Kinetic theory of Jeans instability

Trigger, S. A.; Ershkovich, A. I.; Heijst, G. J. F. van; Schram, Ppjm Piet

doi:10.1103/physreve.69.066403

Cited by 54 publications

(65 citation statements)

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“…In 2003, Shukla studied the radiation condensation instability in magnetized and un‐magnetized self‐gravitating astrophysical dusty plasmas and discussed the instabilities attributed to dust acoustic (DA) and dust lower hybrid waves. Trigger et al considered a coupled set of Boltzmann–Poisson equations for studying the Jeans instability by taking into account the collisions between the light masses as well as between the light and heavy plasma components. Significant modifications caused by the collisions were examined on the oscillation spectrum, whereas the Jeans instability criterion remained unchanged.…”

Section: Introductionmentioning

confidence: 99%

Twisted electrostatic waves in a self‐gravitating dusty plasma

Bukhari

Ali

Rafique

et al. 2017

Contrib. Plasma Phys

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A generalized response (dielectric) function for twisted electrostatic waves is derived for an un-magnetized self-gravitating thermal dusty plasma, whose constituents are the Boltzmann-distributed electrons and positive ions in the presence of negatively charged micrometre-sized massive dust particulates. For this purpose, a set of Vlasov-Poisson coupled equations is solved along with the perturbed Laguerre-Gauss distribution function, as well as the electrostatic and gravitational potentials in the limit of paraxial approximation. For plane wave solution, the wavefronts of the dust-acoustic (DA) wave are assumed to have a constant phase with electric and gravitational field lines propagating straight along the propagation axis. On the other hand, non-planar wave solutions show helical (twisted) wavefronts, in which field lines spiral around the propagation axis owing to the azimuthal velocity component to account for the finite orbital angular momentum (OAM) states. The dispersion relation and damping rate for twisted DA waves are studied both analytically and numerically. It is shown that finite OAM states, the dust to electron temperature ratio, and dust self-gravitation effects significantly affect the linear dispersion and Landau damping frequencies. In particular, the phase speed of twisted DA waves is reduced with the variation of the twist parameter (= k/lq ), dust concentration (= n d0 /n i0 ), and dust self-gravitation (= Jd / pd ). The relevance of our findings to interstellar dust clouds is also discussed for micrometre-sized massive dust grains. KEYWORDS dusty plasma, electrostatic twisted waves, landau damping, orbital angular momentum INTRODUCTIONLight beam exchanges its energy and momentum [1] with matter upon interaction with it. The total angular momentum of the light beam can be composed of spin and orbital parts due to planar and helical wavefronts, respectively. In other words, the spin and orbital angular momenta have their origin from the polarization states and azimuthal phase structure, which are the well-known properties of polarized light beams. Using a specific experimental set-up, Beth [2] was the first to verify Poynting's idea and measure the mechanical torque of circularly polarized light by transferring the angular momentum to a half-wave plate. Later, Allen et al. [3] ) discussed a theoretical model for calculating the average angular momentum density per unit power and studied the well-defined orbital angular momentum (OAM) states due to the Laguerre-Gaussian (LG) light beams. In 2011, Yao and Padgett [4] presented a historical background of the angular momentum to explain various aspects of the OAM states, e.g. the generation of helical beams, the origin and behaviour of OAM, its transformation and possible applications, mode conversion and beam coherence, etc. Recently, several investigations [5][6][7][8][9][10][11][12] have been made with reference to the plasma physics to study the importance of the plasma modes and instabilities with finite OAM, e.g. nonlinear wave couplin...

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Section: Introductionmentioning

confidence: 99%

Twisted electrostatic waves in a self‐gravitating dusty plasma

Bukhari

Ali

Rafique

et al. 2017

Contrib. Plasma Phys

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“…G is the gravitational constant and I col is the collision integral. Following [6], we choose the form of the collision integral suggested in [7]:…”

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“…The basic equations (5), (8) and (9) now have exactly the same form as (5), (3) and (4), respectively, in [6], and, hence, the standard procedure of linearization by using Laplace transformation results in the same dispersion relation [6, (15)], but Ω 2 ≡ 4πGρ is now to be replaced by…”

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confidence: 99%

“…Several cases when the dispersion relation, similar to (12), allows an analytical treatment have been considered in [6]. Exact solution of the dispersion relation (12) with any value of the collision frequency ν exists with kD = 1, where D = v T /|Ω 0 | is an analog of the Debye radius (Ω 0 = 0).…”

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confidence: 99%

“…Following [6], let us neglect collisions, ν = 0, assuming that kv T Ӷ|ω|. Then, replacing Ω 2 by Ω 2 0 in [6, (20)] one obtains…”

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Kinetic treatment of gravitational-Coulomb coupling in the Jeans model

Ershkovich¹,

Israelevich²

2008

J. Plasma Phys.

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The conventional Jeans model is modified by the addition of electric charging. The standard procedure of kinetic treatment results in a dispersion relation which describes both the Jeans instability and Langmuir oscillations, with the analog of Landau damping. Coulomb interactions tend to stabilize the Jeans instability diminishing the growth rate whereas the gravitational field tends to destabilize Langmuir oscillations. Collisions between particles are taken into account.

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2023

Collective Phenomena in Plasmas and Elsewhere

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Kinetic theory of Jeans instability

Cited by 54 publications

References 12 publications

Twisted electrostatic waves in a self‐gravitating dusty plasma

Twisted electrostatic waves in a self‐gravitating dusty plasma

Kinetic treatment of gravitational-Coulomb coupling in the Jeans model

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