Kinetic Eigenmodes and Discrete Spectrum of Plasma Oscillations in a Weakly Collisional Plasma

Ng, C. S.; Bhattacharjee, A.; Skiff, F.

doi:10.1103/physrevlett.83.1974

Cited by 58 publications

(92 citation statements)

References 10 publications

(26 reference statements)

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“…2 the important result presented in [73], and rediscussed in [74]. It is well known that Landau damping in a collisionless plasma is due to the effect of the destructive interference of a continuous spectrum of singular eigenmodes (the Case-Van Kampen modes).…”

Section: Filamentation and Artificial Collisionalitymentioning

confidence: 99%

“…It is well known that Landau damping in a collisionless plasma is due to the effect of the destructive interference of a continuous spectrum of singular eigenmodes (the Case-Van Kampen modes). [73] have shown that a Lenard-Bernstein collisional operator changes the spectrum of the linear Vlasov problem by replacing the singular continuous spectrum with a set of proper discrete eigenmodes, and that the Landau damping is recovered as a discrete mode (along with other modes). In this context, Fig.…”

Section: Filamentation and Artificial Collisionalitymentioning

confidence: 99%

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On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Camporeale

Delzanno

Bergen

et al. 2016

Computer Physics Communications

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a b s t r a c tWe describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Lapenta (2011) andChen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

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Section: Filamentation and Artificial Collisionalitymentioning

confidence: 99%

Section: Filamentation and Artificial Collisionalitymentioning

confidence: 99%

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Camporeale

Delzanno

Bergen

et al. 2016

Computer Physics Communications

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“…One could argue that such a model is a good approximation of hot fusion plasmas since the collision frequency in such plasmas is small. However, it has been shown numerically 5 and later proved analytically 6 that for any non-zero collision frequency, collisions are important even for a correct qualitative description of the system (at least, if collisions are modeled via the Lenard-Bernstein collision operator first introduced in Ref. 4).…”

Section: Comparison Between Different Discretization Schemes For Tmentioning

confidence: 99%

“…Ng et al 5 use a Hermite representation in order to compute the Case-Van Kampen spectrum. Our first goal is to investigate if the same result can be obtained by using finite differences on an equidistant grid in velocity space which is the most common one used in numerical studies, e.g., in GENE.…”

Section: Comparison Between Different Discretization Schemes For Tmentioning

confidence: 99%

“…Using a simplified collision term of a Fokker-Planck type, Lenard and Bernstein found that the results of Landau do not change qualitatively in the presence of collisions, 4 i.e., the Landau solutions change continuously with the collision frequency. Later, however, a similar investigation was conducted also for the Case-Van Kampen spectrum, and it was found numerically 5 as well as analytically 6 that collisions alter the Van Kampen spectrum completely; the continuum of marginally stable modes vanishes, and instead the spectrum consists of countably infinitely many eigenvalues that converge to the collisionless Landau solutions when the collision frequency tends to zero, i.e., collisions represent a singular perturbation of the system.…”

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Aspects of linear Landau damping in discretized systems

et al. 2013

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Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: A numerical study Phys. Plasmas 20, 012125 (2013) Non-planar ion-acoustic solitary waves and their head-on collision in a plasma with nonthermal electrons and warm adiabatic ions Phys. Plasmas 20, 012122 (2013) The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas Phys. Plasmas 20, 012118 (2013) Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons Phys. Plasmas 20, 012306 (2013) Additional information on Phys. Plasmas Basic linear eigenmode spectra for electrostatic Langmuir waves and drift-kinetic slab ion temperature gradient modes are examined in a series of scenarios. Collisions are modeled via a Lenard-Bernstein collision operator which fundamentally alters the linear spectrum even for infinitesimal collisionality [Ng et al., Phys. Rev. Lett. 83, 1974(1999. A comparison between different discretization schemes reveals that a Hermite representation is superior for accurately resolving the spectra compared to a finite differences scheme using an equidistant velocity grid. Additionally, it is shown analytically that any even power of velocity space hyperdiffusion also produces a Case-Van Kampen spectrum which, in the limit of zero hyperdiffusivity, matches the collisionless Landau solutions. V C 2013 American Institute of Physics. [http://dx

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The Linearized Vlasov and Vlasov–Fokker–Planck Equations in a Uniform Magnetic Field

Bedrossian

Wang

2019

J Stat Phys

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We study the linearized Vlasov equations and the linearized Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform magnetic field. In both cases, we consider periodic confinement and Maxwellian (or close to Maxwellian) backgrounds. In the collisionless case, for modes transverse to the magnetic field, we provide a precise decomposition into a countably infinite family of standing waves for each spatial mode. These are known as Bernstein modes in the physics literature, though the decomposition is not an obvious consequence of any existing arguments that we are aware of. We show that other modes undergo Landau damping. In the presence of collisions with collision frequency ν 1, we show that these modes undergo uniform-in-ν Landau damping and enhanced collisional relaxation at the time-scale O(ν −1/3 ). The modes transverse to the field are uniformly stable and exponentially thermalize on the timescale O(ν −1 ). Most of the results are proved using Laplace transform analysis of the associated Volterra equations, whereas a simple case of Yan Guo's energy method for hypocoercivity of collision operators is applied for stability in the collisional case. †

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Kinetic Eigenmodes and Discrete Spectrum of Plasma Oscillations in a Weakly Collisional Plasma

Cited by 58 publications

References 10 publications

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Aspects of linear Landau damping in discretized systems

The Linearized Vlasov and Vlasov–Fokker–Planck Equations in a Uniform Magnetic Field

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