension of the so-called Direct Implicit Method [D. Hewett, A.B. Langdon, Electromagnetic direct implicit plasma simulation, J. Comput. Phys. 72 (1987) 121-155]. Dissipation-free propagation of light waves into vacuum is achieved by an adjustable-damping electromagnetic solver. In the highdensity case where the Debye length is not resolved, satisfactory energy conservation is ensured by the use of high-order weight factors. In this paper, we first derive the electromagnetic direct implicit method as a simplified Newton scheme. Its linear properties are then investigated through numerically solving the relation dispersions obtained for both light and plasma waves, accounting for finite space and time steps. Finally, our code is successfully benchmarked against explicit particle-in-cell simulations for two kinds of physical problems: plasma expansion into vacuum and relativistic laser-plasma interaction. In both cases, we will demonstrate the robustness of the implicit solver for crude discretizations, as well as the gains in efficiency which can be realized over standard explicit simulations.

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Section: Dispersion Relation Of Electrostatic Plasma Wavessupporting

confidence: 82%

Particle-in-cell modeling of relativistic laser–plasma interaction with the adjustable-damping, direct implicit method

Drouin

Grémillet

Adam

et al. 2010

Journal of Computational Physics

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“…In a simulation of an open system, such as a discharge, one should ensure that this spurious heating rate is small compared to the physical heating rate. The dependence of the self-heating rate on the numerical parameters has been extensively discussed in earlier works [9,10,17]. The second kind of error is spurious relaxation of the distribution function toward a Maxwellian, an effect sometimes called "collisions," although to minimize confusion we will generally avoid this term in the present discussion.…”

Section: Limitations Of the Particle-in-cell Methodsmentioning

confidence: 96%

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

Turner

2006

Physics of Plasmas

103

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The particle-in-cell method with Monte Carlo collisions is frequently employed when a detailed kinetic simulation of a weakly collisional plasma is required. In such cases, one usually desires, inter alia, an accurate calculation of the particle distribution functions in velocity space. However, velocity space diffusion affects most, perhaps all, kinetic simulations to some degree, leading to numerical thermalization, and consequently distortion of the velocity distribution functions, among other undesirable effects. The rate of such thermalization can be considered a figure of merit for kinetic simulations. This paper shows that, contrary to previous assumption, the addition of Monte Carlo collisions to a one-dimensional particle-in-cell simulation seriously degrades certain properties of the simulation. In particular, the thermalization time can be reduced by as much as three orders of magnitude. This effect makes obtaining a strictly converged simulation results difficult in many cases of practical interest. * Electronic address: miles.turner@dcu.ie

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“…This may not always pertain to observations. In addition, numerical noise causes unwanted numerical particle diffusion [21]. In contrast, Vlasov codes have very low noise levels and are not subject to mass scaling.…”

Section: Introductionmentioning

confidence: 93%

A New Code for Electrostatic Simulation by Numerical Integration of the Vlasov and Ampère Equations Using MacCormack's Method

Horne¹,

Freeman²

2001

Journal of Computational Physics

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A study of the numerical heating in electrostatic particle simulations

Cited by 30 publications

References 14 publications

Particle-in-cell modeling of relativistic laser–plasma interaction with the adjustable-damping, direct implicit method

Particle-in-cell modeling of relativistic laser–plasma interaction with the adjustable-damping, direct implicit method

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

A New Code for Electrostatic Simulation by Numerical Integration of the Vlasov and Ampère Equations Using MacCormack's Method

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