Properties of the Lenard–Balescu collision operator: A numerical study

Ricci, Paolo; Lapenta, Giovanni

doi:10.1063/1.1418720

Cited by 8 publications

(4 citation statements)

References 16 publications

(15 reference statements)

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“…Finally, it should be mentioned that, on longer timescales, the two streams are destroyed by the instability and the system evolves towards thermal equilibrium. This occurs over a characteristic time that scales as g −2 ∼ (nλ De ) 2 , in agreement with earlier results [9,11,12].…”

Section: Two-stream Instabilitysupporting

confidence: 92%

“…The relaxation towards a Maxwellian distribution was also studied, revealing different scalings of the relaxation time for sub-populations of the particles and for the overall population [11]. The relaxation times were compared to the results of the Lenard-Balescu equation [12]. Other works investigated similar relaxation problems for the dynamics of self-gravitating systems [13].…”

Section: Introductionmentioning

confidence: 99%

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Collision rates estimated from exact N-body simulations of a one-dimensional plasma

et al. 2023

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In a plasma, the charged particles interact via long-range forces, and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible, while collective effects dominate the dynamics. In contrast, when [Formula: see text] collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the two-stream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations.

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Section: Two-stream Instabilitysupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Collision rates estimated from exact N-body simulations of a one-dimensional plasma

et al. 2023

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“…In any case the classical equation considered by Dolinsky is divergent at large k and, unlike the quantum version, an artificial cutoff is needed. Besides Dolinksy, we know only of the somewhat related work of Ricci and Lapenta 15 , in which they consider a one-dimensional version of the Lenard-Balescu equation. While certainly interesting, their system is primarily of theoretical value (it cannot equilibrate, for example).…”

Section: Quantum Lenard-balescu Equationmentioning

confidence: 99%

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

et al. 2016

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We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation and a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.

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“…Recognition of this similarity aids in deriving properties a physically meaningful collision operator should possess such as conservation laws and the Boltzmann H-theorem. By doing so, we generalize the Lenard-Balescu equation, which is typically referred to as a highly accurate correction of the Landau collision operator, 7,8 to describe scattering by a fundamentally different physical mechanism that can be applied to an entirely new class of problems. Problems of interest involving convective instabilities include collisions in the presence of the ion-acoustic instability, 9 non-Maxwellian plasmas, 10 and anomalous resistivity.…”

Section: Introductionmentioning

confidence: 99%

A kinetic equation for unstable plasmas in a finite space-time domain

Callen

Hegna

2008

Physics of Plasmas

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A generalization of the Lenard-Balescu equation is derived that includes wave-particle scattering by collective instabilities in finite space-time domain plasmas. It is shown that wave-particle interactions can dominate conventional particle-particle Coulomb scattering when finite times are considered or convective instabilities are present in a medium of finite spatial extent before the instabilities grow to nonlinear or turbulent amplitudes. The modified Lenard-Balescu operator retains important physical properties including particle, momentum, and energy conservation laws and the Boltzmann H-theorem. To demonstrate its utility, the theory is applied to the simple example of convectively growing ion-acoustic instabilities in a finite spatial domain.

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Properties of the Lenard–Balescu collision operator: A numerical study

Cited by 8 publications

References 16 publications

Collision rates estimated from exact N-body simulations of a one-dimensional plasma

Collision rates estimated from exact N-body simulations of a one-dimensional plasma

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

A kinetic equation for unstable plasmas in a finite space-time domain

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